Poker Probabilities - Wizard of Odds

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loading="lazy" width="30" height="21" title="Singapore" src="/build/images/flags/svg/4x3/sg.svg" alt="SG"> Singapore Recommended Online Poker Rooms </h2> <div class="top-casinos--block"> <div class="top-casinos--item white-card"> <div class="top-casinos--info"> <div class="casino-logo"> <a href="https://wizardofodds.com/click/everygame-poker" rel="nofollow sponsored" target="_blank"> <img class="colored-logo" width="115" height="115" src="/media/modules/casino/logos/21027/5e297950-2cc7-4456-b3c4-5a02a8219f77.png" alt="5e297950-2cc7-4456-b3c4-5a02a8219f77" loading="lazy"> </a> </div> <div class="casino-info"> <div class="casino-info--bonus"> <p class="bonus-type">Sign Up Bonus</p> <p><strong>200% </strong> up to</p> <p><strong>1000$</strong></p> <p>+25 spins</p> </div> </div> </div> <div class="top-casinos--action"> <a href="https://wizardofodds.com/click/everygame-poker" rel="nofollow sponsored" target="_blank" class="visit-button">Visit</a> </div> </div> <div class="top-casinos--item white-card"> <div class="top-casinos--info"> <div class="casino-logo"> <a href="https://wizardofodds.com/click/sportsbetting-poker" rel="nofollow sponsored" target="_blank"> <img class="colored-logo" width="115" height="115" src="/media/modules/casino/logos/21183/a3d24f20-3360-45ca-9b3a-f315e8eef672.png" alt="A3d24f20-3360-45ca-9b3a-f315e8eef672" loading="lazy"> </a> </div> <div class="casino-info"> <div class="casino-info--bonus"> <p class="bonus-type">Sign Up Bonus</p> <p><strong>100% </strong> up to</p> <p><strong>1000$</strong></p> </div> </div> </div> <div class="top-casinos--action"> <a href="https://wizardofodds.com/click/sportsbetting-poker" rel="nofollow sponsored" target="_blank" class="visit-button">Visit</a> </div> </div> <div class="top-casinos--item white-card"> <div class="top-casinos--info"> <div class="casino-logo"> <a href="https://wizardofodds.com/click/betonline" rel="nofollow sponsored" target="_blank"> <img class="colored-logo" width="115" height="115" src="/media/modules/casino/logos/2186/041da97e-965e-4db5-b4f3-4a642a4853c4.png" alt="041da97e-965e-4db5-b4f3-4a642a4853c4" loading="lazy"> </a> </div> <div class="casino-info"> <div class="casino-info--bonus"> <p class="bonus-type">Sign Up Bonus</p> <p><strong>100% </strong> up to</p> <p><strong>1000$</strong></p> </div> </div> </div> <div class="top-casinos--action"> <a href="https://wizardofodds.com/click/betonline" rel="nofollow sponsored" target="_blank" class="visit-button">Visit</a> </div> </div> </div> <h2>Five to Ten Card Stud</h2> <p>The following tables show the number of combinations and probability for each poker hand using the best five cards from out of 5 to 10 cards.</p> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Five Card Stud</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>4</td> <td>0.00000154</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>36</td> <td>0.00001385</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>624</td> <td>0.00024010</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>3,744</td> <td>0.00144058</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>5,108</td> <td>0.00196540</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>10,200</td> <td>0.00392465</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>54,912</td> <td>0.02112845</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>123,552</td> <td>0.04753902</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>1,098,240</td> <td>0.42256903</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>1,302,540</td> <td>0.50117739</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Six Card Stud</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>188</td> <td>0.000009</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>1656</td> <td>0.000081</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>14664</td> <td>0.000720</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>165984</td> <td>0.008153</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>205792</td> <td>0.010108</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>361620</td> <td>0.017763</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>732160</td> <td>0.035963</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>2532816</td> <td>0.124411</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>9730740</td> <td>0.477969</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>6612900</td> <td>0.324822</td> </tr> <tr> <td class="left_aligned">Total</td> <td>20358520</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Seven-Card Stud</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>4,324</td> <td>0.00003232</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>37,260</td> <td>0.00027851</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>224,848</td> <td>0.00168067</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>3,473,184</td> <td>0.02596102</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>4,047,644</td> <td>0.03025494</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>6,180,020</td> <td>0.04619382</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>6,461,620</td> <td>0.04829870</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>31,433,400</td> <td>0.23495536</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>58,627,800</td> <td>0.43822546</td> </tr> <tr> <td class="left_aligned">Ace high or less</td> <td>23,294,460</td> <td>0.17411920</td> </tr> <tr> <td class="left_aligned">Total</td> <td>133,784,560</td> <td>1.00000000</td> </tr> </tbody> </table> </div> </div> </div> <p>The next table also shows the probability for seven-card stud, but in more detail.</p> <div class="c"> <div class="box"> <h3 class="box-title">Seven-Card Stud — Detailed</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Details</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probability</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td> </td> <td>4,324</td> <td>0.000032</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>K-9</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>Q-8</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>J-7</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>10-6</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>9-5</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>8-4</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>7-3</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>6-2</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>5-A</td> <td>4,140</td> <td>0.000031</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Aces</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Kings</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Queens</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Jacks</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Tens</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Nines</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Eights</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Sevens</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Sixes</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Fives</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Fours</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Threes</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>Twos</td> <td>17,296</td> <td>0.000129</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Aces up</td> <td>271,392</td> <td>0.002029</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Kings up</td> <td>270,688</td> <td>0.002023</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Queens up</td> <td>269,984</td> <td>0.002018</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Jacks up</td> <td>269,280</td> <td>0.002013</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Tens up</td> <td>268,576</td> <td>0.002008</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Nines up</td> <td>267,872</td> <td>0.002002</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Eights up</td> <td>267,168</td> <td>0.001997</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Sevens up</td> <td>266,464</td> <td>0.001992</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Sixes up</td> <td>265,760</td> <td>0.001986</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Fives up</td> <td>265,056</td> <td>0.001981</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Fours up</td> <td>264,352</td> <td>0.001976</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Threes up</td> <td>263,648</td> <td>0.001971</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>Twos up</td> <td>262,944</td> <td>0.001965</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>Ace high</td> <td>1,584,704</td> <td>0.011845</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>King high</td> <td>1,046,844</td> <td>0.007825</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>Queen high</td> <td>657,772</td> <td>0.004917</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>Jack high</td> <td>389,000</td> <td>0.002908</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>10 high</td> <td>212,224</td> <td>0.001586</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>9 high</td> <td>103,280</td> <td>0.000772</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>8 high</td> <td>41,964</td> <td>0.000314</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>7 high</td> <td>11,856</td> <td>0.000089</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>A-10</td> <td>747,980</td> <td>0.005591</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>K-9</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>Q-8</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>J-7</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>10-6</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>9-5</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>8-4</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>7-3</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>6-2</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>5-A</td> <td>603,560</td> <td>0.004511</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Aces</td> <td>498,916</td> <td>0.003729</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Kings</td> <td>498,916</td> <td>0.003729</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Queens</td> <td>497,904</td> <td>0.003722</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Jacks</td> <td>496,892</td> <td>0.003714</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Tens</td> <td>495,880</td> <td>0.003707</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Nines</td> <td>495,880</td> <td>0.003707</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Eights</td> <td>495,880</td> <td>0.003707</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Sevens</td> <td>495,880</td> <td>0.003707</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Sixes</td> <td>495,880</td> <td>0.003707</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Fives</td> <td>495,880</td> <td>0.003707</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Fours</td> <td>496,892</td> <td>0.003714</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Threes</td> <td>497,904</td> <td>0.003722</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>Twos</td> <td>498,916</td> <td>0.003729</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Aces up</td> <td>5,042,736</td> <td>0.037693</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Kings up</td> <td>4,575,744</td> <td>0.034202</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Queens up</td> <td>4,110,588</td> <td>0.030725</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Jacks up</td> <td>3,656,340</td> <td>0.027330</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Tens up</td> <td>3,213,000</td> <td>0.024016</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Nines up</td> <td>2,778,300</td> <td>0.020767</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Eights up</td> <td>2,352,240</td> <td>0.017582</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Sevens up</td> <td>1,934,820</td> <td>0.014462</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Sixes up</td> <td>1,526,040</td> <td>0.011407</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Fives up</td> <td>1,128,168</td> <td>0.008433</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Fours up</td> <td>745,740</td> <td>0.005574</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>Threes up</td> <td>369,684</td> <td>0.002763</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Aces</td> <td>4,573,800</td> <td>0.034188</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Kings</td> <td>4,573,800</td> <td>0.034188</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Queens</td> <td>4,538,160</td> <td>0.033921</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Jacks</td> <td>4,502,520</td> <td>0.033655</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Tens</td> <td>4,466,880</td> <td>0.033389</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Nines</td> <td>4,472,820</td> <td>0.033433</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Eights</td> <td>4,472,820</td> <td>0.033433</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Sevens</td> <td>4,472,820</td> <td>0.033433</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Sixes</td> <td>4,472,820</td> <td>0.033433</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Fives</td> <td>4,466,880</td> <td>0.033389</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Fours</td> <td>4,502,520</td> <td>0.033655</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Threes</td> <td>4,538,160</td> <td>0.033921</td> </tr> <tr> <td class="left_aligned">High pair</td> <td>Twos</td> <td>4,573,800</td> <td>0.034188</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>Ace high</td> <td>12,944,820</td> <td>0.096759</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>King high</td> <td>6,386,940</td> <td>0.047740</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>Queen high</td> <td>2,719,500</td> <td>0.020327</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>Jack high</td> <td>963,480</td> <td>0.007202</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>10 high</td> <td>248,640</td> <td>0.001859</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>9 high</td> <td>31,080</td> <td>0.000232</td> </tr> <tr> <td class="left_aligned">Total</td> <td> </td> <td>133,784,560</td> <td>1.000000</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Eight Card Stud</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>64,860</td> <td>0.00008619</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>546,480</td> <td>0.00072618</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>2,529,262</td> <td>0.00336098</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>45,652,128</td> <td>0.06066420</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>50,850,320</td> <td>0.06757175</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>67,072,620</td> <td>0.08912853</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>38,493,000</td> <td>0.05115090</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>257,760,900</td> <td>0.34252204</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>236,092,500</td> <td>0.31372828</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>53,476,080</td> <td>0.07106096</td> </tr> <tr> <td class="left_aligned">Total</td> <td>752,538,150</td> <td>1.00000000</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Nine Card Stud</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal Flush</td> <td>713,460</td> <td>0.000194</td> </tr> <tr> <td class="left_aligned">Straight Flush</td> <td>5,874,656</td> <td>0.001597</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>22,247,616</td> <td>0.006047</td> </tr> <tr> <td class="left_aligned">Full House</td> <td>423,908,824</td> <td>0.115222</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>453,008,864</td> <td>0.123131</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>509,071,920</td> <td>0.138370</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>151,728,780</td> <td>0.041241</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>1,442,570,040</td> <td>0.392101</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>600,163,200</td> <td>0.163129</td> </tr> <tr> <td class="left_aligned">Nonpaying hand</td> <td>69,788,040</td> <td>0.018969</td> </tr> <tr> <td>Total</td> <td>3,679,075,400</td> <td>1.000000</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Ten Card Stud</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal Flush</td> <td>6,135,750</td> <td>0.000388</td> </tr> <tr> <td class="left_aligned">Straight Flush</td> <td>49,346,350</td> <td>0.003119</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>159,262,448</td> <td>0.010067</td> </tr> <tr> <td class="left_aligned">Full House</td> <td>2,971,045,612</td> <td>0.187803</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>3,024,664,090</td> <td>0.191192</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>2,797,153,740</td> <td>0.176811</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>372,408,960</td> <td>0.023540</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>5,560,398,330</td> <td>0.351478</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>842,044,140</td> <td>0.053226</td> </tr> <tr> <td class="left_aligned">Nonpaying hand</td> <td>37,564,800</td> <td>0.002375</td> </tr> <tr> <td class="left_aligned">Total</td> <td>15,820,024,220</td> <td>1.000000</td> </tr> </tbody> </table> </div> </div> </div> <h2>Low Ball</h2> <p>Rules vary in low ball whether aces are high or low, and whether straights and flushes work against the player. The following tables look at two different sets of rules.</p> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">5-Card Low Ball, no Straights or Flushes</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>624</td> <td>0.00024</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>3744</td> <td>0.001441</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>54912</td> <td>0.021128</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>123552</td> <td>0.047539</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>1098240</td> <td>0.422569</td> </tr> <tr> <td class="left_aligned">Ace high</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">King high</td> <td>506880</td> <td>0.195032</td> </tr> <tr> <td class="left_aligned">Queen high</td> <td>337920</td> <td>0.130021</td> </tr> <tr> <td class="left_aligned">Jack high</td> <td>215040</td> <td>0.082741</td> </tr> <tr> <td class="left_aligned">10 high</td> <td>129024</td> <td>0.049644</td> </tr> <tr> <td class="left_aligned">9 high</td> <td>71680</td> <td>0.02758</td> </tr> <tr> <td class="left_aligned">8 high</td> <td>35840</td> <td>0.01379</td> </tr> <tr> <td class="left_aligned">7 high</td> <td>15360</td> <td>0.00591</td> </tr> <tr> <td class="left_aligned">6 high</td> <td>5120</td> <td>0.00197</td> </tr> <tr> <td class="left_aligned">5 high</td> <td>1024</td> <td>0.000394</td> </tr> <tr> <td class="left_aligned">Total</td> <td>2598960</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">5-Card Low Ball — Straights & Flushes Enforced</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>4</td> <td>0.000002</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>36</td> <td>0.000014</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>624</td> <td>0.00024</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>3744</td> <td>0.001441</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>5108</td> <td>0.001965</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>10200</td> <td>0.003925</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>54912</td> <td>0.021128</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>123552</td> <td>0.047539</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>1098240</td> <td>0.422569</td> </tr> <tr> <td class="left_aligned">Ace high</td> <td>502860</td> <td>0.193485</td> </tr> <tr> <td class="left_aligned">King high</td> <td>335580</td> <td>0.129121</td> </tr> <tr> <td class="left_aligned">Queen high</td> <td>213180</td> <td>0.082025</td> </tr> <tr> <td class="left_aligned">Jack high</td> <td>127500</td> <td>0.049058</td> </tr> <tr> <td class="left_aligned">10 high</td> <td>70380</td> <td>0.02708</td> </tr> <tr> <td class="left_aligned">9 high</td> <td>34680</td> <td>0.013344</td> </tr> <tr> <td class="left_aligned">8 high</td> <td>14280</td> <td>0.005495</td> </tr> <tr> <td class="left_aligned">7 high</td> <td>4080</td> <td>0.00157</td> </tr> <tr> <td class="left_aligned">6 high</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">5 high</td> <td>0</td> <td>0</td> </tr> <tr> <td class="left_aligned">Total</td> <td>2598960</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <h2>Omaha</h2> <p>In Omaha the player may use any 2 of his own 4 cards, and any 3 of the 5 community cards, to form the best highest and lowest poker hand. Straights and flushes are not enforced in the low hand. For the low hand aces always count as low. Here are the probabilities for each hand.</p> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Omaha High Hand</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">Royal Flush</td> <td>42807600</td> <td>0.000092</td> </tr> <tr> <td class="left_aligned">Straight Flush</td> <td>368486160</td> <td>0.000795</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>2225270496</td> <td>0.0048</td> </tr> <tr> <td class="left_aligned">Full House</td> <td>29424798576</td> <td>0.063475</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>31216782384</td> <td>0.067341</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>52289648688</td> <td>0.112799</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>40712657408</td> <td>0.087825</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>170775844104</td> <td>0.368398</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>122655542152</td> <td>0.264593</td> </tr> <tr> <td class="left_aligned">All other</td> <td>13851662832</td> <td>0.029881</td> </tr> <tr> <td class="left_aligned">Total</td> <td>463563500400</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box desk-75percent"> <h3 class="box-title">Omaha Low Hand</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading left_aligned">Hand</th> <th class="data-heading centered">Combinations</th> <th class="data-heading centered">Probabilities</th> </tr> <tr> <td class="left_aligned">5 high</td> <td>7439717760</td> <td>0.016049</td> </tr> <tr> <td class="left_aligned">6 high</td> <td>25832342400</td> <td>0.055726</td> </tr> <tr> <td class="left_aligned">7 high</td> <td>51687563904</td> <td>0.111501</td> </tr> <tr> <td class="left_aligned">8 high</td> <td>76415359104</td> <td>0.164843</td> </tr> <tr> <td class="left_aligned">9 high</td> <td>90496557312</td> <td>0.195219</td> </tr> <tr> <td class="left_aligned">10 high</td> <td>87800751360</td> <td>0.189404</td> </tr> <tr> <td class="left_aligned">J high</td> <td>68526662400</td> <td>0.147826</td> </tr> <tr> <td class="left_aligned">Q high</td> <td>39834609408</td> <td>0.085931</td> </tr> <tr> <td class="left_aligned">K high</td> <td>13835276928</td> <td>0.029845</td> </tr> <tr> <td class="left_aligned">Pair or higher</td> <td>1694659824</td> <td>0.003656</td> </tr> <tr> <td class="left_aligned">Total</td> <td>463563500400</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <h2>Median Hand in Five Card Stud</h2> <p>The median five-card stud poker hand is ace,king,queen,jack,6.</p> <h2>Probabilities in Two-Player Texas Hold 'Em</h2> <p>For this topic, please see my separate page on <a href="/games/poker/probabilities/texas-hold-em-two-player/">probabilities in Two-Player Texas Hold 'Em</a>.</p> <h2>Median Hand in Texas Hold 'Em</h2> <p>The following table shows the median hand in Texas Hold 'Em by the number of players. This table assumes that nobody ever folds.</p> <div class="box desk-50percent"> <h3 class="box-title">Median Hand in Texas Hold 'Em</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading centered">Players</th> <th class="data-heading left_aligned">Median Hand</th> </tr> <tr> <td>1</td> <td class="left_aligned">Pair -- JJAT8</td> </tr> <tr> <td>2</td> <td class="left_aligned">Two pair -- 8877J</td> </tr> <tr> <td>3</td> <td class="left_aligned">Two pair -- QQ44T</td> </tr> <tr> <td>4</td> <td class="left_aligned">Two pair -- KKTTJ</td> </tr> <tr> <td>5</td> <td class="left_aligned">Two pair -- AAJJ6</td> </tr> <tr> <td>6</td> <td class="left_aligned">Three of a kind -- 555T7</td> </tr> <tr> <td>7</td> <td class="left_aligned">Three of a kind -- 999T8</td> </tr> <tr> <td>8</td> <td class="left_aligned">Three of a kind -- QQQT8</td> </tr> <tr> <td>9</td> <td class="left_aligned">Three of a kind -- AAAQT</td> </tr> <tr> <td>10</td> <td class="left_aligned">Straight -- 65432</td> </tr> </tbody> </table> </div> </div>  <h2>High Hand Probabilities in Texas Hold 'Em</h2> <p>The following two tables show the probability of the winning hand in Texas Hold 'Em for 2 to 10 players, assuming nobody ever folds. These tables were created to help me analyze <a href="/games/bet-on-poker/">Bet on Poker</a>.</p> <div class="box"> <h3 class="box-title">Texas Hold 'Em -- High Hand Probabilities -- 1 to 5 Players</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading centered">Hand</th> <th class="data-heading centered">1 Player</th> <th class="data-heading centered">2 Players</th> <th class="data-heading centered">3 Players</th> <th class="data-heading centered">4 Players</th> <th class="data-heading centered">5 Players</th> </tr> <tr> <td class="left_aligned">Royal Flush</td> <td>0.000032</td> <td>0.000063</td> <td>0.000094</td> <td>0.000125</td> <td>0.000155</td> </tr> <tr> <td class="left_aligned">Straight Flush</td> <td>0.000279</td> <td>0.000541</td> <td>0.000801</td> <td>0.001058</td> <td>0.001312</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>0.001680</td> <td>0.003120</td> <td>0.004560</td> <td>0.005998</td> <td>0.007437</td> </tr> <tr> <td class="left_aligned">Full House</td> <td>0.025963</td> <td>0.047027</td> <td>0.065383</td> <td>0.081605</td> <td>0.096110</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>0.030258</td> <td>0.052479</td> <td>0.070330</td> <td>0.085043</td> <td>0.097491</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>0.046197</td> <td>0.080196</td> <td>0.107931</td> <td>0.130825</td> <td>0.149905</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>0.048301</td> <td>0.071897</td> <td>0.092473</td> <td>0.110374</td> <td>0.125849</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>0.234949</td> <td>0.314178</td> <td>0.339171</td> <td>0.337678</td> <td>0.323925</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>0.438221</td> <td>0.371200</td> <td>0.299665</td> <td>0.241083</td> <td>0.195945</td> </tr> <tr> <td class="left_aligned">High card</td> <td>0.174120</td> <td>0.059299</td> <td>0.019591</td> <td>0.006212</td> <td>0.001869</td> </tr> </tbody> </table> </div> </div> <br> <div class="box"> <h3 class="box-title">Texas Hold 'Em -- High Hand Probabilities -- 6 to 10 Players</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading centered">Hand</th> <th class="data-heading centered">6 Players</th> <th class="data-heading centered">7 Players</th> <th class="data-heading centered">8 Players</th> <th class="data-heading centered">9 Players</th> <th class="data-heading centered">10 Players</th> </tr> <tr> <td class="left_aligned">Royal Flush</td> <td>0.000186</td> <td>0.000217</td> <td>0.000248</td> <td>0.000279</td> <td>0.000309</td> </tr> <tr> <td class="left_aligned">Straight Flush</td> <td>0.001565</td> <td>0.001814</td> <td>0.002061</td> <td>0.002305</td> <td>0.002547</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>0.008874</td> <td>0.010311</td> <td>0.011747</td> <td>0.013183</td> <td>0.014620</td> </tr> <tr> <td class="left_aligned">Full House</td> <td>0.109234</td> <td>0.121232</td> <td>0.132294</td> <td>0.142568</td> <td>0.152169</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>0.108291</td> <td>0.117875</td> <td>0.126536</td> <td>0.134473</td> <td>0.141819</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>0.165917</td> <td>0.179431</td> <td>0.190885</td> <td>0.200623</td> <td>0.208920</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>0.139101</td> <td>0.150285</td> <td>0.159563</td> <td>0.167088</td> <td>0.172997</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>0.305116</td> <td>0.284805</td> <td>0.264703</td> <td>0.245564</td> <td>0.227706</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>0.161189</td> <td>0.133893</td> <td>0.111931</td> <td>0.093911</td> <td>0.078910</td> </tr> <tr> <td class="left_aligned">High card</td> <td>0.000528</td> <td>0.000138</td> <td>0.000033</td> <td>0.000007</td> <td>0.000001</td> </tr> </tbody> </table> </div> </div> <h2>Chopped Pots in Texas Hold 'Em</h2> Due to the five community cards, chops, or ties, are not unusual in Texas Hold 'Em. The following table shows the following for 2 to 10 players, assuming nobody ever folds: <ul> <li>Probability of a chopped pot.</li> <li>Average winners per hand.</li> <li>Average winners per chopped pot.</li> </ul> <div class="box desk-75percent"> <h3 class="box-title">Texas Hold 'Em — Chopped Pots</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading centered">Players</th> <th class="data-heading centered">Prob.<br> Chop</th> <th class="data-heading centered">Average<br> Winners<br> per Hand</th> <th class="data-heading centered">Average<br> Winners<br> per Chop</th> </tr> <tr> <td>2</td> <td>0.062166</td> <td>1.062166</td> <td>2.000000</td> </tr> <tr> <td>3</td> <td>0.060548</td> <td>1.074952</td> <td>2.237896</td> </tr> <tr> <td>4</td> <td>0.066752</td> <td>1.084148</td> <td>2.260614</td> </tr> <tr> <td>5</td> <td>0.074879</td> <td>1.093894</td> <td>2.253952</td> </tr> <tr> <td>6</td> <td>0.083382</td> <td>1.104460</td> <td>2.252781</td> </tr> <tr> <td>7</td> <td>0.091632</td> <td>1.115304</td> <td>2.258336</td> </tr> <tr> <td>8</td> <td>0.099642</td> <td>1.126432</td> <td>2.268862</td> </tr> <tr> <td>9</td> <td>0.107048</td> <td>1.137478</td> <td>2.284261</td> </tr> <tr> <td>10</td> <td>0.113972</td> <td>1.148436</td> <td>2.302389</td> </tr> </tbody> </table> </div> </div>  <h2>Multi-Deck Probabilities</h2> <p>I've been asked several times about the probabilities of each poker hand in multiple-deck games. Although I strongly feel poker based games should be played with only one deck, I will submit to the will of my readers and present the following tables. The first table shows the number of raw combinations, and the second the probability.</p> <div class="box box--expandable"> <h3 class="box-title">Poker Combinations for 1 to 8 Decks<span class="box-title-expand desk-visible">Expand</span><span class="box-title-expand desk-visible"> </span></h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading" rowspan="2">Hand</th> <th class="data-heading" colspan="8">Number of Decks</th> </tr> <tr> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> </tr> <tr> <td>5 of a kind</td> <td>0</td> <td>728</td> <td>10296</td> <td>56784</td> <td>201552</td> <td>552552</td> <td>1277640</td> <td>2617888</td> </tr> <tr> <td>Royal flush</td> <td>4</td> <td>128</td> <td>972</td> <td>4096</td> <td>12500</td> <td>31104</td> <td>67228</td> <td>131072</td> </tr> <tr> <td>Straight flush</td> <td>36</td> <td>1152</td> <td>8748</td> <td>36864</td> <td>112500</td> <td>279936</td> <td>605052</td> <td>1179648</td> </tr> <tr> <td>4 of a kind</td> <td>624</td> <td>87360</td> <td>926640</td> <td>4542720</td> <td>15116400</td> <td>39783744</td> <td>89434800</td> <td>179512320</td> </tr> <tr> <td>Full house</td> <td>3744</td> <td>244608</td> <td>2265120</td> <td>10483200</td> <td>33789600</td> <td>87145344</td> <td>193179168</td> <td>383784960</td> </tr> <tr> <td>Flush</td> <td>5108</td> <td>261840</td> <td>2291436</td> <td>10337408</td> <td>32836500</td> <td>83889648</td> <td>184732940</td> <td>365208576</td> </tr> <tr> <td>Straight</td> <td>10200</td> <td>326400</td> <td>2478600</td> <td>10444800</td> <td>31875000</td> <td>79315200</td> <td>171431400</td> <td>334233600</td> </tr> <tr> <td>3 of a kind</td> <td>54912</td> <td>3075072</td> <td>27150552</td> <td>122783232</td> <td>390390000</td> <td>997805952</td> <td>2197787592</td> <td>4345516032</td> </tr> <tr> <td>2 pair</td> <td>123552</td> <td>5374512</td> <td>44756712</td> <td>197188992</td> <td>617760000</td> <td>1563982992</td> <td>3422050632</td> <td>6733089792</td> </tr> <tr> <td>Pair</td> <td>1098240</td> <td>40909440</td> <td>325250640</td> <td>1401354240</td> <td>4332900000</td> <td>10875047040</td> <td>23649465840</td> <td>46319370240</td> </tr> <tr> <td>Nothing</td> <td>1302540</td> <td>41681280</td> <td>316517220</td> <td>1333800960</td> <td>4070437500</td> <td>10128551040</td> <td>21891789780</td> <td>42681630720</td> </tr> <tr> <td>total</td> <td>2598960</td> <td>91962520</td> <td>721656936</td> <td>3091033296</td> <td>9525431552</td> <td>23856384552</td> <td>51801822072</td> <td>101346274848</td> </tr> </tbody> </table> </div> </div> <h2>Infinite Decks</h2> <p>The following table shows the number of combinations if each card was dealt from a separate deck, which would be mathematically equivalent to an infinite number of decks.</p> <div class="box desk-50percent"> <h3 class="box-title">Infinite Deck</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading centered">Hand</th> <th class="data-heading centered">Permutations</th> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>480</td> </tr> <tr> <td class="left_aligned">Five of a kind</td> <td>13,312</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>4,320</td> </tr> <tr> <td class="left_aligned">Four of a kind</td> <td>798,720</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>1,597,440</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>1,470,960</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>1,224,000</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>17,503,200</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>26,254,800</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>175,032,000</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>156,304,800</td> </tr> <tr> <td class="left_aligned">Total</td> <td>380,204,032</td> </tr> </tbody> </table> </div> </div> <div class="c"> <div class="box box--expandable"> <h3 class="box-title">Poker Probabilities for 1 to 8 Decks<span class="box-title-expand desk-visible">Expand</span><span class="box-title-expand desk-visible"> </span></h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading" rowspan="2">Hand</th> <th class="data-heading" colspan="8">Number of Decks</th> </tr> <tr> <td>1</td> <td>2</td> <td>3</td> <td>4</td> <td>5</td> <td>6</td> <td>7</td> <td>8</td> </tr> <tr> <td class="left_aligned">5 of a kind</td> <td>0</td> <td>0.00000792</td> <td>0.00001427</td> <td>0.00001837</td> <td>0.00002116</td> <td>0.00002316</td> <td>0.00002466</td> <td>0.00002583</td> </tr> <tr> <td class="left_aligned">Royal flush</td> <td>0.00000154</td> <td>0.00000139</td> <td>0.00000135</td> <td>0.00000133</td> <td>0.00000131</td> <td>0.0000013</td> <td>0.0000013</td> <td>0.00000129</td> </tr> <tr> <td class="left_aligned">Straight flush</td> <td>0.00001385</td> <td>0.00001253</td> <td>0.00001212</td> <td>0.00001193</td> <td>0.00001181</td> <td>0.00001173</td> <td>0.00001168</td> <td>0.00001164</td> </tr> <tr> <td class="left_aligned">4 of a kind</td> <td>0.0002401</td> <td>0.00094995</td> <td>0.00128405</td> <td>0.00146964</td> <td>0.00158695</td> <td>0.00166764</td> <td>0.00172648</td> <td>0.00177128</td> </tr> <tr> <td class="left_aligned">Full house</td> <td>0.00144058</td> <td>0.00265987</td> <td>0.00313878</td> <td>0.00339149</td> <td>0.0035473</td> <td>0.00365291</td> <td>0.0037292</td> <td>0.00378687</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>0.0019654</td> <td>0.00284725</td> <td>0.00317524</td> <td>0.00334432</td> <td>0.00344725</td> <td>0.00351644</td> <td>0.00356615</td> <td>0.00360357</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>0.00392465</td> <td>0.00354927</td> <td>0.0034346</td> <td>0.00337906</td> <td>0.00334631</td> <td>0.00332469</td> <td>0.00330937</td> <td>0.00329794</td> </tr> <tr> <td class="left_aligned">3 of a kind</td> <td>0.02112845</td> <td>0.03343832</td> <td>0.03762252</td> <td>0.03972239</td> <td>0.04098397</td> <td>0.04182553</td> <td>0.04242684</td> <td>0.04287791</td> </tr> <tr> <td class="left_aligned">2 pair</td> <td>0.04753902</td> <td>0.05844242</td> <td>0.06201937</td> <td>0.06379388</td> <td>0.06485375</td> <td>0.06555826</td> <td>0.06606043</td> <td>0.06643648</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>0.42256903</td> <td>0.44484905</td> <td>0.4506998</td> <td>0.4533611</td> <td>0.45487703</td> <td>0.45585478</td> <td>0.45653734</td> <td>0.45704068</td> </tr> <tr> <td class="left_aligned">Nothing</td> <td>0.50117739</td> <td>0.45324204</td> <td>0.4385979</td> <td>0.4315065</td> <td>0.42732316</td> <td>0.42456354</td> <td>0.42260656</td> <td>0.42114652</td> </tr> <tr> <td class="left_aligned">total</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <h2>Wild Deck Probabilities</h2> <p>The next two tables show the probabilities in 5-card stud with one wild card. The first table is for a partially wild card that can only be used to complete a straight, flush, straight flush, or royal flush, otherwise it must be used as an ace (same usage as in pai gow poker). The second table is for a fully wild card.</p> <div class="c"> <div class="box"> <h3 class="box-title">5-Card Stud with Partially Wild Joker</h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Natural<br> Combinations</th> <th class="data-heading">Wild<br> Combinations</th> <th class="data-heading">Total<br> Combinations</th> <th class="data-heading">Probability</th> </tr> <tr> <td>five of a kind</td> <td>0</td> <td>1</td> <td>1</td> <td>0</td> </tr> <tr> <td>royal flush</td> <td>4</td> <td>20</td> <td>24</td> <td>0.000008</td> </tr> <tr> <td>straight flush</td> <td>36</td> <td>144</td> <td>180</td> <td>0.000063</td> </tr> <tr> <td>four of a kind</td> <td>624</td> <td>204</td> <td>828</td> <td>0.000289</td> </tr> <tr> <td>full house</td> <td>3744</td> <td>624</td> <td>4368</td> <td>0.001522</td> </tr> <tr> <td>flush</td> <td>5108</td> <td>2696</td> <td>7804</td> <td>0.002719</td> </tr> <tr> <td>straight</td> <td>10200</td> <td>10332</td> <td>20532</td> <td>0.007155</td> </tr> <tr> <td>3 of a kind</td> <td>54912</td> <td>8448</td> <td>63360</td> <td>0.022079</td> </tr> <tr> <td>2 pair</td> <td>123552</td> <td>15048</td> <td>138600</td> <td>0.048298</td> </tr> <tr> <td>pair</td> <td>1098240</td> <td>116784</td> <td>1215024</td> <td>0.4234</td> </tr> <tr> <td>nothing</td> <td>1302540</td> <td>116424</td> <td>1418964</td> <td>0.494467</td> </tr> <tr> <td>total</td> <td>2598960</td> <td>270725</td> <td>2869685</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box"> <h3 class="box-title">5-Card Stud with Fully-Wild Joker</h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Natural<br> Combinations</th> <th class="data-heading">Wild<br> Combinations</th> <th class="data-heading">Total<br> Combinations</th> <th class="data-heading">Probability</th> </tr> <tr> <td>five of a kind</td> <td>0</td> <td>13</td> <td>13</td> <td>0.000005</td> </tr> <tr> <td>royal flush</td> <td>4</td> <td>20</td> <td>24</td> <td>0.000008</td> </tr> <tr> <td>straight flush</td> <td>36</td> <td>144</td> <td>180</td> <td>0.000063</td> </tr> <tr> <td>four of a kind</td> <td>624</td> <td>2496</td> <td>3120</td> <td>0.001087</td> </tr> <tr> <td>full house</td> <td>3744</td> <td>2808</td> <td>6552</td> <td>0.002283</td> </tr> <tr> <td>flush</td> <td>5108</td> <td>2696</td> <td>7804</td> <td>0.002719</td> </tr> <tr> <td>straight</td> <td>10200</td> <td>10332</td> <td>20532</td> <td>0.007155</td> </tr> <tr> <td>3 of a kind</td> <td>54912</td> <td>82368</td> <td>137280</td> <td>0.047838</td> </tr> <tr> <td>2 pair</td> <td>123552</td> <td>0</td> <td>123552</td> <td>0.043054</td> </tr> <tr> <td>pair</td> <td>1098240</td> <td>169848</td> <td>1268088</td> <td>0.441891</td> </tr> <tr> <td>nothing</td> <td>1302540</td> <td>0</td> <td>1302540</td> <td>0.453897</td> </tr> <tr> <td>Total</td> <td>2598960</td> <td>270725</td> <td>2869685</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <a name="twojokers"></a> <p>The next table shows the combinations and probability with two fully-wild jokers. Note that the full house and four of a kind are equal in probability.</p> <div class="c"> <div class="box"> <h3 class="box-title">5-Card Stud with Two Fully-Wild Jokers</h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Natural<br> Combinations</th> <th class="data-heading">One Joker<br> Combinations</th> <th class="data-heading">Two Jokers<br> Combinations</th> <th class="data-heading">Total<br> Combinations</th> <th class="data-heading">Probability</th> </tr> <tr> <td>Five of a Kind</td> <td>0</td> <td>26</td> <td>52</td> <td>78</td> <td>0.000025</td> </tr> <tr> <td>Royal flush</td> <td>4</td> <td>40</td> <td>40</td> <td>84</td> <td>0.000027</td> </tr> <tr> <td>Straight Flush</td> <td>36</td> <td>288</td> <td>216</td> <td>540</td> <td>0.000171</td> </tr> <tr> <td>Four of a Kind</td> <td>624</td> <td>4992</td> <td>3744</td> <td>9360</td> <td>0.002960</td> </tr> <tr> <td>Full House</td> <td>3744</td> <td>5616</td> <td>0</td> <td>9360</td> <td>0.002960</td> </tr> <tr> <td>Flush</td> <td>5108</td> <td>5392</td> <td>888</td> <td>11388</td> <td>0.003601</td> </tr> <tr> <td>Straight</td> <td>10200</td> <td>20664</td> <td>3840</td> <td>34704</td> <td>0.010974</td> </tr> <tr> <td>Three of a kind</td> <td>54912</td> <td>164736</td> <td>13320</td> <td>232968</td> <td>0.073666</td> </tr> <tr> <td>Two pair</td> <td>123552</td> <td>0</td> <td>0</td> <td>123552</td> <td>0.039068</td> </tr> <tr> <td>Pair</td> <td>1098240</td> <td>339696</td> <td>0</td> <td>1437936</td> <td>0.454682</td> </tr> <tr> <td>Nonpaying hand</td> <td>1302540</td> <td>0</td> <td>0</td> <td>1302540</td> <td>0.411869</td> </tr> <tr> <td>Total</td> <td>2598960</td> <td>541450</td> <td>22100</td> <td>3162510</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <p>The next table shows the number of combinations for each hand when a particular rank is wild.</p> <div class="c"> <div class="box box--expandablemax"> <h3 class="box-title">Wild Five-Card Stud Combinations <span class="box-title-expand desk-visible">Expand </span></h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">2's wild</th> <th class="data-heading">3's wild</th> <th class="data-heading">4's wild</th> <th class="data-heading">5's wild</th> <th class="data-heading">6's wild</th> <th class="data-heading">7's wild</th> <th class="data-heading">8's wild</th> <th class="data-heading">9's wild</th> <th class="data-heading">10's wild</th> <th class="data-heading">J's wild</th> <th class="data-heading">Q's wild</th> <th class="data-heading">K's wild</th> <th class="data-heading">A's wild</th> </tr> <tr> <td>Four Wilds</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> <td>48</td> </tr> <tr> <td>Five of a Kind</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> <td>624</td> </tr> <tr> <td>Straight Flush</td> <td>2552</td> <td>2412</td> <td>2272</td> <td>2132</td> <td>2132</td> <td>2132</td> <td>2132</td> <td>2132</td> <td>2132</td> <td>2272</td> <td>2412</td> <td>2552</td> <td>2416</td> </tr> <tr> <td>Four of a Kind</td> <td>31552</td> <td>31568</td> <td>31584</td> <td>31600</td> <td>31600</td> <td>31600</td> <td>31600</td> <td>31600</td> <td>31600</td> <td>31584</td> <td>31568</td> <td>31552</td> <td>31600</td> </tr> <tr> <td>Full House</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> <td>12672</td> </tr> <tr> <td>Flush</td> <td>14472</td> <td>14596</td> <td>14720</td> <td>14844</td> <td>14844</td> <td>14844</td> <td>14844</td> <td>14844</td> <td>14844</td> <td>14720</td> <td>14596</td> <td>14472</td> <td>14560</td> </tr> <tr> <td>Straight</td> <td>62232</td> <td>57108</td> <td>51984</td> <td>46860</td> <td>46860</td> <td>46860</td> <td>46860</td> <td>46860</td> <td>46860</td> <td>51984</td> <td>57108</td> <td>62232</td> <td>60144</td> </tr> <tr> <td>Three of a kind</td> <td>355080</td> <td>356160</td> <td>357240</td> <td>358320</td> <td>358320</td> <td>358320</td> <td>358320</td> <td>358320</td> <td>358320</td> <td>357240</td> <td>356160</td> <td>355080</td> <td>356160</td> </tr> <tr> <td>Two pair</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> <td>95040</td> </tr> <tr> <td>Pair</td> <td>1225008</td> <td>1228032</td> <td>1231056</td> <td>1234080</td> <td>1234080</td> <td>1234080</td> <td>1234080</td> <td>1234080</td> <td>1234080</td> <td>1231056</td> <td>1228032</td> <td>1225008</td> <td>1226016</td> </tr> <tr> <td>Nothing</td> <td>799680</td> <td>800700</td> <td>801720</td> <td>802740</td> <td>802740</td> <td>802740</td> <td>802740</td> <td>802740</td> <td>802740</td> <td>801720</td> <td>800700</td> <td>799680</td> <td>799680</td> </tr> <tr> <td>Total</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> <td>2598960</td> </tr> </tbody> </table> </div> </div> </div> <div class="c"> <div class="box box--expandablemax"> <h3 class="box-title">Wild Five-Card Stud Probabilities<span class="box-title-expand desk-visible">Expand </span></h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">2's wild</th> <th class="data-heading">3's wild</th> <th class="data-heading">4's wild</th> <th class="data-heading">5's wild</th> <th class="data-heading">6's wild</th> <th class="data-heading">7's wild</th> <th class="data-heading">8's wild</th> <th class="data-heading">9's wild</th> <th class="data-heading">10's wild</th> <th class="data-heading">J's wild</th> <th class="data-heading">Q's wild</th> <th class="data-heading">K's wild</th> <th class="data-heading">A's wild</th> </tr> <tr> <td>Four Wilds</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> <td>0.000018</td> </tr> <tr> <td>Five of a Kind</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> <td>0.00024</td> </tr> <tr> <td>Straight Flush</td> <td>0.000982</td> <td>0.000928</td> <td>0.000874</td> <td>0.00082</td> <td>0.00082</td> <td>0.00082</td> <td>0.00082</td> <td>0.00082</td> <td>0.00082</td> <td>0.000874</td> <td>0.000928</td> <td>0.000982</td> <td>0.00093</td> </tr> <tr> <td>Four of a Kind</td> <td>0.01214</td> <td>0.012146</td> <td>0.012153</td> <td>0.012159</td> <td>0.012159</td> <td>0.012159</td> <td>0.012159</td> <td>0.012159</td> <td>0.012159</td> <td>0.012153</td> <td>0.012146</td> <td>0.01214</td> <td>0.012159</td> </tr> <tr> <td>Full House</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> <td>0.004876</td> </tr> <tr> <td>Flush</td> <td>0.005568</td> <td>0.005616</td> <td>0.005664</td> <td>0.005712</td> <td>0.005712</td> <td>0.005712</td> <td>0.005712</td> <td>0.005712</td> <td>0.005712</td> <td>0.005664</td> <td>0.005616</td> <td>0.005568</td> <td>0.005602</td> </tr> <tr> <td>Straight</td> <td>0.023945</td> <td>0.021973</td> <td>0.020002</td> <td>0.01803</td> <td>0.01803</td> <td>0.01803</td> <td>0.01803</td> <td>0.01803</td> <td>0.01803</td> <td>0.020002</td> <td>0.021973</td> <td>0.023945</td> <td>0.023142</td> </tr> <tr> <td>Three of a kind</td> <td>0.136624</td> <td>0.137039</td> <td>0.137455</td> <td>0.137871</td> <td>0.137871</td> <td>0.137871</td> <td>0.137871</td> <td>0.137871</td> <td>0.137871</td> <td>0.137455</td> <td>0.137039</td> <td>0.136624</td> <td>0.137039</td> </tr> <tr> <td>Two pair</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> <td>0.036568</td> </tr> <tr> <td>Pair</td> <td>0.471345</td> <td>0.472509</td> <td>0.473673</td> <td>0.474836</td> <td>0.474836</td> <td>0.474836</td> <td>0.474836</td> <td>0.474836</td> <td>0.474836</td> <td>0.473673</td> <td>0.472509</td> <td>0.471345</td> <td>0.471733</td> </tr> <tr> <td>Nothing</td> <td>0.307692</td> <td>0.308085</td> <td>0.308477</td> <td>0.30887</td> <td>0.30887</td> <td>0.30887</td> <td>0.30887</td> <td>0.30887</td> <td>0.30887</td> <td>0.308477</td> <td>0.308085</td> <td>0.307692</td> <td>0.307692</td> </tr> <tr> <td>Total</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <h2>Four Card Stud</h2> <p>The next table is for four-card stud with no jokers.</p> <div class="c"> <div class="box desk-50percent"> <h3 class="box-title">Four Card Stud — No Jokers</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Combinations</th> <th class="data-heading">Probabilities</th> </tr> <tr> <td>Four of a kind</td> <td>13</td> <td>0.000048</td> </tr> <tr> <td>Straight Flush</td> <td>44</td> <td>0.000163</td> </tr> <tr> <td>Flush</td> <td>2816</td> <td>0.010402</td> </tr> <tr> <td>Straight</td> <td>2772</td> <td>0.010239</td> </tr> <tr> <td>Three of a kind</td> <td>2496</td> <td>0.00922</td> </tr> <tr> <td>Two pair</td> <td>2808</td> <td>0.010372</td> </tr> <tr> <td>Pair</td> <td>82368</td> <td>0.30425</td> </tr> <tr> <td>Nonpaying hand</td> <td>177408</td> <td>0.655307</td> </tr> <tr> <td>Total</td> <td>270725</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <p>The next table is for four-card stud one fully wild joker.</p> <div class="c"> <div class="box desk-50percent"> <h3 class="box-title">Four Card Stud — One Joker</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Combinations</th> <th class="data-heading">Probabilities</th> </tr> <tr> <td>Four of a kind</td> <td>65</td> <td>0.000222</td> </tr> <tr> <td>Straight Flush</td> <td>180</td> <td>0.000615</td> </tr> <tr> <td>Flush</td> <td>3824</td> <td>0.013059</td> </tr> <tr> <td>Straight</td> <td>4812</td> <td>0.016433</td> </tr> <tr> <td>Three of a kind</td> <td>6240</td> <td>0.02131</td> </tr> <tr> <td>Two pair</td> <td>2808</td> <td>0.009589</td> </tr> <tr> <td>Pair</td> <td>97488</td> <td>0.332922</td> </tr> <tr> <td>Nonpaying hand</td> <td>177408</td> <td>0.60585</td> </tr> <tr> <td>Total</td> <td>292825</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <p>The next table is for four-card stud with two fully-wild jokers.</p> <div class="c"> <div class="box desk-50percent"> <h3 class="box-title">Four Card Stud — Two Jokers</h3>  <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Combinations</th> <th class="data-heading">Probabilities</th> </tr> <tr> <td>Four of a kind</td> <td>195</td> <td>0.000617</td> </tr> <tr> <td>Straight Flush</td> <td>460</td> <td>0.001455</td> </tr> <tr> <td>Flush</td> <td>5000</td> <td>0.01581</td> </tr> <tr> <td>Straight</td> <td>7284</td> <td>0.023032</td> </tr> <tr> <td>Three of a kind</td> <td>10488</td> <td>0.033164</td> </tr> <tr> <td>Two pair</td> <td>2808</td> <td>0.008879</td> </tr> <tr> <td>Pair</td> <td>112608</td> <td>0.356072</td> </tr> <tr> <td>Nonpaying hand</td> <td>177408</td> <td>0.560972</td> </tr> <tr> <td>Total</td> <td>316251</td> <td>1</td> </tr> </tbody> </table> </div> </div> </div> <p>The next table is for a seven-card stud game with one fully wild joker.</p> <div class="c"> <div class="box desk-50percent"> <h3 class="box-title">Seven Card Stud — One Joker</h3> <div class="box-content"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">Combinations</th> <th class="data-heading">Probabilities</th> </tr> <tr> <td class="left_aligned">Natural Royal Flush</td> <td>4,512</td> <td>0.000029</td> </tr> <tr> <td class="left_aligned">Five of a Kind</td> <td>14,664</td> <td>0.000095</td> </tr> <tr> <td class="left_aligned">Wild Royal Flush</td> <td>21,620</td> <td>0.000140</td> </tr> <tr> <td class="left_aligned">Straight Flush</td> <td>184,832</td> <td>0.001199</td> </tr> <tr> <td class="left_aligned">Four of a Kind</td> <td>1,121,024</td> <td>0.007273</td> </tr> <tr> <td class="left_aligned">Full House</td> <td>5,997,144</td> <td>0.038906</td> </tr> <tr> <td class="left_aligned">Flush</td> <td>6,027,224</td> <td>0.039101</td> </tr> <tr> <td class="left_aligned">Straight</td> <td>11,083,940</td> <td>0.071907</td> </tr> <tr> <td class="left_aligned">Three of a kind</td> <td>13,315,300</td> <td>0.086383</td> </tr> <tr> <td class="left_aligned">Two pair</td> <td>31,433,400</td> <td>0.203924</td> </tr> <tr> <td class="left_aligned">Pair</td> <td>61,644,960</td> <td>0.399920</td> </tr> <tr> <td class="left_aligned">All other</td> <td>23,294,460</td> <td>0.151122</td> </tr> <tr> <td class="left_aligned">Total</td> <td>154,143,080</td> <td>1.000000</td> </tr> </tbody> </table> </div> </div> </div> <h2>Player Must Use Every Card</h2> <p>The following table shows the number of combinations for 2 to 10 cards from a single 52-card deck, with no wild cards. For the purpose of this table, a royal flush, straight flush, flush, and straight must use all cards. A royal flush is defined as an ace-high straight flush. For example, with three cards, a royal flush would be suited QKA.</p> <div class="box box--expandable"> <h3 class="box-title">2 to 10 Cards — Straight, Flush, Straight Flush, and Royal Flush Must Use All Cards<span class="box-title-expand desk-visible">Expand </span></h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading">Hand</th> <th class="data-heading">2 cards</th> <th class="data-heading">3 cards</th> <th class="data-heading">4 cards</th> <th class="data-heading">5 cards</th> <th class="data-heading">6 cards</th> <th class="data-heading">7 cards</th> <th class="data-heading">8 cards</th> <th class="data-heading">9 cards</th> <th class="data-heading">10 cards</th> </tr> <tr> <td>Royal flush</td> <td>4</td> <td>4</td> <td>4</td> <td>4</td> <td>4</td> <td>4</td> <td>4</td> <td>4</td> <td>4</td> </tr> <tr> <td>Straight flush</td> <td>48</td> <td>44</td> <td>40</td> <td>36</td> <td>32</td> <td>28</td> <td>24</td> <td>20</td> <td>16</td> </tr> <tr> <td>Four of a kind</td> <td>-</td> <td>-</td> <td>13</td> <td>624</td> <td>14,664</td> <td>224,848</td> <td>2,529,462</td> <td>22,256,520</td> <td>159,455,868</td> </tr> <tr> <td>Full house</td> <td>-</td> <td>-</td> <td>-</td> <td>3,744</td> <td>165,984</td> <td>3,473,184</td> <td>45,659,328</td> <td>424,213,504</td> <td>2,977,017,472</td> </tr> <tr> <td>Flush</td> <td>260</td> <td>1,096</td> <td>2,816</td> <td>5,108</td> <td>6,828</td> <td>6,832</td> <td>5,120</td> <td>2,836</td> <td>1,124</td> </tr> <tr> <td>Straight</td> <td>156</td> <td>720</td> <td>2,772</td> <td>10,200</td> <td>36,828</td> <td>131,040</td> <td>458,724</td> <td>1,572,840</td> <td>5,242,860</td> </tr> <tr> <td>Three of a kind</td> <td>-</td> <td>52</td> <td>2,496</td> <td>54,912</td> <td>732,160</td> <td>6,589,440</td> <td>42,172,416</td> <td>196,804,608</td> <td>674,758,656</td> </tr> <tr> <td>Two pair</td> <td>-</td> <td>-</td> <td>2,808</td> <td>123,552</td> <td>2,532,816</td> <td>32,123,520</td> <td>282,625,200</td> <td>1,836,229,824</td> <td>9,178,554,528</td> </tr> <tr> <td>Pair</td> <td>78</td> <td>3,744</td> <td>82,368</td> <td>1,098,240</td> <td>9,884,160</td> <td>63,258,624</td> <td>295,206,912</td> <td>1,012,137,984</td> <td>2,530,344,960</td> </tr> <tr> <td>Garbage</td> <td>780</td> <td>16,440</td> <td>177,408</td> <td>1,302,540</td> <td>6,985,044</td> <td>27,977,040</td> <td>83,880,960</td> <td>185,857,260</td> <td>294,648,732</td> </tr> <tr> <td>Total</td> <td>1,326</td> <td>22,100</td> <td>270,725</td> <td>2,598,960</td> <td>20,358,520</td> <td>133,784,560</td> <td>752,538,150</td> <td>3,679,075,400</td> <td>15,820,024,220</td> </tr> </tbody> </table> </div> </div>  <p>I would like to thank <a href="http://Wizardofvegas.com/member/miplet/" target="_blank">Miplet</a> for confirming the table above.</p> <h2>Two-Player Game</h2> <p>The next table shows the number of combinations for a two-player game of five-card stud. This would be easy if I assumed a separate deck for each player. But, no, your faithful Wizard counted all four trillion ways two five-card hands can be drawn from a single 52-card deck. So appreciate it!</p> <div class="box box--expandablemax"> <h3 class="box-title">Two-Player Game of Five-Card Stud<span class="box-title-expand desk-visible">Expand </span></h3>  <div class="box-content has-data"> <table border="0" cellpadding="0" cellspacing="0" class="data"> <tbody> <tr> <th class="data-heading" rowspan="2">Player 1</th> <th class="data-heading" colspan="10">Player 2</th> </tr> <tr> <th class="data-heading">Royal flush</th> <th class="data-heading">Straight flush</th> <th class="data-heading">Four of a kind</th> <th class="data-heading">Full house</th> <th class="data-heading">Flush</th> <th class="data-heading">Straight</th> <th class="data-heading">Three of a kind</th> <th class="data-heading">Two pair</th> <th class="data-heading">Pair</th> <th class="data-heading">Nothing</th> </tr> <tr> <td>Royal flush</td> <td>12</td> <td>124</td> <td>1376</td> <td>8496</td> <td>15532</td> <td>28692</td> <td>126008</td> <td>287208</td> <td>2581200</td> <td>3087108</td> </tr> <tr> <td>Straight flush</td> <td>124</td> <td>1052</td> <td>12384</td> <td>76464</td> <td>139836</td> <td>220644</td> <td>1134072</td> <td>2584872</td> <td>23230800</td> <td>27821556</td> </tr> <tr> <td>Four of a kind</td> <td>1376</td> <td>12384</td> <td>295152</td> <td>1770912</td> <td>1757152</td> <td>3508800</td> <td>23612160</td> <td>53127360</td> <td>425018880</td> <td>448073760</td> </tr> <tr> <td>Full house</td> <td>8496</td> <td>76464</td> <td>1770912</td> <td>10048896</td> <td>10849392</td> <td>21664800</td> <td>138707712</td> <td>299242944</td> <td>2494103040</td> <td>2766594960</td> </tr> <tr> <td>Flush</td> <td>15532</td> <td>139836</td> <td>1757152</td> <td>10849392</td> <td>19852668</td> <td>30908664</td> <td>160912216</td> <td>366764616</td> <td>3296192400</td> <td>3947967936</td> </tr> <tr> <td>Straight</td> <td>28692</td> <td>220644</td> <td>3508800</td> <td>21664800</td> <td>30908664</td> <td>63665904</td> <td>321320400</td> <td>732380400</td> <td>6582060000</td> <td>7890419496</td> </tr> <tr> <td>Three of a kind</td> <td>126008</td> <td>1134072</td> <td>23612160</td> <td>138707712</td> <td>160912216</td> <td>321320400</td> <td>1948607232</td> <td>4280335488</td> <td>36324288000</td> <td>41032615080</td> </tr> <tr> <td>Two pair</td> <td>287208</td> <td>2584872</td> <td>53127360</td> <td>299242944</td> <td>366764616</td> <td>732380400</td> <td>4280335488</td> <td>9339913440</td> <td>80921617920</td> <td>93524977080</td> </tr> <tr> <td>Pair</td> <td>2581200</td> <td>23230800</td> <td>425018880</td> <td>2494103040</td> <td>3296192400</td> <td>6582060000</td> <td>36324288000</td> <td>80921617920</td> <td>714035013120</td> <td>840529062000</td> </tr> <tr> <td>Nothing</td> <td>3087108</td> <td>27821556</td> <td>448073760</td> <td>2766594960</td> <td>3947967936</td> <td>7890419496</td> <td>41032615080</td> <td>93524977080</td> <td>840529062000</td> <td>1007846286084</td> </tr> </tbody> </table> </div> </div>  <p>The probability for a tie in a two-player game of five-card stud is 0.000344739, or 1 in 2,901.</p> <h2>Internal Links</h2> <ul> <li><a href="/video/probabilities-in-five-card-stud-poker/">Video: Probabilities in Five Card Stud Poker</a></li> <li><a href="/games/poker-math/">Poker Math</a> - How to derive the combinations for five-card stud.</li> <li><a href="/games/poker/probabilities/texas-hold-em-two-player/">Probabilities in Two-Player Texas Hold 'Em</a> — Lots of tables based on two-player Texas Hold 'Em.</li> </ul></body> <p class="article-author">Written by: <a href="https://wizardofodds.com/site/about/">Michael Shackleford</a></p> </div> </div> <div class="col-lm-24"> <div class="banner-block content"></div> </div> </div> </div> </main> <footer> <div class="network"> <ul class="network-list"> <li class="network-list--item"> <a href="https://wizardofvegas.com/" target="_blank" class="network-list--link wov lazy-load" class="lazy-load" data-src="/build/images/footer/css-sprite-combined.png">The Wizard of Vegas</a> </li> <li class="network-list--item"> <a href="https://wizardofmacau.com/" target="_blank" class="network-list--link wom lazy-load" class="lazy-load" data-src="/build/images/footer/css-sprite-combined.png">The Wizard of Macau</a> </li> <li class="network-list--item"> <a href="https://lasapuestas.mx/" target="_blank" class="network-list--link la lazy-load" class="lazy-load" data-src="/build/images/footer/css-sprite-combined.png">Las Apuestas</a> </li> </ul> </div> <div class="social"> <a href="https://www.facebook.com/Wizard-of-Odds-569798273073532/" class="social-item fb" rel="nofollow" target="_blank" aria-label="Visit our Facebook page"><i class="fa-brands fa-facebook"></i></a> <a href="https://www.youtube.com/user/TheOddsMustBeCrazy" class="social-item yt" rel="nofollow" target="_blank" aria-label="Visit our YouTube channel"><i class="fa-brands fa-youtube"></i></a> <a href="https://twitter.com/Wizard0fOdds" class="social-item twitter" rel="nofollow" target="_blank" aria-label="Visit our Twitter page"><i class="fa-brands fa-twitter"></i></a> </div> <ul class="footernav-list footernav-list--primary"> <li class="footernav-item"> <a class="footernav-link" href="/games/">Game Odds & Strategies</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/calculators/">Game Calculators</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/gambling/">Gambling Info</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/play/">Play For Fun</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/online-gambling/">Gambling Online</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/ask-the-wizard/">Ask The Wizard</a> </li> </ul> <ul class="footernav-list footernav-list--secondary"> <li class="footernav-item"> <a class="footernav-link" href="/site/about/">About</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/site/contact/">Contact</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/gambling/directory/">Links</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/site/updates/">What‘s New</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/audio/">Radio</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/video/">Video</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/blog/">Blog</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/site/map/">Site Map</a> </li> <li class="footernav-item"> <a class="footernav-link" href="/fiction/">Fiction</a> </li> </ul> <div class="footer-separator"></div> <div class="credits"> <a class="credits-item" href="http://www.gamcare.org.uk/" rel="nofollow" target="_blank"> <img loading="lazy" src="/build/images/footer/gam_care.svg" width="150" height="43.5" alt="GamCare logo"> </a> <a class="credits-item" href="https://wizardofodds.com/terms-conditions/" rel="nofollow"> <img loading="lazy" src="/build/images/footer/18_woo.png" width="200" height="51" alt="Gamble Responsibly logo"> </a> <a class="credits-item" href="https://www.gambleaware.org/" rel="nofollow" target="_blank"> <img loading="lazy" src="/build/images/footer/gamble-aware.svg" alt="Gamble Aware logo" width="95" height="85"> </a> <a class="credits-item" href="https://www.gamblingtherapy.org/" rel="nofollow" target="_blank"> <img loading="lazy" src="/build/images/footer/gordon_moody.svg" alt="Gordon Moody logo" width="150" height="51"> </a> <br> </div> <p> Copyright & 1998-2024. 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