Hold Em All In
Texas Hold'em ALL IN United States Veteran Honor Service Ribbon Patch 5.5 x 3 Inch Cap Hat Shoulder High Quality Embroidering Iron or Sew-on Application. Seller assumes all responsibility for this. A game of Texas hold 'em in progress. 'Hold 'em' is a popular form of poker. Poker is any of a number of card games in which players wager over which hand is best according to that specific game's rules in. Find the best tournament in town with our real-time list of all upcoming poker tournaments in the Las Vegas area. To customize your search, you can filter this list by game type, buy-in, day, starting time.
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Introduction
World Poker Tour All-In Hold'em is poker based table game found at many of the MGM/Mirage casinos in Las Vegas. There are two versions, both with the same name. In one, the player can raise up to 3X hit ante, and in the other, up to 10X his ante. In the version addressed on this page, the player can raise up to 10X his ante bet. See World Poker Tour 3X Raise Hold 'Em, for the other 3X version. The rules are very true to real poker and the Element of Risk is only 0.23%.
Rules
- The game uses a single 52-card deck.
- Play begins with the player making an ante bet and two optional side bets
- Player gets two 'hole' cards face down, which he may examine.
- Player has three choices: (1) fold, (2) raise, or (3) go all-in.
- If player folds he forfeits his ante bet.
- If player raises he must make a raise bet equal to five times the ante.
- If player goes all-in he must make a raise bet equal to ten times the ante.
- The dealer will examine his cards.
- If the player raised the dealer will call with any pair or a blackjack point value of 13 or higher.
- If the player went all-in the dealer will call with any pair or a blackjack point value of 17 or higher.
- If the dealer does not call then he will fold. In this case the player will win even money on the ante and the raise will push.
- Five community cards will be dealt.
- If both player and dealer are still in the game the higher poker hand will win. If the player has the higher hand both ante and raise will pay even money. If dealer has the higher hand the ante and raise will lose. A tie will result in a push.
- The 'Player's Hole Cards Bonus Bet' is paid according to the value of the player's two hold cards. The pay table is below.
- The 'Player's Final Hand Bonus Bet' is paid according to the value of the player's final seven cards hand. The pay table is below.
- Even if the player folds the cards will still be played out to resolve any side bets. In the event one or more players raise and one or more go all-in the dealer will separately adjudicate each hand according to the above rules.
Player's Hole Cards Bonus Bet
| Hand | Pays |
|---|---|
| Two red aces | 50 to 1 |
| Ace/king suited | 25 to 1 |
| Pair of aces | 20 to 1 |
| Pair J-K | 8 to 1 |
| Pair 6-10 | 3 to 1 |
| Pair 2-5 | 2 to 1 |
| Suited | 1 to 1 |
| All other | Loss |
Player's Final Hand Bonus Bet
| Hand | Pays |
|---|---|
| Royal flush | 500 to 1 |
| Straight flush | 100 to 1 |
| Four of a kind | 40 to 1 |
| Full house | 8 to 1 |
| Flush | 6 to 1 |
| Straight | 4 to 1 |
| Three of a kind | 2 to 1 |
| All other | Loss |
Strategy
The strategy is interesting, with the player going all in on both strong and weak hands, and raising on hands in between. The logic behind going all-in on weak hands is the dealer has a higher qualifying point to call, so the player has a greater chance of bluffing and winning the ante.
House Edge
The following table shows the probability and return for all possible outcomes, assuming optimal strategy. The lower right cell shows a house edge of 1.50%. The average wager is 6.64 units, so the Element of Risk is a very low 0.23%.
World Poker Tour All-In Hold'Em — Return Table under Optimal Strategy
| Win | Combinations | Probability | Return |
|---|---|---|---|
| 11 | 98702588268 | 0.035487 | 0.390356 |
| 6 | 619924796200 | 0.222884 | 1.337303 |
| 1 | 893261052288 | 0.321157 | 0.321157 |
| 0 | 56412833364 | 0.020282 | 0 |
| -1 | 327221294400 | 0.117647 | -0.117647 |
| -6 | 646292343200 | 0.232364 | -1.394183 |
| -11 | 139566094680 | 0.050179 | -0.551966 |
| Total | 2781381002400 | 1 | -0.01498 |
The following table shows the probability and return for all possible outcomes, assuming the player always raises 5X. The lower right cell shows a house edge of 7.93%. With a total wager of 6 units, the Element of Risk is 1.32%.
World Poker Tour All-In Hold'Em — Return Table Raising 5X Blindly
| Win | Combinations | Probability | Return |
|---|---|---|---|
| 6 | 886754626972 | 0.318818 | 1.912909 |
| 1 | 771906643200 | 0.277526 | 0.277526 |
| 0 | 70538503612 | 0.025361 | 0 |
| -6 | 1052181228616 | 0.378295 | -2.269767 |
| Total | 2781381002400 | 1 | -0.079332 |
The following table shows the probability and return for all possible outcomes, assuming the player always raises 10X. The lower right cell shows a house edge of 13.58%. With a total wager of 11 units, the Element of Risk is 1.23%.
World Poker Tour All-In Hold'Em — Return Table Raising 10X Blindly
| Win | Combinations | Probability | Return |
|---|---|---|---|
| 11 | 425606185356 | 0.15302 | 1.683217 |
| 1 | 1711619078400 | 0.615385 | 0.615385 |
| 0 | 28611529392 | 0.010287 | 0 |
| -11 | 615544209252 | 0.221309 | -2.434397 |
| Total | 2781381002400 | 1 | -0.135796 |
Expected Value Table
The following table shows the expected value by raising and going all-in for all possible hands. The probability of the 2-card hand the contribution to the total return are also indicated.
World Poker Tour All-In Hold'Em Expected Value Table
| Higher Card | Lower Card | Type | Raise | All-in | Probability | Return |
|---|---|---|---|---|---|---|
| A | A | Pair | 3.256714 | 3.38796 | 0.004525 | 0.01533 |
| K | K | Pair | 2.955794 | 3.032434 | 0.004525 | 0.013721 |
| Q | Q | Pair | 2.680206 | 2.696242 | 0.004525 | 0.0122 |
| J | J | Pair | 2.405882 | 2.356818 | 0.004525 | 0.010886 |
| 10 | 10 | Pair | 2.13058 | 2.008352 | 0.004525 | 0.009641 |
| 9 | 9 | Pair | 1.817215 | 1.636141 | 0.004525 | 0.008223 |
| 8 | 8 | Pair | 1.532584 | 1.288469 | 0.004525 | 0.006935 |
| 7 | 7 | Pair | 1.267937 | 0.956145 | 0.004525 | 0.005737 |
| 6 | 6 | Pair | 1.015836 | 0.737001 | 0.004525 | 0.004597 |
| 5 | 5 | Pair | 0.769033 | 0.600678 | 0.004525 | 0.00348 |
| 4 | 4 | Pair | 0.522357 | 0.470139 | 0.004525 | 0.002364 |
| 3 | 3 | Pair | 0.292924 | 0.340995 | 0.004525 | 0.001543 |
| 2 | 2 | Pair | 0.105286 | 0.21424 | 0.004525 | 0.000969 |
| A | K | Suited | 1.735451 | 1.863577 | 0.003017 | 0.005622 |
| A | Q | Suited | 1.635463 | 1.710668 | 0.003017 | 0.00516 |
| A | J | Suited | 1.536697 | 1.562202 | 0.003017 | 0.004713 |
| A | 10 | Suited | 1.439779 | 1.420573 | 0.003017 | 0.004343 |
| A | 9 | Suited | 1.238514 | 1.169927 | 0.003017 | 0.003736 |
| A | 8 | Suited | 1.13748 | 1.034798 | 0.003017 | 0.003431 |
| A | 7 | Suited | 1.028783 | 0.876154 | 0.003017 | 0.003103 |
| A | 6 | Suited | 0.927189 | 0.688188 | 0.003017 | 0.002797 |
| A | 5 | Suited | 0.896956 | 0.709154 | 0.003017 | 0.002706 |
| A | 4 | Suited | 0.809963 | 0.672951 | 0.003017 | 0.002443 |
| A | 3 | Suited | 0.738821 | 0.638418 | 0.003017 | 0.002229 |
| A | 2 | Suited | 0.646591 | 0.605168 | 0.003017 | 0.001951 |
| K | Q | Suited | 1.282533 | 1.272537 | 0.003017 | 0.003869 |
| K | J | Suited | 1.183943 | 1.123067 | 0.003017 | 0.003571 |
| K | 10 | Suited | 1.089875 | 0.983123 | 0.003017 | 0.003288 |
| K | 9 | Suited | 0.892813 | 0.735017 | 0.003017 | 0.002693 |
| K | 8 | Suited | 0.71424 | 0.525408 | 0.003017 | 0.002155 |
| K | 7 | Suited | 0.627124 | 0.391476 | 0.003017 | 0.001892 |
| K | 6 | Suited | 0.543869 | 0.263266 | 0.003017 | 0.001641 |
| K | 5 | Suited | 0.448997 | 0.247376 | 0.003017 | 0.001354 |
| K | 4 | Suited | 0.361685 | 0.211107 | 0.003017 | 0.001091 |
| K | 3 | Suited | 0.287827 | 0.174822 | 0.003017 | 0.000868 |
| K | 2 | Suited | 0.202969 | 0.139123 | 0.003017 | 0.000612 |
| Q | J | Suited | 0.92214 | 0.827414 | 0.003017 | 0.002782 |
| Q | 10 | Suited | 0.827144 | 0.684957 | 0.003017 | 0.002495 |
| Q | 9 | Suited | 0.631537 | 0.436965 | 0.003017 | 0.001905 |
| Q | 8 | Suited | 0.456304 | 0.229659 | 0.003017 | 0.001376 |
| Q | 7 | Suited | 0.278809 | 0.011835 | 0.003017 | 0.000841 |
| Q | 6 | Suited | 0.214581 | -0.059747 | 0.003017 | 0.000647 |
| Q | 5 | Suited | 0.121683 | -0.069533 | 0.003017 | 0.000367 |
| Q | 4 | Suited | 0.034479 | -0.105591 | 0.003017 | 0.000104 |
| Q | 3 | Suited | -0.039268 | -0.143252 | 0.003017 | -0.000118 |
| Q | 2 | Suited | -0.104517 | -0.18177 | 0.003017 | -0.000315 |
| J | 10 | Suited | 0.604397 | 0.448795 | 0.003017 | 0.001823 |
| J | 9 | Suited | 0.40683 | 0.202754 | 0.003017 | 0.001227 |
| J | 8 | Suited | 0.233363 | -0.003658 | 0.003017 | 0.000704 |
| J | 7 | Suited | 0.05842 | -0.21943 | 0.003017 | 0.000176 |
| J | 6 | Suited | -0.103745 | -0.347228 | 0.003017 | -0.000313 |
| J | 5 | Suited | -0.175922 | -0.334942 | 0.003017 | -0.000531 |
| J | 4 | Suited | -0.262481 | -0.370008 | 0.003017 | -0.000792 |
| J | 3 | Suited | -0.335616 | -0.40825 | 0.003017 | -0.001012 |
| J | 2 | Suited | -0.381993 | -0.448772 | 0.003017 | -0.001152 |
| 10 | 9 | Suited | 0.220895 | 0.031039 | 0.003017 | 0.000666 |
| 10 | 8 | Suited | 0.046468 | -0.174214 | 0.003017 | 0.00014 |
| 10 | 7 | Suited | -0.128313 | -0.38708 | 0.003017 | -0.000387 |
| 10 | 6 | Suited | -0.289594 | -0.48357 | 0.003017 | -0.000874 |
| 10 | 5 | Suited | -0.462436 | -0.5659 | 0.003017 | -0.001395 |
| 10 | 4 | Suited | -0.528482 | -0.581272 | 0.003017 | -0.001594 |
| 10 | 3 | Suited | -0.600439 | -0.619297 | 0.003017 | -0.001811 |
| 10 | 2 | Suited | -0.62893 | -0.661009 | 0.003017 | -0.001897 |
| 9 | 8 | Suited | -0.11851 | -0.300328 | 0.003017 | -0.000357 |
| 9 | 7 | Suited | -0.284848 | -0.461445 | 0.003017 | -0.000859 |
| 9 | 6 | Suited | -0.442111 | -0.522285 | 0.003017 | -0.001334 |
| 9 | 5 | Suited | -0.610891 | -0.609492 | 0.003017 | -0.001839 |
| 9 | 4 | Suited | -0.779772 | -0.730825 | 0.003017 | -0.002205 |
| 9 | 3 | Suited | -0.821222 | -0.747773 | 0.003017 | -0.002256 |
| 9 | 2 | Suited | -0.841233 | -0.790025 | 0.003017 | -0.002383 |
| 8 | 7 | Suited | -0.372107 | -0.439334 | 0.003017 | -0.001122 |
| 8 | 6 | Suited | -0.522238 | -0.494451 | 0.003017 | -0.001492 |
| 8 | 5 | Suited | -0.685613 | -0.581817 | 0.003017 | -0.001755 |
| 8 | 4 | Suited | -0.843035 | -0.707633 | 0.003017 | -0.002135 |
| 8 | 3 | Suited | -0.988616 | -0.833501 | 0.003017 | -0.002514 |
| 8 | 2 | Suited | -0.986191 | -0.854317 | 0.003017 | -0.002577 |
| 7 | 6 | Suited | -0.548293 | -0.463903 | 0.003017 | -0.001399 |
| 7 | 5 | Suited | -0.692191 | -0.548412 | 0.003017 | -0.001654 |
| 7 | 4 | Suited | -0.839553 | -0.674108 | 0.003017 | -0.002034 |
| 7 | 3 | Suited | -0.985481 | -0.805828 | 0.003017 | -0.002431 |
| 7 | 2 | Suited | -1.098878 | -0.937943 | 0.003017 | -0.002829 |
| 6 | 5 | Suited | -0.651371 | -0.464342 | 0.003017 | -0.001401 |
| 6 | 4 | Suited | -0.793105 | -0.588727 | 0.003017 | -0.001776 |
| 6 | 3 | Suited | -0.938151 | -0.721253 | 0.003017 | -0.002176 |
| 6 | 2 | Suited | -1.054893 | -0.856131 | 0.003017 | -0.002583 |
| 5 | 4 | Suited | -0.727057 | -0.484697 | 0.003017 | -0.001462 |
| 5 | 3 | Suited | -0.868369 | -0.611891 | 0.003017 | -0.001846 |
| 5 | 2 | Suited | -0.984017 | -0.745473 | 0.003017 | -0.002249 |
| 4 | 3 | Suited | -0.932884 | -0.657755 | 0.003017 | -0.001984 |
| 4 | 2 | Suited | -1.047644 | -0.78502 | 0.003017 | -0.002368 |
| 3 | 2 | Suited | -1.111078 | -0.832553 | 0.003017 | -0.002511 |
| A | K | Unsuited | 1.592941 | 1.724771 | 0.00905 | 0.015609 |
| A | Q | Unsuited | 1.486513 | 1.561763 | 0.00905 | 0.014134 |
| A | J | Unsuited | 1.381169 | 1.403164 | 0.00905 | 0.012698 |
| A | 10 | Unsuited | 1.277688 | 1.25145 | 0.00905 | 0.011563 |
| A | 9 | Unsuited | 1.06084 | 0.980187 | 0.00905 | 0.0096 |
| A | 8 | Unsuited | 0.95059 | 0.834449 | 0.00905 | 0.008603 |
| A | 7 | Unsuited | 0.832439 | 0.661931 | 0.00905 | 0.007533 |
| A | 6 | Unsuited | 0.722882 | 0.450468 | 0.00905 | 0.006542 |
| A | 5 | Unsuited | 0.689569 | 0.470809 | 0.00905 | 0.00624 |
| A | 4 | Unsuited | 0.594272 | 0.431335 | 0.00905 | 0.005378 |
| A | 3 | Unsuited | 0.515894 | 0.393682 | 0.00905 | 0.004669 |
| A | 2 | Unsuited | 0.411147 | 0.3574 | 0.00905 | 0.003721 |
| K | Q | Unsuited | 1.111704 | 1.095389 | 0.00905 | 0.010061 |
| K | J | Unsuited | 1.006489 | 0.935634 | 0.00905 | 0.009108 |
| K | 10 | Unsuited | 0.905999 | 0.785679 | 0.00905 | 0.008199 |
| K | 9 | Unsuited | 0.693583 | 0.517121 | 0.00905 | 0.006277 |
| K | 8 | Unsuited | 0.501053 | 0.292453 | 0.00905 | 0.004534 |
| K | 7 | Unsuited | 0.405958 | 0.146232 | 0.00905 | 0.003674 |
| K | 6 | Unsuited | 0.316233 | -0.000783 | 0.00905 | 0.002862 |
| K | 5 | Unsuited | 0.213574 | -0.020025 | 0.00905 | 0.001933 |
| K | 4 | Unsuited | 0.118028 | -0.059524 | 0.00905 | 0.001068 |
| K | 3 | Unsuited | 0.036817 | -0.099016 | 0.00905 | 0.000333 |
| K | 2 | Unsuited | -0.05988 | -0.137881 | 0.00905 | -0.000542 |
| Q | J | Unsuited | 0.730072 | 0.623157 | 0.00905 | 0.006607 |
| Q | 10 | Unsuited | 0.628555 | 0.470482 | 0.00905 | 0.005688 |
| Q | 9 | Unsuited | 0.417675 | 0.201974 | 0.00905 | 0.00378 |
| Q | 8 | Unsuited | 0.228684 | -0.02023 | 0.00905 | 0.00207 |
| Q | 7 | Unsuited | 0.037465 | -0.255449 | 0.00905 | 0.000339 |
| Q | 6 | Unsuited | -0.031884 | -0.341527 | 0.00905 | -0.000289 |
| Q | 5 | Unsuited | -0.132402 | -0.354121 | 0.00905 | -0.001198 |
| Q | 4 | Unsuited | -0.227802 | -0.393331 | 0.00905 | -0.002062 |
| Q | 3 | Unsuited | -0.308865 | -0.434246 | 0.00905 | -0.002795 |
| Q | 2 | Unsuited | -0.384258 | -0.476087 | 0.00905 | -0.003477 |
| J | 10 | Unsuited | 0.393521 | 0.221158 | 0.00905 | 0.003561 |
| J | 9 | Unsuited | 0.180553 | -0.04541 | 0.00905 | 0.001634 |
| J | 8 | Unsuited | -0.006574 | -0.266667 | 0.00905 | -0.000059 |
| J | 7 | Unsuited | -0.195063 | -0.499933 | 0.00905 | -0.001765 |
| J | 6 | Unsuited | -0.368704 | -0.644872 | 0.00905 | -0.003337 |
| J | 5 | Unsuited | -0.447026 | -0.633822 | 0.00905 | -0.004045 |
| J | 4 | Unsuited | -0.54171 | -0.671908 | 0.00905 | -0.004902 |
| J | 3 | Unsuited | -0.622087 | -0.713394 | 0.00905 | -0.00563 |
| J | 2 | Unsuited | -0.676917 | -0.757342 | 0.00905 | -0.006126 |
| 10 | 9 | Unsuited | -0.015401 | -0.226476 | 0.00905 | -0.000139 |
| 10 | 8 | Unsuited | -0.203565 | -0.446541 | 0.00905 | -0.001842 |
| 10 | 7 | Unsuited | -0.391911 | -0.67693 | 0.00905 | -0.003547 |
| 10 | 6 | Unsuited | -0.5646 | -0.787951 | 0.00905 | -0.00511 |
| 10 | 5 | Unsuited | -0.750188 | -0.877612 | 0.00905 | -0.006789 |
| 10 | 4 | Unsuited | -0.822889 | -0.894484 | 0.00905 | -0.007447 |
| 10 | 3 | Unsuited | -0.90198 | -0.935689 | 0.00905 | -0.008163 |
| 10 | 2 | Unsuited | -0.937244 | -0.980874 | 0.00905 | -0.008482 |
| 9 | 8 | Unsuited | -0.379737 | -0.583215 | 0.00905 | -0.003437 |
| 9 | 7 | Unsuited | -0.559041 | -0.757514 | 0.00905 | -0.005059 |
| 9 | 6 | Unsuited | -0.72736 | -0.830208 | 0.00905 | -0.006582 |
| 9 | 5 | Unsuited | -0.908688 | -0.924981 | 0.00905 | -0.008223 |
| 9 | 4 | Unsuited | -1.090962 | -1.055001 | 0.00905 | -0.00905 |
| 9 | 3 | Unsuited | -1.137159 | -1.073457 | 0.00905 | -0.00905 |
| 9 | 2 | Unsuited | -1.163143 | -1.119204 | 0.00905 | -0.00905 |
| 8 | 7 | Unsuited | -0.652332 | -0.7329 | 0.00905 | -0.005903 |
| 8 | 6 | Unsuited | -0.812954 | -0.799624 | 0.00905 | -0.007236 |
| 8 | 5 | Unsuited | -0.988555 | -0.894536 | 0.00905 | -0.008095 |
| 8 | 4 | Unsuited | -1.158478 | -1.02928 | 0.00905 | -0.00905 |
| 8 | 3 | Unsuited | -1.31556 | -1.164172 | 0.00905 | -0.00905 |
| 8 | 2 | Unsuited | -1.317381 | -1.186744 | 0.00905 | -0.00905 |
| 7 | 6 | Unsuited | -0.841291 | -0.767186 | 0.00905 | -0.006943 |
| 7 | 5 | Unsuited | -0.995646 | -0.858892 | 0.00905 | -0.007773 |
| 7 | 4 | Unsuited | -1.154632 | -0.993258 | 0.00905 | -0.008989 |
| 7 | 3 | Unsuited | -1.312111 | -1.134313 | 0.00905 | -0.00905 |
| 7 | 2 | Unsuited | -1.437653 | -1.276028 | 0.00905 | -0.00905 |
| 6 | 5 | Unsuited | -0.951466 | -0.774928 | 0.00905 | -0.007013 |
| 6 | 4 | Unsuited | -1.104414 | -0.907676 | 0.00905 | -0.008214 |
| 6 | 3 | Unsuited | -1.260954 | -1.049341 | 0.00905 | -0.00905 |
| 6 | 2 | Unsuited | -1.390101 | -1.193775 | 0.00905 | -0.00905 |
| 5 | 4 | Unsuited | -1.033054 | -0.797771 | 0.00905 | -0.00722 |
| 5 | 3 | Unsuited | -1.185512 | -0.933614 | 0.00905 | -0.008449 |
| 5 | 2 | Unsuited | -1.313431 | -1.076576 | 0.00905 | -0.00905 |
| 4 | 3 | Unsuited | -1.254766 | -0.982707 | 0.00905 | -0.008893 |
| 4 | 2 | Unsuited | -1.381622 | -1.118842 | 0.00905 | -0.00905 |
| 3 | 2 | Unsuited | -1.449838 | -1.169612 | 0.00905 | -0.00905 |
| Total | -0.079332 | -0.135796 | -0.01498 |
Player Hole Cards Side Bet
The following table shows the possible outcomes of the Player Hole Cards side bet. The lower right cell shows a house edge of 7.24%.
Player Hole Cards Side Bet
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Two red aces | 50 | 1 | 0.000754 | 0.037707 |
| Ace/king suited | 25 | 4 | 0.003017 | 0.075415 |
| Pair of aces | 20 | 5 | 0.003771 | 0.075415 |
| Pair J-K | 8 | 18 | 0.013575 | 0.108597 |
| Pair 6-10 | 3 | 30 | 0.022624 | 0.067873 |
| Pair 2-5 | 2 | 24 | 0.0181 | 0.036199 |
| Suited | 1 | 308 | 0.232278 | 0.232278 |
| All other | -1 | 936 | 0.705882 | -0.705882 |
| Total | 1326 | 1 | -0.072398 |
Final Hand Side Bet
The following table shows the possible outcomes of the Final Hand side bet. The lower right cell shows a house edge of 6.55%.
Texas Hold Em All In Rules
Final Hand Side Bet
| Hand | Pays | Combinations | Probability | Return |
|---|---|---|---|---|
| Royal flush | 500 | 4324 | 0.000032 | 0.01616 |
| Straight flush | 100 | 37260 | 0.000279 | 0.027851 |
| Four of a kind | 40 | 224848 | 0.001681 | 0.067227 |
| Full house | 8 | 3473184 | 0.025961 | 0.207688 |
| Flush | 6 | 4047644 | 0.030255 | 0.18153 |
| Straight | 4 | 6180020 | 0.046194 | 0.184775 |
| Three of a kind | 2 | 6461620 | 0.048299 | 0.096597 |
| All other | -1 | 113355660 | 0.8473 | -0.8473 |
| Total | 133784560 | 1 | -0.065472 |
Practice Game
Practice playing here. Not only will you enjoy playing, but the game teaches you proper strategy as well.
Written by:Michael Shackleford
Poker players need to be acquainted with math. Most of the time, they are concerned with the odds on making whatever hand they are drawing to, making sure the pot odds and/or implied odds are sufficientBob Ciaffone is one of America’s best-known poker players, writers, and teachers. He has numerous poker tournament wins and placings, the most prominent being third place in the 1987 World Championship. He has been a poker teacher since 1995, with his students having earned well over a million dollars in tournament play. Bob's website is www.pokercoach.us to stay in. But there are other odds that also are relevant to poker situations. For no-limit hold'em, especially tournament play with its high frequency of players going all in preflop, it is important to know the approximate chances for each hand on the more frequent matchups. Let's discuss the odds in various types of situations when we get all in before the flop. (Note: Odds given are approximate.)
One of the worst situations you can be in is when someone has an overpair to both of your cards. Whether you have a pocket pair or not, you are really hurting. Two aces are a big favorite against two kings. If the aces are of the same suits as the kings, they are a 4.75-to-1 favorite. It is slightly better for the kings if they can make nut flushes, but the aces are still a 4.4-to-1 favorite against two kings of differing suits from the aces. Smaller pairs actually have a better chance than kings of drawing out, because of improved straight possibilities, but 7-7 is still a 4-to-1 underdog to the aces.
Non-pair hands can be either better or worse than an underpair is against an overpair. For example, K-Q offsuit is a 6.5-to-1 underdog to the bullets. Being suited of course helps, but K-Q suited is still a 4.6-to-1 dog versus the aces. Midsize connectors have the best chance; a 7-6 suited is about a 3.5-to-1 underdog. That is better than any pair would have, but still, obviously, no bargain.
Texas Hold'em All In Memo
An important concept to understand is that of domination, meaning the superior hand has one or two cards that are of the same rank as a card in an inferior hand. If one hand dominates another, it has that hand in serious trouble. It will be difficult for the weaker hand to draw out, whether the hands are all in against each other before the flop or both hit the flop with the card that is common to both hands.
Domination, of course, occurs more often in practice between two good hands than between a good hand and a bad hand. For example, if one is all in against an A-K, a hand that contains an ace is in worse shape than a clunker like 8-7 offsuit.
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One hand can be dominated by another in several ways:
1. Bigger kicker. The classical matchup here is A-K against A-Q. The actual odds vary a meaningful amount according to whether the hands are suited or unsuited. The weaker hand finds that being suited is significantly beneficial in trying to draw out. Against an A-K offsuit, an A-Q offsuit is a 2.8-to-1 dog if the queen has no cards of its suit in the opposing hand, and 2.95-to-1 if the opponent's ace or king is of the queen's suit. With the A-Q being suited, the odds drop to 2.3-to-1 in favor of the A-K, which is quite an improvement for the underdog's chances. Whether the A-K is suited is not as important, but it still matters. With an A-K suited, those odds against A-Q suited are 3.1-to-1, and against A-Q suited, 2.5-to-1. Note that if a hand is dominated, the gap between the kickers of each hand is of little importance. For example, with the superior hand being A-K, it hardly matters whether the weaker hand is A-Q, A-J, or A-10, because the method of drawing out is the same. The weaker hand needs to hit its kicker, and have the stronger hand not hit its kicker. Having a midsize kicker (for straights) is of only tiny help to the underdog. For example, the A K is a 2.75-to-1 favorite over the A 10. (If the 10 were instead the Q, the odds would be 2.8-to-1.)
2. Pair matches the lower card. An example would be A-Q against two queens. If your lower-ranking card is tied up, you are in approximately the same amount of trouble as the previous situation; you need to hit your kicker. Actually, it is measurably easier for the dominated hand to fight against the pair than against the higher kicker, since the boss hand has only the case card of a rank to lock you out of winning, rather than three cards that do it. With A-Q offsuit, you are a 2.35-to-1 underdog to a pair of queens. With A-Q suited, you are a 1.9-to-1 underdog to a pair of queens. The odds show about the same ratios for A-K against K-K.
3. Pair matches the higher card. If your higher-ranking card is tied up, as when A-Q runs into two aces, the weaker hand is obviously in dire straits. It takes some sort of parlay in hitting the flop for the underdog to draw out, rather than simply making a pair for a card in your hand. Two aces are an 11.65-to-1 favorite against A-Q offsuit and a 6.95-to-1 favorite against A-Q suited. Even though the underdog is still buried when suited, the improvement in chances is noteworthy.
What conclusions can be drawn from the statistics of all-in situations that we have been looking at so far? First, it is desirable to avoid these traps of running into an overpair or dominating hand. Of course, this is easier said than done. You cannot see your opponent's hand. But such a situation is easier to avoid if you are the bettor instead of the caller. An all-in bettor has a chance to win without a fight, whereas an all-in caller is certainly risking all of his chips. Second, the benefit of being suited is apparent in all of these matchups. If you run into an unexpectedly good hand and are dominated, the chance to win with a flush significantly changes the odds against you. This suited factor is especially important when you are thinking about going all in with an ace-rag.
I think it is highly worthwhile to look at how various hands do against each other when no hand is dominated by another. The most common example here is A-K against two queens. Two red queens against a black A-K offsuit is a 57-to-43 favorite. (I think one gets a better feel for these closer matchups when we use percentages to give the winning ratios.) The relative percentages are virtually the same if the queens are of the same suits as the A-K. It is harder for the A-K to make a flush, but the queens can never win by making a flush.
If the A-K is suited, this is of meaningful help to it. The queens are favored by 54-to-46, whether one of the queens is of big slick's suit or not.
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If the A-K runs into a significantly smaller pair than queens, it has another way to win the pot. The A-K wins when there are two pair on the board that are both higher than the opponent's pair. This is impossible when facing two jacks, and highly unlikely when facing two tens. But as we approach the tiny pairs, it is meaningful. It is also helpful to the A-K if the pair is lower than tens, because it greatly increases big slick's straight-making chances. A-K suited is a 52-48 underdog against two red nines, and a 51.5-to-48.5 underdog against two red fours.