Heads-up No-Limit Texas Hold'em on a short stack.
All-In or fold on preflop. Equilibrium strategy under the Theory of Games.
$, BB |
Est, % BB |
Strategy of the player "A" on small blind |
Strategy of the player "B" on big blind |
||
Bet |
% |
Call |
% |
||
1 |
0 |
All |
100 |
All |
100 |
| 1.5 | 0,03 | 32s 54 43 | 98,2 | All | 100 |
| 2 | 0,95 | 52s 43s 92 84 74 64 54 | 89,4 | All | 100 |
| 3 | 5,16 | 92s 84s 74s 64s 54s T2 (31%) 95 85 (91%) 76 | 77,9 | 32s 92 84 74 63 (47%) 53 43 | 92,3 |
| 3.5 | 6,32 | T2s 93s 84s 74s 64s 54s J2 T4 95 86 76 | 75,6 | 82s 73s 63s 52s 43s T2 95 85 75 65 54 (95%) | 83,4 |
| 4 | 6,60 | T2s 93s 84s 74s 64s 54s J2 T5 96 86 76 | 73,8 | T2s 93s 84s 74s 64s 53s J2 T5 96 86 76 | 74,1 |
| 5 | 5,62 | T2s 94s 84s 74s 64s 54s 43s Q2 J5 T6 96 (22%) 86 76 | 71,5 | J2s T4s 95s 86s 76s Q2 J5 T7 97 (81%) | 62,1 |
| 6 | 3,82 | T2s 95s 84s 74s 64s 53s 43s Q2 J5 T7 97 86 76 | 68,3 | Q2s J4s T6s 97s 87s K2 Q4 J7 T8 98 | 54,4 |
| 7 | 1,69 | J2s T3s 95s 84s 74s 63s 53s 43s Q2 J7 T7 97 86 (77%) 76 | 66,3 | Q2s J6s T7s 97s (43%) K2 Q6 J8 T9 | 48,5 |
| 8 | -0,41 | J2s T4s 95s 85s 74s 64s 53s K2 Q4 (19%) J7 T7 97 87 76 | 61,9 | K2s Q4s J7s T8s 98s K2 Q7 (57%) J9 T9 | 45,0 |
$, BB - size of game (in Big Bet),
Est, % BB - estimation of game for the player "A" measured in percentage of BB,
% - percentage hands which should be played.
Example: The player "A" has $3000, player "B" has $7000. Blinds - $300/$600. What equilibrium strategy?
Amount of money in game $3000, that makes 5 BB. Means, the player "A" (small blind) should put All-In on cards T2s 94s 84s 74s 64s 54s 43s Q2 J5 T6 97 86 76 and better and sometimes on 96 and there will be it of 71,5 % of distributions. All other hands fold. If the player "A" (small blind) has put, the player "B" (big blind) should call on J2s T4s 95s 86s 76s Q2 J5 T7 98 and is frequent on 97 and there will be it in 62,1 % of distributions. Following of this strategy will provide to both players an estimation 0,0562*BB in favour of the player "A". If any of players, say, the player "A", will use other strategy use by the player "B" equilibrium strategy all the same guarantees to him result not below, than an estimation of game. Thus if strategy of the player "A" is known, the player "B" can find strategy which will give him still the best result.
Whether equilibrium strategy is optimum or how to play actually
If you know in the situation heads-up on a short stack, that the opponent plays ideally, it is necessary to use equilibrium strategy which in this case is optimum. If you know nothing about the opponent, too it is necessary to use equilibrium strategy not to give the opponent of an opportunity to get advantage.
If you know, that your opponent plays incorrectly and know how it. You may find another strategy against him, which will give the best result, than equilibrium strategy.
- opponent call less often - raise more often
- opponent call more often - raise less often
- opponent raise less often - call less often
- opponent raise more often - call more often