Push Or Fold Poker
Pusher | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
A | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ |
K | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 19.9 | 19.3 |
Q | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 16.3 | 13.5 | 12.7 |
J | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 18.6 | 14.7 | 13.5 | 10.6 | 8.5 |
T | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 11.9 | 10.5 | 7.7 | 6.5 |
9 | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 14.4 | 6.9 | 4.9 | 3.7 |
8 | 20+ | 18.0 | 13.0 | 13.3 | 17.5 | 20+ | 20+ | 20+ | 20+ | 18.8 | 10.1 | 2.7 | 2.5 |
7 | 20+ | 16.1 | 10.3 | 8.5 | 9.0 | 10.8 | 14.7 | 20+ | 20+ | 20+ | 13.9 | 2.5 | 2.1 |
6 | 20+ | 15.1 | 9.6 | 6.5 | 5.7 | 5.2 | 7.0 | 10.7 | 20+ | 20+ | 16.3 | * | 2.0 |
5 | 20+ | 14.2 | 8.9 | 6.0 | 4.1 | 3.5 | 3.0 | 2.6 | 2.4 | 20+ | 20+ | ** | 2.0 |
4 | 20+ | 13.1 | 7.9 | 5.4 | 3.8 | 2.7 | 2.3 | 2.1 | 2.0 | 2.1 | 20+ | *** | 1.8 |
3 | 20+ | 12.2 | 7.5 | 5.0 | 3.4 | 2.5 | 1.9 | 1.8 | 1.7 | 1.8 | 1.6 | 20+ | 1.7 |
2 | 20+ | 11.6 | 7.0 | 4.6 | 2.9 | 2.2 | 1.8 | 1.6 | 1.5 | 1.5 | 1.4 | 1.4 | 20+ |
Caller | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
A | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ |
K | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 17.6 | 15.2 | 14.3 | 13.2 | 12.1 | 11.4 | 10.7 |
Q | 20+ | 20+ | 20+ | 20+ | 20+ | 16.1 | 13.0 | 10.5 | 9.9 | 8.9 | 8.4 | 7.8 | 7.2 |
J | 20+ | 20+ | 19.5 | 20+ | 18.0 | 13.4 | 10.6 | 8.8 | 7.0 | 6.9 | 6.1 | 5.8 | 5.6 |
T | 20+ | 20+ | 15.3 | 12.7 | 20+ | 11.5 | 9.3 | 7.4 | 6.3 | 5.2 | 5.2 | 4.8 | 4.5 |
9 | 20+ | 17.1 | 11.7 | 9.5 | 8.4 | 20+ | 8.2 | 7.0 | 5.8 | 5.0 | 4.3 | 4.1 | 3.9 |
8 | 20+ | 13.8 | 9.7 | 7.6 | 6.6 | 6.0 | 20+ | 6.5 | 5.6 | 4.8 | 4.1 | 3.6 | 3.5 |
7 | 20+ | 12.4 | 8.0 | 6.4 | 5.5 | 5.0 | 4.7 | 20+ | 5.4 | 4.8 | 4.1 | 3.6 | 3.3 |
6 | 20+ | 11.0 | 7.3 | 5.4 | 4.6 | 4.2 | 4.1 | 4.0 | 20+ | 4.9 | 4.3 | 3.8 | 3.3 |
5 | 20+ | 10.2 | 6.8 | 5.1 | 4.0 | 3.7 | 3.6 | 3.6 | 3.7 | 20+ | 4.6 | 4.0 | 3.6 |
4 | 18.3 | 9.1 | 6.2 | 4.7 | 3.8 | 3.3 | 3.2 | 3.2 | 3.3 | 3.5 | 20+ | 3.8 | 3.4 |
3 | 16.6 | 8.7 | 5.9 | 4.5 | 3.6 | 3.1 | 2.9 | 2.9 | 2.9 | 3.1 | 3.0 | 20+ | 3.3 |
2 | 15.8 | 8.1 | 5.6 | 4.2 | 3.5 | 3.0 | 2.8 | 2.6 | 2.7 | 2.8 | 2.7 | 2.6 | 15.0 |
« Push or Fold Poker » tells you in 5 seconds if it’s profitable to shove or whether to fold your hand regarding your situation (stacks, blinds, positions, action before you). Maximize your wins and Minimize your loses Take the best decision in less than 5 seconds Many options to suit your style. The concrete application of this mathematical resolution are Jennifear's charts used in our push or fold Calculator Tool. If poker is simplified to push or fold actions, then decisions become calculable. How the tool works Before using our tool, you need to know several factors. For live poker, the push/fold strategy works, but because the pace of play is faster with online poker, push/fold is even more important to understand when it comes to online poker strategy. That’s because a live poker player might be dealt around 30 hands per hour.
* | 63s: | 7.1 - 5.1, 2.3 |
** | 53s: | 12.9 - 3.8, 2.4 |
*** | 43s: | 10.0 - 4.9, 2.2 |
Pusher | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
A | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ |
K | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ |
Q | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 18.6 | 15.5 | 14.5 |
J | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 18.5 | 15.4 | 12.4 | 10.3 |
T | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 13.6 | 12.4 | 8.9 | 7.4 |
9 | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 16.5 | 8.0 | 6.0 | 4.7 |
8 | 20+ | 20+ | 14.9 | 15.4 | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 11.8 | 3.3 | 3.0 |
7 | 20+ | 18.3 | 11.8 | 9.7 | 10.4 | 12.4 | 16.8 | 20+ | 20+ | 20+ | 15.9 | 3.0 | 2.5 |
6 | 20+ | 17.4 | 11.3 | 7.5 | 6.7 | 6.5 | 8.5 | 13.5 | 20+ | 20+ | 18.8 | * | 2.4 |
5 | 20+ | 16.4 | 10.3 | 7.1 | 4.9 | 4.2 | 3.8 | 3.3 | 3.0 | 20+ | 20+ | ** | 2.4 |
4 | 20+ | 15.0 | 9.5 | 6.4 | 4.6 | 3.2 | 2.8 | 2.6 | 2.5 | 2.5 | 20+ | *** | 2.2 |
3 | 20+ | 14.3 | 8.6 | 5.8 | 4.2 | 3.0 | 2.3 | 2.2 | 2.1 | 2.1 | 2.0 | 20+ | 2.1 |
2 | 20+ | 13.3 | 8.1 | 5.5 | 3.7 | 2.7 | 2.2 | 1.9 | 1.8 | 1.9 | 1.7 | 1.6 | 20+ |
Caller | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
A | K | Q | J | T | 9 | 8 | 7 | 6 | 5 | 4 | 3 | 2 | |
A | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ |
K | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 20+ | 17.4 | 16.4 | 15.1 | 13.9 | 12.9 | 12.3 |
Q | 20+ | 20+ | 20+ | 20+ | 20+ | 18.5 | 14.9 | 12.0 | 11.4 | 10.2 | 9.7 | 8.8 | 8.2 |
J | 20+ | 20+ | 20+ | 20+ | 20+ | 15.4 | 12.2 | 10.0 | 8.1 | 7.9 | 7.0 | 6.6 | 6.4 |
T | 20+ | 20+ | 17.8 | 15.1 | 20+ | 13.0 | 10.6 | 8.5 | 7.2 | 6.0 | 5.9 | 5.5 | 5.1 |
9 | 20+ | 19.8 | 13.5 | 10.9 | 9.7 | 20+ | 9.5 | 8.0 | 6.7 | 5.6 | 4.8 | 4.6 | 4.3 |
8 | 20+ | 16.1 | 11.3 | 8.8 | 7.7 | 6.9 | 20+ | 7.4 | 6.4 | 5.5 | 4.7 | 4.0 | 3.9 |
7 | 20+ | 14.3 | 9.2 | 7.4 | 6.5 | 5.7 | 5.4 | 20+ | 6.0 | 5.5 | 4.7 | 4.0 | 3.6 |
6 | 20+ | 12.8 | 8.4 | 6.2 | 5.2 | 4.9 | 4.6 | 4.5 | 20+ | 5.5 | 4.7 | 4.2 | 3.7 |
5 | 20+ | 11.8 | 7.8 | 5.9 | 4.5 | 4.1 | 4.0 | 4.0 | 4.1 | 20+ | 5.1 | 4.5 | 3.9 |
4 | 20+ | 10.5 | 7.1 | 5.4 | 4.3 | 3.7 | 3.5 | 3.6 | 3.7 | 3.8 | 20+ | 4.2 | 3.8 |
3 | 19.1 | 9.9 | 6.7 | 5.0 | 4.2 | 3.6 | 3.2 | 3.2 | 3.3 | 3.5 | 3.3 | 20+ | 3.6 |
2 | 18.1 | 9.4 | 6.4 | 4.8 | 3.9 | 3.4 | 3.1 | 2.9 | 3.0 | 3.1 | 3.0 | 2.9 | 16.9 |
* | 63s: | 8.9 - 4.7, 2.8 |
** | 53s: | 15.2 - 3.8, 2.9 |
*** | 43s: | 11.5 - 4.7, 2.6 |
The tables show the highest effective stack size in big blinds where a hand can be pushed or called. Values bigger than 20 are only displayed as 20+, which means the hand can be played for any stack size of 20bb or less. (Playing push-or-fold is typically only recommended up to around 10bb, depending on the situation. Using push-or-fold for >20bb is almost certainly a bad idea.)
Push Or Fold Poker
Some hands have gaps in their pushing strategies, they are marked with * and the details are displayed below the charts. For example 63s is included in the pushing strategy for stack sizes between 7.1 and 5.1bb, and stacks below 2.3bb.
SB (9.0bb): T3s
BB (6.0bb): Q2o
The effective stack size is the smaller of the two, before posting any blinds. So the relevant stack size for both players in this hand is 6.0 big blinds.
To find the strategy for SB's T3s, check the green area (suited hands) of the 'Pusher' chart. The value for T3s is 7.7bb, and since that is larger than the current effective stacks the hand is a push in the Nash Equilibrium strategy.
To determine if the BB should call with his Q2o, check the orange area (offsuit hands) of the 'Caller' chart and locate Q2o. The value there is 5.6bb. The effective stacks in the current hand are larger than the value for Q2o, so this hand is a fold in the Nash Equilibrium strategy.
This example refers to the no ante solution. If the table values don't match the example then make sure the 'No Ante' tab is selected above.
The solution available on this site was independently calculated and published in 2007 as part of a coding experiment, inspired by the discussion of the topic in Mathematics of Poker.
Similar charts have been published by various sources, including SNGPT and Mathematics of Poker, and there are some minor differences between them. The exact Nash solution is considerably more complex and the chart only shows a simplified version. Most hands are actually played with mixed strategies for at least a few stack sizes, and many hands have multiple smaller gaps in their strategy, similar to the 63s, 53s, 43s hands. These details are omitted in the chart to allow a compact representation of the strategy.
The differences in published solutions are most likely due to choices made when simplifying the exact solution into easy-to-use charts. Due to the considerable number of rather arbitrary choices when simplifying into chart form, it is actually quite unlikely that two independently created charts would perfectly match.
The file linked below contains the unsimplified push-or-fold equilibrium strategies for all stacks of 1bb ≤ stacks ≤ 200bb in steps of 0.05bb. This data can be used to derive the charts. For practical purposes the chart form should be completely sufficient though.
888 Poker Push Or Fold
The data linked here was re-calculated with a later version than the original chart data, so there may be some very slight differences.