Poker
All-in preflop — simulator
All-in model pre-flop: equity, re-raises, and outcome distribution.
Set the number of hands, minimum equity, and advantage, then run the simulation. The data will come from the JSON API without reloading the page.
Expected equity is the average over the actual hand imbalances. Actual equity is the share of wins of player 1 taking into account half of the splits. A small discrepancy is normal: this is sample variance, not a model error.
The histogram shows the extent to which player 1 was ahead when going all-in. A shift to the right indicates an advantage from the parameters, and the clipped edges indicate the minimum equity.
| Deal | Equity 1 | Final | Outcome | Event |
|---|---|---|---|---|
| Run the simulation — the last 15 deals will appear here. | ||||
This is an educational simulator of poker mathematics and variance. It is not a gambling game: bets are not accepted, no prize fund is formed, winnings are not paid out, the results have no monetary value. Legal information
All-in preflop: equity, bad beats and variance
"All-in preflop" simulates a situation familiar to everyone who has played poker: two players go all-in before the flop, and one of them is the favorite. The higher the equity, the more often they should win the pot. But 'should' does not mean 'must': the simulator shows how theory looks in practice.
What is equity
Equity is the average share of the pot that a player gets when the hand is repeated. If a player has 1 equity of 60%, then out of 100 such all-ins, he will on average win 60. In the equity model, it is set by an advantage. ftp: a number from 1 to 10,000, where 5,000 means equal chances, and 8,800 means an 88% chance of winning.
The 'minimum equity' parameter trims the distribution: hands weaker than the push threshold are pushed up to it. The 'advantage' parameter shifts a random bias in favor of the first player — this way, you can see what happens if they regularly go all-in with the stronger hand.
Where do bad beats come from?
A cooler is a favorite's loss. If a player went in with 70% equity, they still lose about 30% of the time. Over a short run, such hands accumulate into a 'bad streak,' and it is precisely because of them that the bankroll can drop significantly even for a player with a positive expectation.
Supermoves 88/12 are the rarest and most memorable: an 88% advantage, yet victory goes to the underdog. In the simulator, they occur at the edges of the distribution, so they are few — but they exist, and this is an honest part of the model.
Why the fact does not equal the expectation
Expected equity is the average across all hands in the sample. Actual equity is the result of a specific run: a deviation of a few percentage points is normal over 100 hands, whereas over 3000 hands it is noticeably smaller. Increase the number of hands to see how the actual moves closer to the expected: this is how the law of large numbers works.
How to read the results
- Wins and split pots — outcomes of deals in absolute numbers.
- Bad beats — how many times the favorite lost and what percentage that is.
- Equity fact / expectation — how much the sample deviated from the model.
- Accumulated victories — how the score increased during the simulation.
- Edge distribution — with what chances did player 1 go all-in.