Non mathematician here. My poker enthusiast friends talk about playing "mathematically correct" bets.

I understand it involves considering the size of the pot, my expected chance of winning the hand,

and somehow calculating my bet in a way that gives me better odds.

But I confess I am rather mystified that changing my bet somehow changes my odds.

Why would that be? Can anyone explain simply how that works?

## How does changing a bet alter the odds?

**Moderators:** gmalivuk, Moderators General, Prelates

### Re: How does changing a bet alter the odds?

Keeping things simple, in poker, you have two ways to win the pot: You can make a bet and your opponent folds, handing you the pot right there and then, or you make a bet, your opponent calls, and you show the best hand.

Likewise, your opponent has a fairly straightforward calculation to make: If you bet the size of the pot, he only has to have a better hand than you 1/3 of the time to call (because he calls, say, $10 to win a $20 pot) - whereas if you bet half the size of the pot, he only has to have a better hand than you 1/4 of the time (calling, say, $5 to win a $15 pot).

Again, keeping things simple, there are two occasions you want to bet big: When you have the nuts and you think your opponent has such a good hand he won't let it go no matter how much you bet - so why not bet big - and when you think your opponent has a better hand than you and he'd fold to a big bet but not a small one (because of the logic detailed above). The latter is known as 'fold equity' - and mathematically it's not typically enough on its own to justify making a big bet - you usually need to also have 'outs' to improving your hand above his - making it a 'semi-bluff' rather than an outright 'bluff'.

OTOH, you bet small if you have a mediocre hand but think your opponent won't call any sized bet - so why not bet small and hence lose less on the occasions you're wrong.

Likewise, your opponent has a fairly straightforward calculation to make: If you bet the size of the pot, he only has to have a better hand than you 1/3 of the time to call (because he calls, say, $10 to win a $20 pot) - whereas if you bet half the size of the pot, he only has to have a better hand than you 1/4 of the time (calling, say, $5 to win a $15 pot).

Again, keeping things simple, there are two occasions you want to bet big: When you have the nuts and you think your opponent has such a good hand he won't let it go no matter how much you bet - so why not bet big - and when you think your opponent has a better hand than you and he'd fold to a big bet but not a small one (because of the logic detailed above). The latter is known as 'fold equity' - and mathematically it's not typically enough on its own to justify making a big bet - you usually need to also have 'outs' to improving your hand above his - making it a 'semi-bluff' rather than an outright 'bluff'.

OTOH, you bet small if you have a mediocre hand but think your opponent won't call any sized bet - so why not bet small and hence lose less on the occasions you're wrong.

### Re: How does changing a bet alter the odds?

In simple gambling games with no strategy other than wager (so not poker) you can calculate a bet that will maximize your expected winnings after repeated plays, this is called the Kelly criterion. Note that if the game has an expected loss, the Kelly criterion will always be 0 (don't even bother playing). If the game is an expected win, you might naively think that you should bet as much as possible, but an unlucky play would wipe out your bankroll and you wouldn't be able to play anymore. Even if you only bet most of your bankroll, a few unlucky plays will set you deeply back and it will take a long time to recover your losses. Bet too little however and your bankroll won't grow quickly. The Kelly Criterion calculate the optimal fraction of your bankroll to bet on each play.

### Re: How does changing a bet alter the odds?

Likewise, your opponent has a fairly straightforward calculation to make: If you bet the size of the pot, he only has to have a better hand than you 1/3 of the time to call (because he calls, say, $10 to win a $20 pot) - whereas if you bet half the size of the pot, he only has to have a better hand than you 1/4 of the time (calling, say, $5 to win a $15 pot).

so it sounds like calculating "pot odds" has nothing to do with the actual cards in play. You just consider the ratio of your bet to the pot.

### Re: How does changing a bet alter the odds?

It's the odds you have to have in order that it be profitable to stick with that particular pot.

### Re: How does changing a bet alter the odds?

I see so a loose algorithm would be

1.) estimate my odds of a winning hand (based on cards known)

2.) adjust my bet such that the ratio of bet:pot matches this estimation

Do I have the right idea?

1.) estimate my odds of a winning hand (based on cards known)

2.) adjust my bet such that the ratio of bet:pot matches this estimation

Do I have the right idea?

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### Re: How does changing a bet alter the odds?

Well, it's still poker, so at level 1 it's more like:

1) estimate my odds of a winning hand (based on cards known, and current estimates of cards unknown)

2) calculate the ratio of bet:pot I'd have to make to stay in the game

If (1) > (2) I'd be OK with calling (not that calling is necessarily the correct play, but that it's an option), but if (2) > (1) then I don't particularly want to go to a showdown, so either fold or raise and try to make my opponent fold (which one depends on the situation, and would require someone less awful at poker than I am to explain).

1) estimate my odds of a winning hand (based on cards known, and current estimates of cards unknown)

2) calculate the ratio of bet:pot I'd have to make to stay in the game

If (1) > (2) I'd be OK with calling (not that calling is necessarily the correct play, but that it's an option), but if (2) > (1) then I don't particularly want to go to a showdown, so either fold or raise and try to make my opponent fold (which one depends on the situation, and would require someone less awful at poker than I am to explain).

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