#### ChuckTs

##### Legend

as with all theoretical poker, there are arguments to be made though

the situation you stated

Quote:

*"A♥ J♣*

And the board shows:

A♣ 10♣ 5♦ 8♣ 3♣

You're in first position, the pot is $100, and the big bet is $10. Do you bet?

Let's say, for the sake of argument, that your opponent can hold any two cards and will always fold if he doesn't have a club. Let's also stipulate that he'll call a bet with any club, and make it two bets if he has the K♣ or Q♣. Let's also say that in case you check, he will bet with any club and check with no clubs.

Let's do the math. Since he can hold any two cards, each of the individual clubs is as likely to be in his hand (and let's pretend that he can't have two of them - because we know him well enough to know that he would have raised the turn if he did).

And the board shows:

A♣ 10♣ 5♦ 8♣ 3♣

You're in first position, the pot is $100, and the big bet is $10. Do you bet?

Let's say, for the sake of argument, that your opponent can hold any two cards and will always fold if he doesn't have a club. Let's also stipulate that he'll call a bet with any club, and make it two bets if he has the K♣ or Q♣. Let's also say that in case you check, he will bet with any club and check with no clubs.

Let's do the math. Since he can hold any two cards, each of the individual clubs is as likely to be in his hand (and let's pretend that he can't have two of them - because we know him well enough to know that he would have raised the turn if he did).

*Note: We do not bother adding in the times when he has no club at all, in these scenarios. Your opponent will fold if you bet, and check if you check in these cases, and you will then always win the pot uncontested. For the mathematically curious, this actually has implications on the expected value for the situation as a whole, but not for the specific purpose that we're discussing it here: Determining the correct strategy."*

i know this is just a basic situation, but of course real hands never occur exactly as theory predicts and neither do these kinds of statements apply to all kinds of players.

ie, most players won't call when bet into with a 4-flush showing if they have a [2c] or even up to [5c] or higher. Nor will the average player bet with the same hand if checked to.

There are always people who play differently, and thus you can't apply exact calculations like that to real games sometimes, could you?

just wanted to point it out

this was my first time reading about expected value applied to poker and I thought it was well done, paulsson! Nice article, I enjoyed reading it. Gave me some good insight + info in expected values

-ChuckTs