Odds calculation with 2 cards to come

[theblitz]

I tried posting this on the probability forum but got no answer.

Assuming I am drawing on flop and I know my odds for hitting (and winning):

F: Odds for hitting first card (turn)
S: Odds for hitting second card (river) if I missed first card
E: Odds for hitting one or other

So, given a pot size of P and a bet of B on the flop I need to know if to call.
Now, if it was all-in then it is easy to calculate using B since no more money is going in.

However, I am wondering about a case where there is more money going in and I know that, should I miss, my opponent is going to give me correct odds to call on the turn.

How do I calculate what is the maximum amount I can call on the flop so that the amount I call on the flop+turn together will not be more than my odds of hitting together?

[Copernicus]

Im not sure I understand the question, but if it is what i think it is:

You know you have one card calling odds on the turn, so worst case you just need once card calling odds on the flop.

If you know he is going to give you an overlay on the turn then you can "spend" a portion of that overlay by calling with something less than 1 card calling odds on the flop..the portion you can spend being (1 - probability of hitting the turn).

[theblitz]

Looking back now I see that my question doesn't add up.

I should ask it the other way:

Is there any reason to fold on the flop even if I have correct odds - if I am scared he will bet out again on the turn when I miss?

[DrJ]

If you know he will give you correct odds both times, then it works itself out by playing your odds on each individual street.

Say the pots is 200, you have a flush draw.

He bets 70, giving you about correct odds, you call. Pot is now 340.

Turn comes and you miss.

He bets 120, still right around your odds. You call.

Overall in this scenario, you have risked 190 to win 190 + the original 200. About 2 to 1. Which was your odds of hitting the flush on both the turn + river.

If you end up betting more than your odds at either of these streets and the correct amount at the other, you will have bet against your explicit odds as a whole...

[Unknown Soldier]

[ QUOTE ]
Looking back now I see that my question doesn't add up.

I should ask it the other way:

Is there any reason to fold on the flop even if I have correct odds - if I am scared he will bet out again on the turn when I miss?

[/ QUOTE ]

definitely not. If you are getting good odds on hitting your card on the turn then you should call. You shouldnt think about the odds with two cards to come because they dont come at once (unless, like you pointed out, you are all-in). As soon as the turn comes it's a different situation.

[theblitz]

The whole thing started because of a program I am writing to analyse PT data. The idea is to see whether your bet/call/raise is +EV. That's the easy bit.

I then wanted to add a bit to find out how many SklanskyBucks you are missing out on by an in-action. So, for example, if you fail to bet when you are ahead then you have missed out on a certain amount of possible equity.

For the purpose of the calculations I am assuming that both (or all) players play perfect poker. They will call if they have the odds, fold if they don't and will not pay off at the end if they miss. So, to get maximum EV from betting out you need to bet an amount that would give the same result whether the villain called or folded.
I do this by making a "bet" that would give the villain perfect odds to call. In this way his EV for calling vs folding is 0 thus giving "me" a +EV.

So far - so good.

Then the question came up as to what happens if the villain decides to fold the flop - since his EV is 0. Is that good for me or would I prefer him to call the flop so that I can get that bet in on the turn (which again would be 0 EV for the villain)?

Thinking now it seems to me that either result is good and I would get the same EV in either case. Does that sound logical?

Now all I need to figure out is how to deal with more than two people in the hand. [img]/images/graemlins/smile.gif[/img]