[macdaddy991]

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Preflop: Hero is MP2 with 5[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/heart.gif[/img].
2 folds, Hero calls, 1 folds, CO calls, Button calls, 1 folds, BB checks.

Flop: J[img]/images/graemlins/club.gif[/img], 5[img]/images/graemlins/club.gif[/img], 9[img]/images/graemlins/heart.gif[/img] (4 players)
BB checks, Hero?

If we somehow get it HU with a flop c/r(or flop raise in another situation):

I will assume: villain has a FD 1/3 of the time. so he makes a flush ~1/10 of the time. we will make a boat+ about 25% of the time villain makes flush. The times this happens, we will make an average of 4BB on the turn and river combined. When we lose to the flush (with a just our set) we will lose an average of 3BB

no Matter what, 1BB each goes in on the flop.

When the flush card comes and he as a flush (1/10 of the time):
we make 4BB 25% of the time

we lose 3BB 75% of the time

When the flush card doesn't come, or comes and they don't have it(9/10 times):

we make 1.75 BB (sometimes we get called down, sometimes a turn call and river fold, sometimes we get a bit extra when they hit trips/2-pair.

so when we win:
((9/10)*1.75 + (.25/10)*4) + (9.25/10)*3
just for turn and river already in pot(less your bet)

= 1.575 + .1 + 2.775 = 5.35 BB

and then, when we lose we loser 4BB (1 on flop, 3 later)

5.35BB + (.75/10)*-4BB ~ 5BB

So when we get it HU, we win, on average, 5BB


IF WE DO NOT TRY TO PROTECT OUR HAND:




on flop: on average, 2 players put in .75BBs for a total of 1.5BB going in (from other players)

when flush card comes and somebody has the flush (1/5) of the time): assume that there's a 1/3 chance each person has a FD, so then the chance that somebody had a FD = 1 - .67^2.5 = 63%. So, somebody will make a flush ~1/5 of the time. When this happens, we lose 3BB, and when the flush comes and we fill up, we will win an an average of 2.5BB (on turn and river combined)from each person that saw the turn.

when flush card doesn't come (or comes and nobody has it): Assume that when the flush doesn't come, we make an average of 1.5 BB from each person that saw the turn (I recommended 1.75 in my earlier reply, but I think this is too high).

so when we win:

4/5*1.75BB*2 players + (1/5*1/4*2 players*2.5BB) + (17/20)*3.5
just for turn and river already in pot(less your bet)
= 2.8 + .25 + 3 = 6 BB

so overall, on average we win:

6BB + (1/5*3/4*- 3.75BB) ~ 5.5BB

So when we keep it multiway, we win 5.5BB on average

But this is not what makes the betting and raising so profitable.

Here are some things that I never take into consideration that make it even better to bet and raise on the flop:

1) the chance you can bet/3bet the flop
2) I have assumed VERY decent opponents. If you're against anybody who is fairly aggressive, betting and raising is even better
3) If you are against a larger number of opponents, betting and raising is even more profitable
4) if it has been raised preflop, betting and raising is even more profitable


This post is quite mathy, but te gist of it is, bet the [censored] out of your sets.

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very nice work