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Alrighty I did the math. God my head hurts. The results are pretty interesting though! I might post up the whole math, so others can review it and fidget with it etc, but for now I'll stick to a general rundown:
Actually, the conclusions justify what the expertienced players have been doing intuitively! This gives me confidence I did the math right 
So here it is:
First we make a bunch of assumptions:
Person A is a draw-chaser holding a suited connector. He will win if he gets anything that tops one pair.
Person B has high cards and will hit TPTK on the flop.
Person B will raise postflop.
Other people in the pot will fold after person B raises postflop, so it's heads-on between the draw-chaser and the TPTK guy after that.
Person A will fold postflop if he gets nothing.
I've varied 2 parameters: There are 2, 3, 4 or 5 people in the pot; And person B (with TPTK) will raise 1/2xpot, 1xpot or 2xpot. This gives 12 combinations.
Alright then. The more people in the pot, the more profitable it is to chase a draw. Ofcourse that is intuitively obvious. "Only chase a draw in position if there are enough limpers." Well, what are the exact numbers?
2 people in the pot (so noone besides our two protagonists) gives a chaser bad odds. 3 people in the pot give him slightly bad pot odds. 4 people in the pot give him slightly good pot odds. 5+ people in the pot is a DEFINITE go if you hold a suited connector!
Ok, now here's the surprise: Might be counter-intuitive, but the more you raise postflop, the better pot odds you give the draw chaser! Weird isn't it? We would expect the opposite. Ideally you would want to bet nothing! But ofcourse you have to bet just enough to make him fold if he has nothing. (otherwise the assumption that he will fold if he gets nothing doesn't hold out anymore)
That is why people say, raise 1/2-3/4 pot! They don't say 2-3x the pot.
Now, how is it possible that postflop raises give draw-chasers good odds? Simple. Let's look at what can happen:
I'm holding a suited connector, flop comes around:
a) 73% I get nothing
b) 11% I get a flush draw
c) 11% I get a straight draw
d) 5% I get something bigger: straight, flush, 2 pair, trips, 4 of a kind, full house
It is mainly because of this 5% that postflop raises hurt a raiser. Anything raised postflop will go directly to the stack of the draw chaser.
Ofcourse, this is math, not an actual poker game. If you can't capitolize on the times you 'hit something big' with a chase, you kill your own pot odds. Similarly, if you routinely get destacked the very moment a chaser hits something, he'll even get good 'pot odds' at 3 people!
This is where 'good poker play' gives you an edge over exact pot odds.
In my calculations I have assumed the following:
1. in the 5% chance person A hits something big, person B will keep raising at his preset amount, both after the turn and the river. (so half pot, pot or twice pot)
=> so if you lure your opponent into committing more to the pot in this case, your pot odds increase. If you are on the other end of the table, and you can 'sense' he has hit something big and you bail out, you ruin his pot odds too. So good poker play can change these odds.
2. In the 22% of either a straight draw or a flush draw, if the flush hits on the turn, person B will keep raising his set amount, with person A calling til the showdown. If the flush does not hit the table on the turn, person A will call the raise from person B. If the flush consecutively hits on the river, then person B will call the river-raise, otherwise he will fold. Same in the case of a straight.
=> Again, good poker play gives you better odds, regardless of what the math says. If you can't milk your opponent for the most when you hit your straight/flush, this isn't very profitable. If you can destack him, all the better. Or the other way around, if you can minimize your losses if your opponent 'connects' his straight or flush, you improve your chances.
Another important note:
Say you are person B and you KNOW your opponent is either chasing a draw or chasing a flush, then you need to bet 2x the pot or more to give him bad pot odds.
(remember.. you have to be certain he is chasing and not holding onto triplets or something, because in this case you are burning yourself)
To be more specific: 2x the pot gives a flush-chaser bad pot odds, 1.5x the pot gives a straight-chaser bad pots.
In the unlikely event your opp is chasing both, ie a double-ended straight flush draw, he has the best odds to win whatever you raise.
If we turn the tables.. to be on the safe side, don't pay more than 1x the pot if chasing a draw postflop. And if you are holding a DE str-flush draw, pay ANYTHING your opp throws at you to chase. You have 56% to win.
That's it for now
EDIT: ah what the heck, to be complete I'll post the math:
POT: $10
x = bet-size preflop
y = bet-size pstflop
2 people: x=5
3 people: x=3.33
4 people: x=2.5
5 people: x=2
1/2 pot raise: y=5
1x pot raise: y=10
2x pot raise: y=20
Formula (with the assumptions explained above)
-(0.73) (x)................... (1)
-(0.11)(1.32) (x+y)...... (2)
+(0.05)(10+4y)........... (3)
+(0.11)(0.68)(10+2y).. (4)
(1): what you lose in the 73% chance you nothing on the flop
(2): what you lose if you get a straight or flush draw but nothing on the turn+river
(3): what you win in the 5% chance you hit something big on the flop (2 pair, trips, flush, etc)
(4): what you win if you chase a draw and you get your flush/straight on the turn+river
NOTE: for simplicity.. because these are big uncertainties, I've run under the assumption that any possible raise after the turn the chaser has to pay to see the river, is offset by the implied odds of his win in the case either turn or river give him his chased hand. Under the current model, these assumptions are pretty much valid since about 1/3 of the time you will win 4y this way and 2/3 of the time you will lose 2y, evening each other out.
Any math buff is more than welcome to check my math, or recalculate with different assumptions (ie different odds).
/next up: to calculate the odds your opponent gets 'something' (pair or better) for any given hand, on the flop, and then turn, and river. Will try to get that done tomorrow.
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Pot roast, pot luck, and pot odds
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Originally Posted by AHiltz
