Pot odds; raising a draw on the turn

[Josh Chud]

I recently posted this on the mid-high stakes forum so if you read it there dont feel the need to respond twice /images/graemlins/wink.gif. But i figured some of you might not read that forum and this post definately applied here.

Live 10/20$ At Gold Strike in Tunica MS.

Player to my right is big LAG. Ive seen him raise J7o and J9o, betting out with nothing, etc.

He raises and i look down to find Q/images/graemlins/heart.gif 9/images/graemlins/heart.gif in late position. Playing the player i decide to call, though i thought a raise to isolate with this hand wouldn't have been a terrible play either. Anyways, 4 callers (8 SB).

Flop is J/images/graemlins/heart.gif 8/images/graemlins/club.gif 7/images/graemlins/heart.gif

Check, Check, Villain bets and i raise, fold, fold, Villain re-raises. Im now in the precarious position of figuring out how i got involved with him the one time he hits a monster. Is it a set of jacks? J8? J7?... i try to slow him down one more time with a raise and he caps it. followed by an immediate bet on the turn when the turn comes.

Turn: 4/images/graemlins/spade.gif

an obvious blank to both of us. Now its decision time. I think for a while and realize it can only be one of two things.. A Set or T9. Against both hands i was an underdawg. Against the Set it was 2-1, against T9 it was only 57-43. So now the question. The pot has 9 BB going into the turn, 10 with his bet. If im my outs are 9 hearts and 3 Tens (2 if he's holding T9). That puts me at 3-1. But the pot is offering 10-1. Does that mean i raise again until the pot is marginal to the amount im placing in? (If i raise and he reraises, i would've put in 3 Big Bets and gotten 13-3, or if i let him cap it, it would be 15-5, right on the line). Now im asking strictly from an EV standpoint here. The hands are declared, i'm 90% sure he has T9, 10% sure its a set. And i can tell he's got me read for a flush draw, thats why he refused to slow down. Thus i will *have* to hit to win, there will be no bluff opportunities here, and my reverse implied odds only apply if a non-heart Ten comes, where it will induce a bet from him, but giving me the nuts i can get an extra bet (and maybe up to 4) out of him, but if the heart comes he will just check-call.

[Stephen H]

I suppose you could get into a whole discussion on the difference between pot odds and pot equity, and why pot odds apply when you're calling a bet, but pot equity (and related equity values such as folding equity) applies when you're betting out or raising. But maybe illustrating the EV calculations will be the easiest way to demonstrate this.

But, let's just look over some EV calculations.
To simplify, let's look at what happens if:
You're exactly a 3-1 underdog.
The action on the river is check/check. This shouldn't change the relative EV calcs as I doubt the turn action is going to significantly change the way the river actually plays out, so if, say, you're picking up 2 more bets on the river when you hit, you're getting those no matter what you do on the turn.
Evaluating calling 1 bet vs raising/getting reraised vs putting in the 4th bet.

Calling 1 bet:
3 times you will lose that one bet
1 time you will win 10 bets
3x(-1) + 1(10) = -3 + 10 = 7 BB over 4 hands or 1.75BB/hand EV

Raising / getting reraised:
3 times you will lose 3 bets
1 time you will win 12 bets
3x(-3) + 1(12) = -9 + 12 = 3 BB over 4 hands; .75 BB/hand EV

Putting in the 4th bet:
3 times you will lose 4 bets
1 time you will win 13 bets
3x(-4) + 1x(13) = -12 + 13 = 1 BB/4 hands; .25 BB/hand EV

As you can see, you get less and less expected value as you add raises on the turn. Using pot odds to determine if you should raise is to attempt to set your EV to 0, not to maximize it. This is because while you have the pot odds to call the bet, you only have a 25% pot equity. For each bet each player puts in, you win 25% of it. However, there's only 2 players in the pot, so you're making 50% of the bets. This means every bet you put in and get called, you're losing half a bet.

Now, I'm by no means an expert, and if I've made any mistakes, one of the friendly regular denizens of the board will likely set things straight. But the basic lesson is: Use pot odds to determine if you should call a bet when you think you're behind and need to improve. Use pot equity to determine if you should bet/raise, regardless on where you think you are in the hand. For example, if there were 3 more people calling in your situation, and you somehow knew all of your outs were still good (no one had a better flush draw or a straight draw, etc), you would raise all day, as you would be gaining .25BB of EV for every bet you put in the pot.

[AaronBrown]

I agree with Stephen H. Pot odds tell you whether or not to fold, not whether or not to raise.

If you are a completely straightforward player, you raise when you have better than a 50% chance of winning, not otherwise. Any raise when you have less than 50% chance of winning (and any call when you have more) is done for strategic reasons.

In this case, you don't have much bluff potential, as you say. A raise now isn't going to scare him into going easy after the river, and anyway that doesn't help you (if you make your hand, you'll raise, otherwise you won't call).

The one thing in your favor that he doesn't suspect is the Queen high straight. If a heart comes on the river, you won't make much money. But if a ten of another suit comes, you could get rich. Therefore, you need to play exactly like a guy with a flush draw and nothing else. A raise would kill this picture.

One amusing variant of this occurs if you switch the suits of the 7 and 8. Then you're in the rare position of praying you DON'T get the straight flush, or even the flush, you just want the straight.

[d10]

It is not +EV to keep raising here. The only reason why you don't fold immediately is because there is money already IN the pot that you might win if you catch the right card. With every bet you put into the pot at this point, your opponent is only putting in 1 bet. So at this point you are getting 1:1 on your money, but you are less than 1:1 to win, so it is not in your best interest to put any money into the pot. You lose money when you put it into the pot. But you can call 1 bet because, although you expect to lose a good portion of that bet on average, the money you expect to win from the pot if you hit your card is more on average than what you lose by calling the bet. So it is profitable to call, but with every additional bet you put in, your profits shrink.

This does not mean that when you are an underdog to win you should always avoid putting money into the pot. If you flop the nut flush draw with 9 opponents, and you know one of your opponents flopped a very strong hand, but you know if you make your flush you will win, you will lose this pot more often than not, but you should raise the hell out of this hand. You still have great pot odds, but the difference is for every $1 you put into the pot your opponents are putting in a total of $9. Since you are getting 9:1 on your money and you are about 2:1 to win at showdown, you're making huge profits for every bet you put into the pot which is matched by 2+ opponents.

Use pot odds to determine whether you should call or fold, use the odds you're getting on the current betting round to determine whether you should call or raise.