Opponents pot odds

[Mike]

I have heard that if you want to bet on (let's say the flop) to give your opponent bad pot odds, it's sometimes better to go all in directly if a bet on the next street would give you to little relative effect since the pot is so big.

This depends on:
+ min(Hero stack size, Opponent stack size)
+ pot size.

Can someone explain in what situation I should go all in on the first bet and why (a mathematical approach)?

[BankItDrew]

Sorry, I don't really understand your question.

[givememyleg]

If you're pot commited.. say you have AA in a sng at 50/100 blinds, with a stack ~ 1000 and you make it 300 to go pf, opp calls on the button and blinds fold. You would have 700 behind, in a 750 pot, on any flop just goooo with it. You're never folding.

But your question is pretty general, would only really apply to sng or mtt when you are generally short stacked... Usually when 100+ bbs deep you won't be faced with this often.

Don't be scurred of draws.

[Anosmic]

I have heard that if you want to bet on (let's say the flop) to give your opponent bad pot odds, it's sometimes better to go all in directly if a bet on the next street would give you to little relative effect since the pot is so big.

This depends on:
+ min(Hero stack size, Opponent stack size)
+ pot size.

Can someone explain in what situation I should go all in on the first bet and why (a mathematical approach)?

The thing is you're really on the margin here that it's probably not worth calculating to this depth, the situation is rarely sufficiently clear cut.

Let's say you're holding A A have a stack of $9
while villain has $15, you're sure has A K because of the way his left eye twitched when he saw the flop:

5 6 T

http://twodimes.net/h/?z=2135652
pokenum  -h ah kh  - ad ac  -- 5h 6h td 
Holdem Hi: 990 enumerated boards containing Td 6h 5h
cards  win   %win  lose  %lose  tie  %tie     EV
Ah Kh  369  37.27   621  62.73    0  0.00  0.373
Ac Ad  621  62.73   369  37.27    0  0.00  0.627

So he's 37% to win here.
So if the pot is $5 and you bet $5 then it's 2:1 odd's he's paying 33% for a 37% shot. He's got odds to call here.

The pot would now be $15. Depending on the turn the odds will change.
If a heart falls you can fold. So that has no relevance.
If the board pairs or the As falls he's got a 20% chance.
If a blank comes up then he's a little over 25%.

If you push in your remaining $4 the pot is $19 he's getting a litle under 5:1. If the board has paired or a A has flopped he may have bad odds to call, if it's blank he's fine. But he's left to make that decision at that point (and usually it's right to call).

So he can twice make a good decision and take your stack. In poker you want your opponents to make bad decisions.

By pushing the flop here you will give him bad odds to call and calling would be a mistake in cash play.

The point with draws is that you want to shutdown if they hit on the turn (which happens 1 time in 5) so denying them implied odds and raising solidly on a blank turn (so they don't have the odds to call at 5:1) giving them bad effective odds on the flop.

We don't pay off the flush and we make them fold or make a huge mistake on the turn. So they pay 33% for a 20% shot, effectively.

The problem is if the pot relative to either stack is so large that one cannot effectively punish on the turn (by, say, potting it again, or 3/4 pot) then he's really getting good odds on the flop and able to evaluate on the turn.
So a push forces the fold or the mistake.

Of course in a tournament this would be irrelevant because if he's short-stacked like that he's going to have to call; if you're short-stacked he may well take the gamble because he has you covered and he could knock you out and set himself up for a win.

So sure it can be worth pushing if one of you is that short. But for the most part it's pot-sized bets that we need.

[Mike]

Thanks for the answer. Obviuosly when the stacks are relatively big compared to the pot, this is not a concern. However, when the probability that something happen is pretty low, but the implied odds of it is high, when it hit, such as when I limp in pf with a small pair. Then I need to know that the potetial opponents I will meet in the pot have chip stacks big enough (and that mine are big too so that it may match the opponents). Lets say:

Big blind=10

I limp in with 10 pf and have pocket hand 55.
All other oppnents fold (to make it simple).
My chip stack is 100 and opponents chip stack is 100 also after pf contribution.
That makes the pot 20.

Let's say the flop is AQ5 - rainbow.

Any ideas about this situation?

[swiggidy]

bet, either he has an A and you're getting paid, or he doesn't and you're not getting paid

[Xanadu]

This is somewhat off-topic, but here's something to remember in a case like your 55 example. Stacks need to be very deep to play small pairs and connectors and such for implied value when they hit the flop big. In the example given, stacks were only 10x the blind. That's not enough. Harrington went through this in HOH2. Basically 3 things all have to happen for you to get paid off big:

1. you don't get pushed out of the pot by a big preflop raise after you limp
2. you make your hand
3. one of your opponents makes a hand that is strong enough to pay you off, but not strong enough to beat you

Put all these together, and Harrington says you need stacks to be about 30x the big blind in order to limp a small pair for set value. Opponent's tendencies change this # a great deal. Stacks 15 bets deep might be enough against some opponents, and against others, you might need 50 or more. Implied odds are usually not as high as you think because you just don't get paid off enough.

[Mike]

It's not off topic. Now we are getting somewhere. Maybe I should look into Harrington 2 agan. My feeling is that it's easy to give general ideas about what one need to think about, such as the 3 points you mention. The problem is to get the math in there. Let pretend we start to look into hitting a set on the flop. That is point 2: 11% of the time we hit it.

Getting pushed off? How do we calculate this? Late position => less chance of being pushed off, but what does that look like in the math?

3. Make his hand less then ours - probably we have to estimate what each player will play for hands, but where do we start to get this expresse in math.

1. you don't get pushed out of the pot by a big preflop raise after you limp
2. you make your hand
3. one of your opponents makes a hand that is strong enough to pay you off, but not strong enough to beat you

[swiggidy]

As you are hopefully noticing this gets intractable very quickly. Are you trying to make a function where you input the villains hand range, then the probablility they stack off with, TPNK, TPGK, TPTK, T2pair, B2pair, Tset, Bset, etc...

What are you going to come up with? 30xBB against a generic opponent. 15xBB against a loose maniac. 50xBB against a nit. Or something very similar at least.

[jackvance]

If your stack is lower than the pot if your bet gets called, then you're pretty much pot committed. Simplistic rule of thumb.