a theoretical question for everyone |
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Posted Thu Nov 16, 2006 5:54 pm GMT by suitedaces84
I was playing in a NL cash game with an effective stack of $200. I had AA on a board of T522r. On the turn I bet $40 into a $60 pot and my opponent raised to $80. The pot is now contains $180. I have $130 left. I know my opponent is bluffing exactly 40% of the time. If you neglect the chance that I will outdraw him OTR, the chance that he will outdraw me OTR, bankroll stuff and any metagame/image type stuff is there any reason to fold?
edit: to simplify the problem I'm assuming that if he's raising for value we'll never win; if he's raising as a bluff we'll never lose (unless we fold).
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Posted Thu Nov 16, 2006 8:58 pm GMT by shorn7
This is hard to answer because we don't have complete information. Specifically, what was the action up to the turn? How well do you know this opponent (I assume pretty well if you can say with certainty that he is bluffing 40% of the time)?
That being said, it all depends upon the 60% remaining in his probability and what hand range that represents. My inclination is that getting 3-1 or better on the call, it would be hard to fold, but there are a few players where I would consider it. You also have to bear in mind that you will likely have to face another bet to get to showdown so that factors into potentially folding as well.
As with many things, I think the answer is it depends.
Posted Thu Nov 16, 2006 9:17 pm GMT by supafrey
if it's 40%, wouldn't a raise be better?
Posted Thu Nov 16, 2006 10:46 pm GMT by suitedaces84
| shorn7 wrote: | | You also have to bear in mind that you will likely have to face another bet to get to showdown so that factors into potentially folding as well. |
You're on the right track here.
The action leading up to this/image stuff/metagame stuff etc, can all be summed up by the fact that we know we're being bluffed 40% of the time.
| supafrey wrote: | | if it's 40%, wouldn't a raise be better? |
I should have specified this earlier, but to simplify the problem I'm saying that if he's raising for value we'll never win; if he's raising as a bluff we'll never lose (unless we fold).
So a raise would be bad as it forces him to fold his worse hands and call with his better ones. If he's drawing dead there's no reason to force him out.
Posted Fri Nov 17, 2006 9:33 am GMT by shorn7
Well, if you call the pot will have $220 in it and you will have $90 left. Assuming that the river comes not something horrible (like another T), I don't see us getting away from this hand if we call his raise. But again, it all depends on the % of the remaining 60% of his non-bluffing hands that we are ahead of right now. Frankly, now that I see it more clearly, it doesn't have to be that high for us to keep going getting such a good pot price.
In theoretical space given the pot size, our remaining stack, and his probability of bluffing I don't think we can fold here (assuming that he will bluff the river 40% f the time again).
Posted Fri Nov 17, 2006 2:25 pm GMT by suitedaces84
| shorn7 wrote: | | In theoretical space given the pot size, our remaining stack, and his probability of bluffing I don't think we can fold here (assuming that he will bluff the river 40% f the time again). |
If you know he will go all-in on the river after you call the turn what would the EV of calling down be? Is it greater than the EV of folding of to the turn raise?
Posted Fri Nov 17, 2006 2:37 pm GMT by shorn7
| Quote: | If you know he will go all-in on the river after you call the turn what would the EV of calling down be? Is it greater than the EV of folding of to the turn raise?
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EV of calling down river would be ((40% + % of remaining 60% we are ahead) * remaining stack after turn call) + pot size before river. Given the pot size ans our stack size, without crunching the numbers, I do believe that the EV of calling down is higher than that of folding to the turn raise (which is the same calculation, but with a smaller pot).
Posted Fri Nov 17, 2006 2:45 pm GMT by tame_deuces
Bleh, now I'm confused and editing this out.
Posted Fri Nov 17, 2006 2:56 pm GMT by suitedaces84
You are both right, you should call his turn bet if even if you know he will follow through on the river.
But you don't know he'll follow through with a bluff on the river. He will go all-in on the river everytime he has a winner. When he was bluffing on the turn and you called he'll bluff again on the river with an all-in X% of the time (the rest of the time he'll check). Given this, are there any values of X for which you should fold on the turn?
Posted Fri Nov 17, 2006 3:02 pm GMT by Gunslinger
| tame_deuces wrote: | Odds lain by the pot:
Turn: 180:80 - 18:8 - 9:4 - 4.5:2 - 2.25:1 |
OP only has to call $40 more to the turn min-raise. The pot is laying him 4.5:1.
Posted Fri Nov 17, 2006 3:13 pm GMT by tame_deuces
Bah, your right, I read poorly today.
Posted Fri Nov 17, 2006 9:34 pm GMT by suitedaces84
To clarify what's going on:
If you know your opponent will move in everytime on the river you should call the turn bet for the following reason. To win a $400 pot 40% of the time you'd have to risk $130. $400*0.40 = $160 > $130, so calling down would be better than folding, if your opponent moves in on the river everytime.
I thought that's what you were saying, which is correct.
Calculate the EV of calling down if your opponent gives up his bluff 50% of the time. Hint: if your opponent gives up his bluff 50% of the time his river actions will be as follows:
value bet 60%
bluff 20%
check 20%
25% of his river bets will be bluff. Since you'll be looking at 310:90 pot odds you'll have to call his river bet.
Posted Tue Nov 28, 2006 11:52 pm GMT by suitedaces84
The EV of calling down if he gives up his bluff on the river half the time is 0.2*$90 less than calling down would be if he continued his bluff everytime. That EV turns out to be greater than the EV of folding to the turn raise by $12.
I intended for the EV of calling the turn raise to be less than the EV of folding to the turn raise if your opponent bluffed at a near optimal rate; and for the EV of calling down to be greater than the EV of folding if your opponent continued his bluff everytime. But I screwed up the numbers so it didn't quite turn out that way.
What I thought was interesting about this seemingly obvious idea is that it can make folding to a min raise that's a bluff X% of the time correct, while folding to a larger all-in raise that's a bluff the same percent of the time incorrect.
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