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Old 12-12-2005, 07:05 AM
Tommy Angelo Tommy Angelo is offline
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Default Dead Man Drawing

He was in the cutoff and I was on the button. It was folded to him and he limped. I put him firmly on no ace and no pair. I raised. Both blinds folded and he called and we were headsup.

The flop was K-3-3 rainbow.

He checked. One thousandth of a second later, I moved a muscle. This caused him, one hundredth of a second after that, to move several. But barely. It was a tiny quiet little inadvertent hitch that he did. It screamed at me. What it said was, "I am folding when you bet."

A tenth of a second after he hitched, he realized what had happened, and he caught himself, and for the next entire second, he held still, like a teetering gymnast. Then, without moving his head, he looked his eyes up to me, to see if I saw, but I saw his look coming, and I was gone when he got there.

I had a secret.

He had been trained to either trap me or bluff me. I didn’t think this was a trap, so I went for the bluff. I checked behind him on the flop, figuring he was drawing dead, unless he could suppress the urge to bet the turn, and I didn’t think he could.

After I checked the flop, while the turn card was on the way, he reached for chips to bet with. The turn was a 4. He came out with a stack and he had just begun to cut it when my single-terraced raise appeared in place. He looked up at me fast, all ashock. “Kings full? Really?”

I sat.

“Nice hand, whatever you got,” he said, sincerely, as he relaxed. With one hand he mucked while with the other he finished relinquishing eight chips.


* * *


I occurred to me in the car that my check on the flop on this hand is uncommonly analyzable. If we start from when My Opponent (MO) checked on the flop, and examine from there, it turns out that all paths to the finish are knowable, assuming that my assumptions are correct.

The assumptions below exactly reflect the assumptions I made while playing the hand. They were based on the betting of MO and on specific reads of MO and on general profiling of MO and on my assumptions about the assumptions MO had made about me. Rather than describe MO in a way that fits my assumptions, I find it simpler to state the assumptions and move on. I think these assumptions are all rock solid with the possible exception of my assumption that MO would fold when I raised the turn, even if he caught a pair. But we’ll get to that. What I want to say here is that even if all these assumptions are wrong, we are allowed to pretend they are right, just to see where they go.

My hand was A2.

Assumptions:

1) I assumed that I had MO beat before the flop (because he openlimped).

2) I assumed that MO would fold if I bet the flop (because he hitched).

3) I assumed that if I checked the flop, MO would bet the turn.

4) I assumed that I would raise the turn.

5) I assumed that MO would fold to my turn raise if he had no pair.

6) I assumed that MO would fold to my turn raise even if he caught a pair on the turn. We’ll come back to this one.

If we take if from right after MO’s check on the flop, there are two possible paths:

A) I bet the flop.

B) I check the flop.

Let’s compare.

(Warning and disclaimer: The following text contains actual integers and arithmetic. This is risky territory for me and I approach it with caution and respect.)

Because MO happens to have 6 outs on the turn, meaning he had one chance in nine of improving, I am going to show my work by considering nine trials.

The size of the pot after MO checked the flop is 2.75BB.

1) I bet the flop:

If I bet the flop, MO will always fold, so betting the flop wins 2.75BB x 9 = 24.75BB. This means that in order for it to be wrong for me to bet the flop and take the pot right there, I would have to make more than 24.75BB per nine trials by checking the flop, right? Okay then. Let’s have a look see.

2) I check the flop:

If I check the flop, then eight out of nine times he will still have queen-high or worse on the turn, and he will always bet, and I will always raise, and he will always fold. This means that eight out of nine times I will win the 2.75BB already in the pot, plus an additional big bet on the turn. That’s 3.75BB x 8 = 30BB.

Now let’s look at the one time in nine when MO catches a pair on the turn. We’re talking about assumption 6 now. I think he would have folded to my turn raise, even with a pair. (Maybe he did!) But let’s forget about what we think MO would actually do with a pair, and how often. On this variable, instead of me asking you to assign it 100% sureness, let’s look at the entire range, from 100% (he always folds, 2A below) to 0% (he never folds, 2B below).

2A) If he catches a pair on the turn, and he folds to my raise 100% of the time, then I win 3.75BB on trial #9, the same as on the eight trials when he missed the turn. That’s 3.75BB x 9 = 33.75BB.

33.75 is 9 greater than 24.75. If he will fold to a turn raise with a pair, then checking behind on the flop makes 1BB more than betting the flop, every time.

2B) If he catches a pair on the turn, and he calls my turn raise 100% of the time, I assume that the betting on the river will be check-check.

(This betting assumption is like the first six assumptions, and those in the add-on, in that 1) I think they are very sound, 2) I ask you to grant them 100% sureness for the sake of variable reduction, and also so that I can come to the conclusion I want to.  )

In this case, after catching a pair on the turn and not folding, he wins the pot. He wins 2BB on the turn and river, plus the 2.75BB from preflop. That’s 4.75BB.

Let’s review.

If I bet the flop and take the pot, I win 24.75BB per nine trials.

If I check the flop, I win an additional 1BB eight out of nine times for sure (when he bet-folds the turn), for a total of 30BB. On the ninth trial, if he never folds after catching a pair, I lose 4.75BB.

30BB - 4.75BB = 25.25BB.

That’s what I make, 25.25BB, per nine trials, if he never folds after making a pair on the turn.

If I bet the flop, I make 24.75BB per nine trials.

Let’s round off and call 25.25 and 24.75 a tie.

This means that checking the flop had the same expectation as betting the flop. And if MO would ever fold on the turn with a pair, then checking the flop was better than betting it, and the amount it was better depended on one thing: the likelihood that he would fold a pair on the turn. Neat.


Tommy


addondum: Late Aces

This hand is not entirely tidy. Sometimes an ace will come on the turn. And sometimes MO will catch a pair on the turn, and bet, and I’ll raise, and he’ll call, and then an ace comes.

If an ace comes on the turn, I will not raise the turn or river. When MO bets the turn, I will call. At that point, MO will either be drawing dead to my top pair, or he will have a gut-shot straight draw with QJ, QT or J10. If he hits the straight on the river, he will bet and I will call. Or he will check, and I will bet, and he will checkraise, and I will fold. Either way, when I lose to runner-runner straight, I lose 4.75BB (2.75BB preflop + 2BB postflop).

If he does not hit the straight on the river, then he ends up with nothing or a rivered pair. With nothing, he will either lose a bet by bluffing, or lose nothing by checkfolding. If he catches a pair on the river, he will lose a bet on the river often I think, by either betting, or checkcalling. Adding everything in these two paragraphs together, my guess is that if an ace comes on the turn, I would not regret checking the flop.

And if MO catches a pair on the turn, and he bets and I raise and he calls, and then I catch an ace on the river, then I really like my check on the flop!
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  #2  
Old 12-12-2005, 07:13 AM
tongni tongni is offline
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Default Re: Dead Man Drawing

I would call the turn and raise the river for ultimate maximum value.
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  #3  
Old 12-12-2005, 07:49 AM
elindauer elindauer is offline
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Join Date: Jun 2003
Posts: 292
Default Re: Dead Man Drawing

Oh man Tommy. You should stick to the story telling and stay away from the math. [img]/images/graemlins/smile.gif[/img]

You could have proven your case in about one line many different ways. Your way is torture. Here are a few:

- if I bet the flop, I win the pot. if I check, I win the pot + 1 BB. Checking is better.


ok, so you want to analyze the situation where he will call with a turned pair and check-check the river? here you go:

I'm betting the pot + 2BB vs his 1BB that he will not pair on the turn. Since I'm laying less than 5:1 and he is like 8:1 against AND I can still catch an ace, checking the flop is best.



By the way, nice hand.

-Eric
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  #4  
Old 12-12-2005, 10:10 AM
Tommy Angelo Tommy Angelo is offline
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Join Date: Sep 2002
Location: Palo Alto
Posts: 1,048
Default Re: Dead Man Drawing

[ QUOTE ]
Oh man Tommy. You should stick to the story telling and stay away from the math. [img]/images/graemlins/smile.gif[/img]... Your way is torture.

[/ QUOTE ]

You are so right! lol

Okay, new year's resolution. I am going to confine all my number usage to accounting. [img]/images/graemlins/smile.gif[/img]


Tommy
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  #5  
Old 12-12-2005, 10:13 AM
bicyclekick bicyclekick is offline
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Location: Morris, MN
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Default Re: Dead Man Drawing

very interesting.
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  #6  
Old 12-12-2005, 10:33 AM
DcifrThs DcifrThs is offline
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Join Date: Aug 2003
Posts: 677
Default Re: Dead Man Drawing

[ QUOTE ]
I had a secret.

[/ QUOTE ]

and you used it well. vnh.

how often do you play with this passive villian? what other flops do you check behind?

Barron
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  #7  
Old 12-12-2005, 10:40 AM
jgorham jgorham is offline
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Join Date: Oct 2004
Location: UCLA
Posts: 236
Default Re: Dead Man Drawing

[ QUOTE ]
I would call the turn and raise the river for ultimate maximum value.

[/ QUOTE ]

Assumption 6 is a much better turn assumption than river assumption. But I do like the term ultimate maximum value.

NH Tommy [img]/images/graemlins/smile.gif[/img]
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  #8  
Old 12-12-2005, 11:11 AM
BarronVangorToth BarronVangorToth is offline
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Posts: 7
Default Re: Dead Man Drawing

Great read, as always, Tommy.

In related news, what's the over/under on how long before TSP chimes in...?

Barron Vangor Toth
BarronVangorToth.com
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  #9  
Old 12-12-2005, 12:31 PM
andyfox andyfox is offline
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Join Date: Sep 2002
Posts: 4,677
Default Re: Dead Man Drawing

"He checked. One thousandth of a second later, I moved a muscle. This caused him, one hundredth of a second after that, to move several. But barely. It was a tiny quiet little inadvertent hitch that he did. It screamed at me. What it said was, "I am folding when you bet."

A tenth of a second after he hitched, he realized what had happened, and he caught himself, and for the next entire second, he held still, like a teetering gymnast. Then, without moving his head, he looked his eyes up to me, to see if I saw, but I saw his look coming, and I was gone when he got there.

I had a secret."

This is why a division of the fora into Internet and B&M would have been better than the division into High Stakes and Medium Stakes. We can call it the Screaming Teetering Gymnast Observation.
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  #10  
Old 12-12-2005, 12:45 PM
chaosuk chaosuk is offline
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Join Date: May 2005
Posts: 35
Default Re: Dead Man Drawing

Given what you know here - oppo no part of a flop, none of your hole cards cards then he is 6 in 45 to improve to a pair, one in every 7.5 trials. I'd also like to run it with a 80% bet on the turn from your oppo. That said, as others have, nh.
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