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!

Re: Dead Man Drawing
 

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

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

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

Re: Dead Man Drawing
 

very interesting.

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

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]

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

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.

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.

Re: Dead Man Drawing
 

While the math presentation of this hand is rather rediculous, this is a very interesting post for me. Thank you for posting it. I would never have played the hand in that fashion and this post has made me a slightly better poker player.

6x9 =54 right?

Re: Dead Man Drawing
 

"6x9 =54 right?"

So you say. [img]/images/graemlins/smile.gif[/img]

"the math presentation of this hand is rather rediculous"

Let me just say for the record that I did in fact write all that stuff while under the influence of thinking that 6x9=45. So even though the math was all screwed up, and needlessly arduous, it was done under a consistently wrong premise, so within its own reality, it was sort of correct.

Re: Dead Man Drawing
 

awesome

ive been using your call a bet and bet when checked to T8 play a lot and its working out very well

Re: Dead Man Drawing
 

[ QUOTE ]
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.

[/ QUOTE ]


Andy, this is going off topic even further, but this is a phenomenal suggestion. Sooooooooooo much of poker is vastly different from when you play live to when you play online. I realize there may be a desire to keep the extra forums at a minimum, but one must wonder if there really is as much "different" between a $20-$40 and $30-$60 hand online as there would be between a $20-$40 hand online and live.

Barron Vangor Toth
BarronVangorToth.com

Re: Dead Man Drawing
 

[ QUOTE ]
Sooooooooooo much of poker is vastly different from when you play live to when you play online. one must wonder if there really is as much "different" between a $20-$40 and $30-$60 hand online as there would be between a $20-$40 hand online and live.

[/ QUOTE ]

I have played poker on my computer and at a casino. I have played golf on my computer and on a golf course. If I had to put these four things in two groups based on my sense of their overall similarities and differences, I would group computer golf with computer poker, and golf-course golf with casino poker.

Re: Dead Man Drawing
 

[ QUOTE ]
awesome

ive been using your call a bet and bet when checked to T8 play a lot and its working out very well

[/ QUOTE ]

link? i missed this one.

Re: Dead Man Drawing
 

[ QUOTE ]
[ QUOTE ]
awesome

ive been using your call a bet and bet when checked to T8 play a lot and its working out very well

[/ QUOTE ]

link? i missed this one.

[/ QUOTE ]

here , i dont usually do the checking the flop part, but sometimes when im in a heads up situation ill call a flop bet without much and bet the turn if checked to(or raise a bet), especially when theres like a pair on the board or something, i dont usually use the exact play, but variations of it, i think the situation had to be perfect for this to work the way he played it

Re: Dead Man Drawing
 

[ QUOTE ]
how often do you play with this passive villian?

[/ QUOTE ]

Please tell me this is sarcasm.

Re: Dead Man Drawing
 

Very nice play.

I never show hands when I don't have to but this looks like as good a spot as any to show. Thoughts?

Re: Dead Man Drawing
 

good post tommy. cant the guy ever have a 3?

Re: Dead Man Drawing
 

"cant the guy ever have a 3?"

Only if he faked the hitch, and we assumed he didn't.

Re: Dead Man Drawing
 

"this looks like as good a spot as any to show. Thoughts?"

I'd rather drink hydrogen than show this hand.

Re: Dead Man Drawing
 

[ QUOTE ]
"this looks like as good a spot as any to show. Thoughts?"

I'd rather drink hydrogen than show this hand.

[/ QUOTE ]

Yeah, if you think showing this hand is +EV then you don't understand the hand very well. This whole hand hinges on Villians read of Tommy. He can't keep that image by showing this hand.

Krishan

Re: Dead Man Drawing
 

"Only if he faked the hitch, and we assumed he didn't."

i think when we're working the math out we need to add in a percent (like 10% or so, it's debatable) that his hitch is not faked, but just random. maybe he had a hiccup of some sort, or thought he caught someone out of the corner of his eye he owes money, or just remembered an errand he forgot to do, or is in the beginning phases of what will become a dramatic life ending case of what michael j. fox has, or well you get the idea.

because i had at least two really nice really supreme live tells on people this year that ended up at the showdown being completely totally and randomly (meaning not faked/reverse tells) wrong. and for that many that were wrong i had at least 30 that were proven precise and correct.

so this needs to be factored in and i think it's what makes a flop bet best.

Re: Dead Man Drawing
 

[ QUOTE ]

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


[/ QUOTE ]

I rather make minimum wage carrying around SteveG's suitcase full of money than read that entire rambling moronic meaningless post.

TSP

Re: Dead Man Drawing
 

Extremely good post, Tommy. This post shows some of the beauties and intricacies of live play.

Re: Dead Man Drawing
 

At least Tommy adds some EXTRA to his stuff -- it makes a great read----and after I get done spitting my coffee on the key board I LEARN stuff from Tommy now and then----like MATH SUCKS thank GOSH TOMMY does it for me ------
Don
Table 7 seat 4 today