Simple Common Tournament Situation

[deuces09]

We've yet to account for the proposed Ev/success rate from stealing on the button/CO with 4xBB with a random hand, given table images. A player more successful in stealing blinds from LP might think moving all-in with QJs from UTG with 1100 chips could be less +EV compared to playing the blinds and moving in with any hand on the button or cutoff with 800.

[David Sklansky]

Quote:
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Basically you move in if the EV of your resultant stack is more than the $1100 you have now and not otherwise.


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This is a dangerously incorrect statement.

Do you see why?



It has been shown earlier that if you are under the gun with a short stack you should move in with a slight negative EV. On the other hand since you are the best player you should avoid close gambles. Those two things approximately cancel out in this case.

By the way, I have not done the math for this question. I'd be surprised however if moving in was wrong. As would Huck Seed, David Gray, Allen Cunningham and Mark Grigorich.

[fnurt]

To elaborate, the point that everyone already appreciates is that if you fold, you are not simply sitting there with T1100. You are sitting there with T1100 and will have to post T300 in blinds in the next 2 hands. That's quite a bit of lost EV since you are right at the point where your folding equity is about to dissipate.

But you're going to have to take those blinds no matter what happens on this hand, so doesn't the negative EV cancel out? No, and here's why.

Let's say you get offered a pure coin flip to double up right now. Half the time you will have T2200, and half the time you will have T0. Would you do it?

If you win, you still have to pay T300 in blinds the next two hands, but obviously it doesn't hurt your stack as much. You will still have plenty to play with after the blinds pass and you will still have substantial folding equity when you are first in. And if you lose, obviously the blinds won't hurt you at all!

So you should definitely take the coin flip if it's offered. Folding carries a lot of negative EV here because you are right at the point where the blinds hurt you most. Gambling on a coin flip, even if it's EV neutral in a cash sense, lessens or eliminates the negative EV associated with taking the blinds and thus is the best move.

I don't see how this would change even if you are the best player at the table. If you blind down to 4xBB, there are going to be very few opportunities to bring skill into play. If you gamble and double up, then you can go back to passing on close gambles and waiting for opportunities to employ skill, if you like.

[Expunge]

[ QUOTE ]
Why? Because almost none of the answers attempted to do any math. I asked several world class players this question. All of them ventured an opinion and then said "am I right?" Because they all realized that this was in fact mainly a math problem. That should be obvious because we are talking about a possible all in move and talking about eight random hands yet to act. All in= math problem. Random opposing hands= math problem.

The fact that this is a tournament or that you are the best player has only a tiny bearing on the correct decision. Basically you move in if the EV of your resultant stack is more than the $1100 you have now and not otherwise. What is relevant is that your opponents are not live ones. This means an all in move will be called by medium pairs and up, big aces and perhaps KQ or KJ suited. Later positions will call with a few more hands than early positions. At this point it is all math. Yet almost none of you tried to do this math. HOW DARE YOU? What makes you think that this question should be attempted by the seat of your pants? Were you just lazy? Or is it because you do not know how to do this relatively simple problem? If you don't, you better learn now because otherwise you are almost certainly destined to go broke.

[/ QUOTE ]

David, The number of assumptions you leave open leaves the question very difficult to pinpoint answer.

My assumptions are as follows. You will get called if any one of your oppents have any of the following. AA-88, AKs-ATs, AKo-ATo, KQs, KJs, QJs. (no difference based on position)
If you are called you are only called by 1 opponent.

This means a single opponent will have a hand 202/2450 or 0.082449 (others made errors here because they incorrectly calculated the chance an opponent has a hand with a Q or J in it there are only 3 of each remaining)
In order to win the blinds outright all 8 opponents must not have a hand = (1-0.082)^8 = 0.502
When you do get called you will get 0.360 of the pot. (weighted average of the twodimes.net results)
The pot is equal to (6*2500+2400+2300)/8
So you expected number of chips after getting called is 887.
Your overall expected number of chips by moving in is 1145.

below are some of the calculations, top right of the square is suited, bottom left is unsuited.

<font class="small">Code:</font><hr /><pre>Combinations
A K Q J T 9 8 7 6 5 4 3 2
A 12 8 6 6 8 8 8 8 8 8 8 8 8
K 24 12 6 6 8 8 8 8 8 8 8 8 8
Q 18 18 6 6 6 6 6 6 6 6 6 6 6
J 18 18 12 6 6 6 6 6 6 6 6 6 6
T 24 24 18 18 12 8 8 8 8 8 8 8 8
9 24 24 18 18 24 12 8 8 8 8 8 8 8
8 24 24 18 18 24 24 12 8 8 8 8 8 8
7 24 24 18 18 24 24 24 12 8 8 8 8 8
6 24 24 18 18 24 24 24 24 12 8 8 8 8
5 24 24 18 18 24 24 24 24 24 12 8 8 8
4 24 24 18 18 24 24 24 24 24 24 12 8 8
3 24 24 18 18 24 24 24 24 24 24 24 12 8
2 24 24 18 18 24 24 24 24 24 24 24 24 12 2450

EV of pot
A K Q J T 9 8 7 6 5 4 3 2
A 0.191 0.365 0.300 0.301 0.419
K 0.392 0.177 0.292 0.292
Q 0.314 0.158 0.500
J 0.315 0.370
T 0.449 0.470
9 0.481
8 0.491
7 0.504
6 0.506
5
4
3
2

Hands that call you
A K Q J T 9 8 7 6 5 4 3 2
A 1 1 1 1 1
K 1 1 1 1
Q 1 1 1
J 1 1
T 1 1
9 1
8 1
7
6
5
4
3
2
202
8.24%

1400 50.2%
0.360 887 49.8%
1145
</pre><hr />

To David, i am very disappointed that you come in here and scold us for not doing the calculations when you have yet to do the calculations.

[David Sklansky]

Yes it is probably correct to move in even if the EV of your stack is a bit below 1100. The smaller your stack, the less it matters that you are the best player. But even without that aspect it still is almost certainly right to move in. Especially because in real life many opponents will fold AT and AJ.

[fnurt]

What are the chances that 2 players have hands in the calling range? If there is a 50% chance someone has a calling hand, it seems like this would happen a non-trivial percentage of the time.

If you are called in 2 places, does that change the EV significantly? QJs seems like a good multiway hand so maybe it makes no difference.

Very interesting calculations. With a few more good souls like you maybe we can keep Mr. Sklansky's blood pressure down.

[Expunge]

[ QUOTE ]
What are the chances that 2 players have hands in the calling range? If there is a 50% chance someone has a calling hand, it seems like this would happen a non-trivial percentage of the time.

If you are called in 2 places, does that change the EV significantly? QJs seems like a good multiway hand so maybe it makes no difference.

Very interesting calculations. With a few more good souls like you maybe we can keep Mr. Sklansky's blood pressure down.

[/ QUOTE ]

8C1*0.082*(1-0.082)^7 = 0.361 = approximately the chance that exactly one person has a hand. (this isn’t true because if one opponent has a hand the chances of a second hand decreases as the first persons hand removes some of the combinations.). But going with this results a 13.7% chance more than one opponent has a hand. Now your less likely to win the put but the pot is bigger. Don’t forget though that if the first person that has a hand might raise reduce the hands the next guys needs to call. Or that the first hand calls and the second raises and the first folds, likely putting you in a more dominated position but for more chips.

This results in exactly what most of us realized immediately. While the individual calculations are simple, the number of assumptions and combinations makes the problem prohibitive to do at the table.

[Kurn, son of Mogh]

I may bet 450-550, but I wont shove all-in.

Why bet half your chips? It's not like you're going to fold on the flop if your're called. or fold if you're reraised.

Clear all-in or fold situation.

[fnurt]

[ QUOTE ]
This results in exactly what most of us realized immediately. While the individual calculations are simple, the number of assumptions and combinations makes the problem prohibitive to do at the table.

[/ QUOTE ]

That is why we are doing it now, rather than waiting to do it at the table.

The Sicilian Defense is tough to work out at the table, too. That is why chess masters learn it ahead of time.

[Faro]

SossMan I thought had it about right except for a math error on amount won being double by mistake. This is quite helpful since I do not even know what to consider when making a decision except what I am told. Perhaps we need something like George or Casey at the tables with us. Just think if we all had a George or a Casey then it would be even for everyone.