Simple Common Tournament Situation

[SossMan]

I guess you missed this post:

All-in. This is undoubtably a +EV situation. If you pick a sufficiently narrow range of hands such that QJs is a 70%-80% dog, your folding equity more than makes up for the times you lose. Once you adjust the calling standards downward, the dead money in the pot is enough to make up for the fact you'll be a slight dog.

Example for a tight table, you get called by AA-99, AK, AQ, AJ, KQ. That's 82 combinations, the probability you will not get called is 44%. If you do get called you lose about 67% of the time (wtd avg of twodimes numbers).

(.44)(300) + (.56)(.67)(-1100) + (.56)(.33)(2400) = about +160

(you win 2,500 if you beat someone outside of the blinds, 2,400 if the small blind calls, 2,300 if the big blind calls, so we'll call it 2,400 conservatively).

All-in.

[js13_tps]

tks. My bad. I was looking for the answer from David. doh! [img]/images/graemlins/shocked.gif[/img]

[Rushmore]

I'm going to get on record and say that this is the first time with one of David's questions where my answer was wrong, and I realized after the fact that it was wrong, and I was ashamed to have gotten it wrong because it seems both important and simple. Play winning poker for long enough, and you start thinking you know what you're doing.

I suppose that's the point. I appreciate the point.

Back to school for me.

P.S. MAN, I HATE writing this post!!!

[Stew]

[ 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 ]

Of course it's a math problem, BUT, what if you look around the table and see some dude bouncing his leg, fiddling his chips checking and re-checking his cards, counting his stack...a player whose played zero hands and has always looked at his cards and then acted uninterested...now he's giving information that he has a huge hand.

I realize and believe me I do realize that poker is a math game. Ask my friends, I tell my wife that constantly. However, there are other things than math that can be important, particularly in No-Limit.

Just wanted to make that point.

[West]

Here's my attempt:

I supposed that the first 4 players will call with 88 and up, and AK-AJ. 1326 suit specific possible hands, these make up 90 of those combos (6 for each pair, 16 for the non pairs) = 90/1326 = 6.8% chance of being called by a player in one of the first 4 positions

Cutoff and the button, I added KQ and 77, for 22 more combos = 112/1326 = 8.4% chance of being called

SB I added KJs and AT for 20 more combos = 132/1326 = 10% chance of being called

BB I supposed A9, 55 and 66 = 160/1326 = 12% chance of being called

I then calculated the chance of not being called by anyone as:

.932 x .932 x .932 x .932 x .916 x .916 x .9 x .88 = 50%

So my estimate is that half the time you'll win the blinds = +300

When you're called by a single hand, your chances of winning are (roughly):

pairs 55 thru TT = 50/50
JJ = 37/63
QQ thru AA = 18/82
AJ, AQ, KQ, KJs = 30/70
AK = 40/60
AT,A9 = 46/54

The times you will be called by each of these hands are:

88 - TT = 18 (of the 1326 possible combos) x 8 (players who will call you with these) = 144
JJ = 6 x 8 = 48
QQ - AA = 18 x 8 = 144
AJ, AQ = 32 x 8 = 256
AK = 16 x 8 = 128
77 = 6 x 4 = 24
KQ = 16 x 4 = 64
KJs = 4 x 2 = 8
AT = 16 x 2 = 32
55 - 66 = 12
A9 = 16

876 player hand combos calling you

Chances of winning x % of time that will be your chances:

(55-TT) 50% x 180/876 (20.5%) = 10.3%
(JJ) 37% x 48/876 (5.5%) = 2%
(QQ-AA) 18% x 144/876 (16.4%) = 3%
(AJ, AQ, KQ, KJs) 30% x 328/876 (37.4%) = 11.2%
(AK) 40% x 128/876 (14.6%) = 5.8%
(AT, A9) 46% x 48/876 (5.5%) = 2.5%

10.3 + 2 + 3 + 11.2 + 5.8 + 2.5 = 34.8%

I estimate you have a 35% chance of winning if called by single player.

Forgetting the possibility to being called by more than one:

When you are called, 18% of time, it will be BB, 15% of time SB. Other 2/3 of time, pot will be 2500 and I will gain 1400 chips.

I just realized this is wrong, but assuming SB and BB have same chance of beating you as other positions that call:

.65 x -1100
+
.35 x .66 x 1400
+
.35 x .18 x 1200
+
.35 x .15 x 1300
= (-715+323+76+68) = -248 chip EV

I'm thinking being called by more than one hand doesn't particularly kill you that much - if one of them is a monster pair, you were just as dead in most cases anyway. There are the few times such as when you will be called by AQ and JJ which are hurting you a lot, but these are going to be fairly rare.

Not accounting for this, my estimated EV of stack is 50% x 300 + 50% x -248 = +26.

So...it looks like this hand is right on the borderline of what we should move in with here, given that you've told us that we should move in if our resultant stack is expected to increase. Changing the assumptions of who will call you with what could change the answer.

Mistakes? Better assumptions? Maybe take away 88 and AJ from first few players? BB less likely to call with 55 or 66 than with say, A8? Feedback is appreciated.

[West]

In that equation, the 2400 s/b 1300, as that is the amount of chips you would profit. Doing so changes the EV to -40.

[SossMan]

the post that I cut and pasted wasn't mine, and I wasn't validating it's correctness...I was just responding to David's accusation that nobody was using math

[West]

It seems to me that posting the BB on your next hand is going to lower your stack expectation immediately in a not insignificant way, and so I would think we would want to be going all in even with some negative chip EV results.

[fnurt]

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

[/ QUOTE ]

This is a dangerously incorrect statement.

Do you see why?

[DonkeyKong]

The pure math of this makes it reasonably close but the fact that the blinds are next means your stack is going down by nearly 30% over next 2 hands. You are unlikely to be picking up a hand that is a dominant favorite over the next orbit. If you get cards such that you become a 70/30 favored position, you figure to get called a higher % of the time due to the fact your stack is so unthreatening -- actually, you are likely to be the caller so you have a very low % chance of picking up the blinds. Others will welcome a match-up with your short-stack knowing your desperation and your unthreatening stack. In this case, I would estimate you get called (or you are the caller) a very high % of the time (mathematically, I would use very loose hand combination math). I am sure there is a bunch of random hand math over the next orbit that comes into play here but I am not going to give that math too much thought at this point. I am aware that I am in trouble and waiting is a serious problem at this point due to the current math.

Rather than run numbers that I will never be able to exactly compute during that moment, I will always make some basic estimates and see if its close:

On average, others will call with top 10% of hands, (top 4-6% of hands for UTG+1 thru UTG+3, top 8-12% for next few players, top 15% for last few). This gets you to 55-60% of the time getting called. 40-45% of the time you will pick up the 300 in blinds...

The fact that you may pick up the blinds 40%+ of the time here is in itself a reason to go ahead and move in. This chance is likely to disappear soon.

The dead money in the pot represents nearly 30% of your stack and will rise to nearly 40% if you don't call... making it correct to then move-in with basically anything.

The fact that you are UTG makes this a move-in situation.

My assumptions end with basically the same answer as West:
55% Called
45% Pick up blinds

When Called:
~33% Chance to win on avg (estd wgt avg of 4-1, 3-1, 2.5-1)
~67% Chance to lose on avg
.33 x (1100+300+1100) = 825
.67 x (0) = 0
so,
~750 + 300 = ~1050 = 'its very close'

If you wait, EV will get worse... move all-in