Dumb risk to knock myself out of the money?

[FOSTERKID1]

I was playing in a regular single-table tournament with a brutal pay structure: second gets his buy-in back, first takes the rest (barring any deals).

Action is three-way, hero is on the second stack, button/UTG with A /images/graemlins/spade.gif Q /images/graemlins/spade.gif Hero raises 10x the bb. SB is the short stack and is a rock. SB thinks for 5 minutes and makes a call. BB is chip leader, and angrily pushes all-in.

Normally I'll get out of the big stack's way at this point with a speculative hand like AQs, let him be heads-up against the short stack and hope they put me in the money. But two things happen. First, big stack says he's upset that short stack just called my raise and would rather short stack pushed all in so big stack can call and wait to see what I do. So I put the big stack on a medium to medium large pair(88 through JJ)--something he'd rather not be three-way with, and something that fears a very big pair behind him. All the more reason to get out of his way as an 11 to 10 dog. But then the short stack decides he wants to talk too, and moans what a mistake it was to call my raise in the first place. Thus its clear he won't call here (even though he's committed a little less than half of his chips to the pot already).

Now, since I know he's a rock, won't call here, and am probably against an underpair in the big stack, I call. My reasoning is I'm almost a coin-flip, will take a dominant lead if I win the hand, and am getting 10 to 1 on my money if I place first versus 1 to 1 on my money if I place second.

Is my thinking sound? Should I swallow my pride, muck it and try to out grind the rock before I get aggressive heads up?

[Lori]

a brutal pay structure: second gets his buy-in back, first takes the rest (barring any deals).

I think this fact alone makes me have to gamble here.

Taking some approximations,

Im going to call the stacks before this hand 6-4-2 and you have all put in 1 unit to this point.
If you fold it will be 8-3-1
Chance of winning tourney = 3 in 12, and chance of coming second approximately 3 in 4 (taking it as a tourney between you and the short stack)

So you have a 25% chance of x units (where x is the first prize) and 3/4 of the other 75% you will get 1 unit = around 56%

Return .25x + .56

If you shove, I'm going to give you a 35% chance of winning this pot, which is probably a little harsh on you, but oh well.

35% of the time you will be in a 2-9-1 chip lead giving a 75% chance of winning and a 100% (yeah I know, I was harsh on your odds of winning the pot, so I'm rounding here in your favour) chance of second place if you don't win.
65% of the time, you will get 0 units and throw your AQs at the dealer.

Your EV here is .35*.75x = .26x + .35*.25*1 (The .35 you win with AQ * the .25 you fail to win the tourney * the 1 unit for coming second) = 0.09

To recap:

Folding = .25x + .56
Playing = .26x + .09

In this scenario, with my 'guesses' at the stacks and odds, you would need .01x to equal .47 units, meaning first prize would need to be 47 buyins to call.

HOWEVER I present this merely as a way to work out what to do, and even slight changes in the numbers would lead to huge differences in the parameters.

If your chances of winning go from 35% to 40% on that hand, then we get .40*.75x + .40*.25 = .30x+.10

going back to our solution now:

Folding: .25x + .56
Playing: .30x + .10

so now .05x only needs to make up .46, so a first prize of 9.2 buyins would do.

Although this is all very interesting, it shows how tight this decision was /images/graemlins/tongue.gif

Please note: I didn't proof read this post, and any errors you think I have made will be real errors, and not you going crazy, I hope it gave you a way to approach analysing this kind of scenario in the future.
(It's easier when you know x, which you did and I didnt)

Lori

[bosoxfan]

wow, I read this 3 times and still don't get it. Do you do these calculations in your head when making a decision like this?

[Lori]

Do you do these calculations in your head when making a decision like this?

No, but over a period of time you get a better and better feel for the situation.

The brain approximates very well in the subconscious as long as it knows what it's trying to do, so doing the occasional (and I'd be lying if I pretended I did it a lot) reality check is very good practise.

Liken it to a fielder catching a ball, he doesn't do the calculations and just runs to the ball, but with input from a coach he can probably get there a little more accurately or take the catch a little more cleanly.

Lori

[FOSTERKID1]

Lori, will you marry me? Damned fine analysis. Anyway, I was right to put the big stack on a mid to mid-large pair. I called and he turned over J /images/graemlins/club.gif J /images/graemlins/heart.gif . They held up and I went home empty handed. The stacks were actually about 10:6:3 or 10:6:2 if I had to put a guess on it.

[tallstack]

I think we need more information about the specific stacks and prizes to make an assessment here, but one thing jumped out at me. With home game quality players, someone who acts like they don't like what they are doing while they are in fact raising usually has a huge hand. I obviously don't have any knowledge of your opponent, and maybe he is better than this, but if not then I would expect that you will be shown a hand that has you drawing slim.

That aside, I think the prize structure coupled with your large initial raise may make it worth a call here even if you think you are a dog right now.

Dave S