Tournament theory question

[M.B.E.]

This is something I've been meaning to calculate but haven't gotten around to it.

It's toward the end of a large tournament, well into the money. Say there are 21 players left on three tables, about a million chips in play, top 90 get paid, a small bump from 19th to 18th, then 18th through 10th get the same amount, with as usual large bumps for each place at the final table. The prize structure isn't really the point of this problem.

Blinds are 1500/3000, ante 400, our stack is 43,000 (around the median for the tournament). It is folded to us on the button. Pot is 7300.

The small blind has 20,000 but is playing very tight -- he actually said that his main goal was to make it to the next prize level (18th place).

The big blind has 130,000, largest stack at the table. He has been playing very aggressively, and if we raise he will come over the top liberally.

For purposes of this problem, assume our only options are: (a) fold, (b) raise to 8000, and (c) raise all-in. (Limping is not an option.)

If we raise any amount, SB will go all in with AA, KK, or QQ, and fold everything else. If SB is in, then BB will fold everything except AA and KK. But if we raise and SB folds, then BB will play as follows:

If we raised to 8000, BB will move in with any pocket pair, any suited ace, offsuit aces down to A8, any suited broadway, KQo, KJo, J9s, T9s, 98s, and 87s. Everything else he will fold.

If we raise all-in, BB will call with 77 and higher, A9s and higher, AJo and higher, and KQs, and fold everything else.

The question is, with what range of hands should we move in and with what range of hands should we raise to 8000.

For example, if we have AQo are we better off moving in (which usually will win the blinds), or raising to 8000 (which won't win the blinds as much, but will often allow us to get our 43,000 all-in as a favourite against BB).

For another example, if we have 72o are we better off folding or raising to 8000 (then folding if reraised)?

EDIT: This turned out to be more complicated than I intended. To simplify it, let's assume that the SB will always fold, even AA. Maybe he's away from the table on a 10-minute penalty. What I'm mainly interested is what kind of hand you need on the button for it to be correct to "trap" an aggressive player in the big blind.

[Lloyd]

My head hurts.

Interesting question which I don't have time to address now but certainly will later.

[A_PLUS]

Wow, great question. I dont think I will have time today, but I would love to take a crack at this tomorrow.

I have an open pushing spreadsheet that I built, it assumes a simple $EV = %of chips x prize pool, but it would be a start. PM me is you want me to send it to you, it will make the math end much easier to calculate.

[woodguy]

[ QUOTE ]
This is something I've been meaning to calculate but haven't gotten around to it.

[/ QUOTE ]

Here you go.




Regards,
Woodguy

[Sluss]

This is an interesting question. I've already answered and deleted it three times. Probably because this is the most common spot where I bust out of a tourney in the money, but not the final table.

What I normally do this with, which seems to work about a 1/4 of the time [img]/images/graemlins/frown.gif[/img], is with 99-AA AK, AQ, AJs.

I think a pretty big leak in my game though at this point is that I very rarely move in in this spot on a steal. Sometimes I will raise and muck, but don't always move in.

I always feel like I play so well at the final table that I don't want to bust out in a spot where I could have been at the final table with an average amount of chips. That felt very Helmuthian to write. I have to go vomit now. [img]/images/graemlins/tongue.gif[/img]

[intheflatfield]

[ QUOTE ]
I always feel like I play so well at the final table that I don't want to bust out in a spot where I could have been at the final table with an average amount of chips. That felt very Helmuthian to write. I have to go vomit now.


[/ QUOTE ]

lmao

[locutus2002]

Its very easy to get lost in the details of a situation, and poker is ultimately a game of situations.

From a theory point of view I think you are asking:

"Under what conditions will you attack an aggressive BB with a huge stack when you only have 14XBB left?"

"Is it possible to make a meaningful bet without committing all your chips in this situation?"

Raise to T8,000 is not meaningful as BB will be getting 3:1 to call any two.

[M.B.E.]

[ QUOTE ]
From a theory point of view I think you are asking:

"Under what conditions will you attack an aggressive BB with a huge stack when you only have 14XBB left?"

"Is it possible to make a meaningful bet without committing all your chips in this situation?"

[/ QUOTE ]
Not exactly; what I was trying to ask is more along these lines:

"With 14xBB if you have a decent hand are you better off trying to win the blinds and antes or trying to get all-in against a worse hand?"

It's based on a real situation where I busted out of a b&m tourney (although the actual hand was a bad beat so I won't post it unless someone absolutely insists).

[ QUOTE ]
Raise to T8,000 is not meaningful as BB will be getting 3:1 to call any two.

[/ QUOTE ]
The problem as I set it up is a bit unrealistic because I have the big blind folding JTo, for example, which is obviously incorrect when it's only 5000 for him to call. I did it that way because it's too difficult to calculate if we are sometimes seeing a flop.

However, are you suggesting that in this scenario, getting 3:1 pot odds, the big blind should never fold? If so I disagree. For example, if you're in the big blind with 94o and button raises to 8K leaving him with 35K behind, you can't correctly call getting 3:1 pot odds. (It would be correct with any two if the 8K raise put the raiser all-in, but here it doesn't.)

[locutus2002]

Well, I'd be disappointed to see 94o, but I'd still make the call. If you include the likely continuation bet, hero is getting ~5:1 to see the flop, or he gets to see 4 cards for 1 1/2XBB. 94 is disappointing because you're never likely to be that far ahead, but it will still be clear when you are likely to be far behind.

[ QUOTE ]
From a theory point of view I think you are asking:

"Is it possible to make a meaningful bet without committing all your chips in this situation?"

Raise to T8,000 is not meaningful as BB will be getting 3:1 to call any two.

[/ QUOTE ]

I agree with this viewpoint. When I am big-stacked at the final table, I am looking to knock players out, or at least prevent opponents from playing any drawing hands. I'm certainly not going to allow any kind of steal if I have any sort of hand.

If I'm getting 2:1 or better and have any kind of playable hand, then I'm very likely to put you to a decision for all of your marbles.

Then the question is up to you. What hands are you willing to play for the rest of your stack?

The situation that the original poster posed is a very unenviable situation to be in.

Off topic but I think it illustrates your scenario a bit:

In a tournament a while ago I had a tremendous run of cards early and got people to pay me off on almost every hand that I made. The net result was that my stack was in excess of 30K early in the tournament and every one else at my table had less than 2500.

I was in an rare opportunity to just play 900 pound gorilla and really push people around. Granted I was getting some playable cards like middle pairs, AK, AQ, etc. But anytime any one player or small group of players limped in or showed any weakness, I just pushed and put them to the ultimate decision.

It afforded me an opportunity to take down a large number of pots without even seeing a flop, and I'm certain in several cases that I was able to make a better hand fold.

More importantly, it allowed me to continue to increase my stack size, all the while knocking out and weakening the other players at the table.

Back to your original scenario, if you are on the bottom end of a situation like this, in many ways you are almost defenseless unless you are fortunate to draw a strong hand, have it hold up, and get paid off with it. And this would have to happen more than just once to start backing off a hyper-aggressive player. It really is a tough spot in which one can get frustrated and really thrown off their game.

About the only thing you can really do is bob and weave and counterpunch. If you catch a hand, let the opponent's hyper-aggressiveness work for you so that you can maximize your payoff if you win. Limp and re-raise. Check and raise. Extract the maximum payoff when you can and take your chances.