Tournament theory question.

Lafortezza

From a post on 2+2, even reading this hurt my brain a little cos its pretty damned complicated. Well done to anyone who can even suggest an answer with reasons.




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
There's a small bump in prize money 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.)

1) 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:

2)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.

3)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)?

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.





Told you it was complicated.

careca

Just gone back to the 'What hole cards do you never play' thread.

NickyOD

Damn you anyway. Now I can't sleep until I work this out. :mad:

NickyOD

NickyOD wrote:

Damn you anyway. Now I can't sleep until I work this out. :mad:

Actually without even working this out I think you should raise 8000 with any hand but I'll try and work it out mathematically anyway.

NickyOD

Having 10xBB and keeping the same ranges, we could probably push with almost any hand.

Quantifying the EV of just raising is much different because in the problem they didn't say what we'd call with. I'll just go with pushing for now and work out the trapping part later because that's hard to work out. Thanks christ the new version of pokerstove save me wokring most of this crap out.

The SB is only going to play about 1.35% of the time.

If we push BB calls us about 8.1% of the time.

So, on aggregate, we get called about 9.35% of the time when we move in. We are risking 43,000 to win 7300.

.9065(7300) is T6617.

Breakeven is when ((.0135)(SBwin%)(25800) + (.0135)(SBlose%)(20000) + (.081)(BBwin%)(47300) + (.081)(BBloss%)(-4300)) equals 6617.

Say we were allin with crap like 7-4o. That's about 26% win% for us. So our EV of moving in would be:

6617 + ((.0135)(SBwin%)(25800) + (.0135)(SBlose%)(-20000) + (.081)(BBwin%)(47300) + (.081)(BBloss%)(-43000)) OR:

6617 + ((.0135)(.15)(25800) + (.0135)(.85)(-20000) + (.081)(.26)(47300) + (.081)(.75)(-43000)) = about 4.8k, or more than one BB.

So we should probably push with anything other than the hands we want to trap the BB with. I think this would be TT-AA, AK and AQ. but its a ****er to work it out.

mewso

Go and have a pint for crying out loud

padraig_f

Armed with such precise information on your opponents, I'd say it's unwise to move all-in with any cards.

The SB is playing back so infrequently, you're correct to raise him with any 2 cards.

The BB is playing back at us about 20% of the time (yes, the new version of PokerStove is good), so 80% of the time we're picking up 7300. I think this makes it correct to raise to 8000 with any 2 cards.

Lafortezza

I haven't used pokerstove or anything so these points were just off the top of my head.

The SB can almost be discounted from the equation. His hand range is so small (if we raise) that it's not going to happen enough to be more than a very slight concern.

So let's say the SB folds all the time for arguments sake. We then have to decide what hands we raise to 8k with. If we raise to 8k, the BB moves in with a wide range of hand, so obviously we should raise to 8k with our strongest hands because it is more likely for the BB to move in with many marginal hands that we should be favourites over.

If we raise to 8k how low should our own standards be? Personally I'd say JJ or better ATo or better. I haven't done the maths but my gut feeling would be this range, with the BB's calling range being so loose we should be ahead enough times when BB moves in to make it a good move.

We should be willing to move in with a looser range of hands. Smaller pairs, suited connectors, almost any two cards since the chance of stealing the blinds is just too high because of the BB tight(er) range of hands for calling.
I could be very wrong but if I was in this situation in a live tournament this is what I'd be thinking.

Thought the poker forum might need something a little more complicated than bad beat posts and "Wat time does teh fitz open at??!".

bohsman

6 o clock weekdays but no poker till 8 30. 4 o clock for poker on sat and sun but no gaming till 6, dont know what language was being spoken in the rest of the thread so cant help there

Hitman Actual

lafortezza wrote:

From a post on 2+2, even reading this hurt my brain a little cos its pretty damned complicated. Well done to anyone who can even suggest an answer with reasons.

Hey lafortezza, you got a link for this on 2+2 by any chance? Very interesting question.

Lafortezza

bohsman wrote:

6 o clock weekdays but no poker till 8 30. 4 o clock for poker on sat and sun but no gaming till 6, dont know what language was being spoken in the rest of the thread so cant help there

ty nh