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Tournament Poker >> STT Strategy

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P.B. Miltersen
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Reged: 02/24/06
Posts: 13
Loc: Denmark

A near-optimal strategy for a heads-up tournament
#4854534 - 02/24/06 06:10 AM

As a requiem for the old PartyPoker sit'n'go blind structure, Troels Bjerre Sørensen and I have computed optimal jam/fold strategies for a heads-up no-limit Hold'em tournament with a total stack size of 8000, a fixed small blind of 300, and a fixed big blind of 600. If interested, please follow the link:

http://www.daimi.au.dk/~bromille/Papers/poker.pdf

Comments are welcome.

Thanks,
Peter Bro Miltersen.

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raptor517
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Re: A near-optimal strategy for a heads-up tournament [Re: P.B. Miltersen]
#4854728 - 02/24/06 07:11 AM

ok i saw that it was like 203580923589023 pages long, so ima save everyone some time. shove EVERY hand from the sb. call with top 70% of hands when pushed into. there ya go. unexploitable strategy. holla

edit: oh, i also didnt even bother reading a word of it. i saw some weird looking symbols that i took to be some part of a math formula. what u read above is merely my PREDICTION of what those 20385092 pages say.

holla

Edited by raptor517 (02/24/06 07:15 AM)

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runner4life7
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Re: A near-optimal strategy for a heads-up tournament [Re: raptor517]
#4854737 - 02/24/06 07:13 AM

holy [censored], nice work for all that work, probably more than necessary but props for doing it, im too lazy to read it. thanks raptor for the summary.

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HesseJam
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Re: A near-optimal strategy for a heads-up tournament [Re: P.B. Miltersen]
#4854758 - 02/24/06 07:21 AM

The paper looks very intimidating, indeed.

I've read only the abstract so far. The interesting stuff is that you quantify how far the all-in strategy is off from the optimal strategy.

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P.B. Miltersen
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Reged: 02/24/06
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Re: A near-optimal strategy for a heads-up tournament [Re: raptor517]
#4855965 - 02/24/06 10:58 AM

Well, this is a bit too loose a strategy for the small blind to be completely unexploitable. Also, you did not completely specify the strategy for the case of the big blind; what should the big blind do if he is NOT pushed into?

If you specify this, we can compute exactly how much the strategy can be exploited compared to the optimal jam/fold strategy.

Incidently, the optimal (i.e., minimax) jam/fold strategy for the big blind ignores the size of the bet made by the small blind, i.e., behaves in the same way no matter what the size of the bet of the small blind is. And it plays looser than the small blind, not tighter. The latter fact may seem somewhat counterintuitive, but in fact it is easy to establish.

Best,
Peter.

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the shadow
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Re: A near-optimal strategy for a heads-up tournament [Re: P.B. Miltersen]
#4857200 - 02/24/06 01:01 PM

Peter,

Very nice work. Anyone who is interested in NE HU play should take a look at your article.

I am particularly interested in your figures 1 and 3. If I am reading both correctly, your work appears to be inconsistent with eastbay's results suggesting that a push-fold game is +EV for the SB when 0<R<8 where R=small stack/BB.

In addition, your results would appear to contradict the assertion that the HU equity function is strictly linear.

Have you performed similar calculations for other R values?

The Shadow

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microbet
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Re: A near-optimal strategy for a heads-up tournament [Re: P.B. Miltersen]
#4857309 - 02/24/06 01:10 PM

Mange tak

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P.B. Miltersen
stranger

Reged: 02/24/06
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Re: A near-optimal strategy for a heads-up tournament [Re: the shadow]
#4857937 - 02/24/06 02:00 PM

These threads look very interesting and it seems we should do a lot of reading before being able to give full answers. Thanks for pointing them out to me. Some preliminary answers:

If I am reading both correctly, your work appears to be inconsistent with eastbay's results suggesting that a push-fold game is +EV for the SB when 0<R<8 where R=small stack/BB.

Note that the graphs represent the guaranteed winning probability of the player about to post the small blind (or the big blind) in next hand to come. But in the following hand (if it comes), he will post the other blind. So the values do not only represent the value of the next hand to come but the value of the rest of the tournament. So I don't see an immediate inconsistency with what you state above (also note that the SB graph is in general above the BB graph, so I do in general prefer starting out as the SB).

In addition, your results would appear to contradict the assertion that the HU equity function is strictly linear.

Okay, I have yet to digest the argument given there, but note that we do NOT consider a symmetric game, since we restrict only our OWN strategy, but NOT that of the opponent, to jam/fold (and this is the case when we post the small blind as well as when we post the big blind) and it seems that the argument given there would not apply to the equity of such a game. Still, our calculations definitely show that the winning probability for the small blind with a stack size of 2500 is strictly bigger than 2500/8000, even when he has lost equity by restricting himself to jam/fold in the rest of the tournament so if this is inconsistent with the argument you refer to, there is indeed something to think about.

Have you performed similar calculations for other R values?

No. One can of course do so. But it also seems that one can get a lot of fun out of looking at just these parameters.

Best,
Peter.

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curtains
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Re: A near-optimal strategy for a heads-up tournament [Re: raptor517]
#4857992 - 02/24/06 02:05 PM

Quote:

ok i saw that it was like 203580923589023 pages long, so ima save everyone some time. shove EVERY hand from the sb. call with top 70% of hands when pushed into. there ya go. unexploitable strategy. holla

edit: oh, i also didnt even bother reading a word of it. i saw some weird looking symbols that i took to be some part of a math formula. what u read above is merely my PREDICTION of what those 20385092 pages say.

holla

raptor man, that is so far from unexploitable its not even funny.

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The Yugoslavian
STTF-HUC II Champion

Reged: 09/24/04
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Re: A near-optimal strategy for a heads-up tournament [Re: curtains]
#4858450 - 02/24/06 02:42 PM

Quote:

Quote:

ok i saw that it was like 203580923589023 pages long, so ima save everyone some time. shove EVERY hand from the sb. call with top 70% of hands when pushed into. there ya go. unexploitable strategy. holla

edit: oh, i also didnt even bother reading a word of it. i saw some weird looking symbols that i took to be some part of a math formula. what u read above is merely my PREDICTION of what those 20385092 pages say.

holla

raptor man, that is so far from unexploitable its not even funny.

I laughed.

Yugoslav

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