Saturday, October 29, 2005

The Magic Glasses

Paul Phillips has two very interesting threads on his live journal (second thread here) regarding a hypothetical pair of magic glasses - that could allow you to see all of your opponents' hole cards. He ponders what % of the time a top player would win a typical WPT blind structure $10k buy-in tournament with this advantage.

This question makes for a great topic of discussion for the analytically inclined player. I am most surprised by Paul's quote:
"I asked two players who I thought would make good sanity checks: if one of
them had a different view I'd try harder to figure out how not to win. Both said
they would win 100% of the time minus some tiny epsilon. Those two guys were
Barry Greenstein and Andy Bloch."

Now, Barry and Andy are two very talented players who are also fundamentally mathematically sound. I'm very interested, therefore, that they believe the answer is virtually 100%. You can read various responses on Paul's threads as to why the answer should be at least SOMEWHAT lower - many of the posters miss the key points though, which I believe are these:

a) You want to be playing "small ball" poker: it's the Chicago White Sox vs the Boston Red Sox... If you have perfect information, you don't want to get into an all-in slugfest: even if you find AA vs 22 preflop, you still don't want to commit all of your chips. In fact, you NEVER want to commit all of your chips unless your pot equity is 100%, which leads me to point "b"

b) This is the essence of "playing your opponents' cards, not your own cards." The majority of your behavior would be predicated on the fact that you can assume your opponent must lay down his hand if you act in a certain manner. You don't need the best hand, you just need to know what your opponent will do. If you have 6-8 suited, aka, The Vortex, and your opponent has JJ, you may still be willing to play a pot with him, since you think you will be able to get him to either 1) lay down his hand on a flop with overcards to his jacks, or 2) pay you off if you make your hand. The key to the "Magic Glasses" is that you hope to be able to win a huge number of small pots, which will more than compensate for the risks you will eventually have to take as the blinds grow relative to stack sizes. One other problem which it seemed most responders ignored was point c:

c) Even if you know your opponents' cards, you cannot predict with certainty how they will act. Case in point: Entonio Esfandiari vs Gus Hansen in the Poker Superstars Invitational. Antonio raised a pot with 7-7. Gus bluff-re-raised holding ten high. Antonio correctly read gus for being weak, and moved all-in. Gus called. Now, again, with the Magic Glasses, we would never move all-in here, unless blinds were huge relative to stack sizes, but nevertheless, opponents can act irrationally/unpredictably, in such a way to each into our edge of perfect card knowledge.
I believe, without doing any simulation of the problem (and i DO believe it could be simluated) that the true winning percentage of a pro with the Magic Glasses would probably be in the mid-90%'s.

It's important that our opponents do not know that we have magic glasses, or they could seriously cut into our edge by simply pushing all-in preflop a very high percentage of the time. This realization brings me to an intriguing dilmena/paradox: IF our opponents had perfect knowledge of OUR cards, our best strategy would be to push all-in a huge percentage of the time. Furthermore, I believe that the perfect poker player would play as if he had knowledge of everyone's cards. Therefore, is it reasonable to conclude that if we are up against the perfect opponent, our strategy should be one of recklessly pushing our stack in preflop?

I think the immortal David Sklansky figured this out a while ago, when he developed his "System" for novices playing against top pro's, to negate the advantage of the professional player.

And it all comes full circle...

1 comment:

Unknown said...

I dont think it would be as high as 90 percent. Given the strategy of "moving all in a lot" to push people off, a wrong call by an opponent will eliminate you if their cards hit. This leads to a higher probability of being knocked out, and lowers the success percentage (especially nearing the final table). Sklansky didnt think of that one!