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Old 01-16-2007, 09:15 PM
Phat Mack Phat Mack is offline
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Default Re: Pre-millenial post: 27 lowball research problems

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I think the right way to approach this is for the players to draw to their "best" draws. "Best" is unambiguous if you play face-up. It requires a little more definition if you want to play with cards hidden. (For example, does the player with 23 know what the player drawing two has to start? Or at least put him on a range?)

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Let's say that both players start by drawing 3 to 23xxx. Player 1 hits K7532 and draws 1. Player 2 hits K 7632 and draws 2?

This is a little different than I imagined. I wonder if "best" draws could become ambiguous as the number of players increases.

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I think in the example you give it is quite likely that it is still correct to draw to 7632. But what about 9632? T632? It's not immediately obvious (though we generally think keeping the 9 is better than discarding it.)

There are some very non-intuitive last-round draws that can occur if one player is drawing two. (For example, the suit of a discarded K can switch a draw from one card to two cards.)

The best (highest-expectation) draw will always be unambiguous when you know all the cards, even multiway, but it might be position-dependent. I came up with a couple examples a while back where the best draws depended on who drew first for the same set of cards.

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I thought about this some more today. I am assuming that the composition of the deck is always known. I couldn't immediately come up with an ambiguous situation, but I believe I could come up with a situation where it didn't matter if the first player drew one or stood pat (in other words, his win% in either case would be identical).

I think having the players play "face up" might provide the easiest-to-define drawing strategies, but the results could be trivialized. It seems that specific drawing stategies could be identified (for example, drawing to the 9632 and T632 you mention above), simmed, benchmarked, and then compared to come up with the pre-drawing EVs. I have to think about this some more.
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