[Buzz]

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Crazy game....

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Jim - Agreed.
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I originally wondered if 23TJn was a better starting hand than 23QKn since 23TJn makes more nut straights than 23QKn. But it isn’t. When you are playing a hand with two wheel cards and two honor cards heads-up, the simple rule seems to be: the higher the honor cards, the better the starting hand. Pairs are better than two different ranks for high. And obviously you generally prefer to have a hand with an ace.
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I have
• 23TJn at 47.49% for one-on-one play and
• 23QKn at 50.11% for one-on-one play.
Both are for 10000 deals against random hands and random boards, using Wilson. Note that these are both rainbow hands. Hands do better if they're single suited, and even better if double suited. Replacing the deuce and trey with other non-paired wheel cards doesn't make as much difference as suitedness. That is, 45TJd is a better heads-up starting hand than 23QKn. (But 45QKd is better than either).
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Recently I ran a whole series of sims with gradually decreasing numbers of players. I was looking for hands that did better short handed and one-on-one than they did in full games. To make the comparison, I multiplied the winning totals I got by the number of players.
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There are some hands that do better one-on-one than in a full game, but they're mostly hands that don't do very well in full game play and they only turn out to be a bit above average in one-on-one play.
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What happens mostly is hands get closer in value when played one-on-one against random hands.
The best one-on-one hand is still AA23d, but what a waste to play that fine hand heads-up, at least in a limit game! (And of course then the flop is 999, you'd prefer to be holding anything with a nine).
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I fiddled with twodimes.net for a while before I started using Wilson. One of the advantages of Wilson is that you can run partial hands or run a hand against unknown (and random) cards instead of always making up particular cards for an opponent.
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Anyhow, interesting post. I'll look it over some more and might (or might not) reply again to it.

Buzz