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#11
07-11-2005, 01:02 PM
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Re: heads up theory
I'm sure there's some sweet math I don't know to solve this, but I had an idea. The button should bet when he has a 50% or greater chance of being called by a worse hand. So, if we will bet with a 40 he will raise with a 70 and we should reraise with an 85 or higher. He should then reraise with a 93 or higher. We'll reraise with a 97 or higher. He'll reraise with a 99 or higher and we should never lose more than 7 bets. To put in the 8th bet, we have to have the 100 card.
FYI, I'm just taking the total range of hands subtracting out the range I wouldn't have put in the prior bet with and dividing by two. That finds the point at which we're indifferent to raising (or sometimes the marginally profitable point because of rounding). I don't think checkraising will ever be profitable. I would think we'd have to checkraise with our best hands. That would allow the button to raise more liberally and only put in two bets when we have our best hands. Betting out seems like a dominant strategy. By betting out and calling we will lose .5 a bet (.4(1)+.3(-1)+.3(-2)=-.5). By checking and calling we'll lose at least half a bet and we won't make as much on our better hands. So, we should bet out with 40 and check/call with 39 or below. Let me know if I've screwed up the math somehow. 
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#12
07-11-2005, 02:40 PM
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Re: heads up theory
It doesn't matter. Either check, or bet, you'll lose .46 on average. You might as well check. In fact, it doesn't matter whether you bet or check no matter what number you choose. You'll win/lose the same amount.
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#13
07-11-2005, 02:58 PM
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This is in the theory of poker
the math for this is in the theory of poker ....
440,000 = (40/100)(2,000,000) - (60/100)(1,000,001) You will naturaly win 40% of the time, and then lose a dollar plus your million dollar ante the other sixty percent. Your EV is positive by 440,000 dollars.
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#14
07-11-2005, 04:13 PM
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Re: heads up theory
[ QUOTE ]
It doesn't matter. Either check, or bet, you'll lose .46 on average. You might as well check. In fact, it doesn't matter whether you bet or check no matter what number you choose. You'll win/lose the same amount. [/ QUOTE ] Actually, it does matter. Sklansky has to know what you're doing. If he doesn't, he'll raise with too many hands and call with too few. A random strategy has an EV of -0.50 as opposed to -0.46 if he you bet with 51+ and check with 50- and he knows this. So in other words you should check.
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#15
07-11-2005, 06:03 PM
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Re: This is in the theory of poker
Just been thinking about this problem, and I was wondering if your chances of winning are are not actually 40%.
If the deck has only one of each number between 1 and 100 (and assuming just integer values), then when you are dealt 40 there are 39 cards you beat, and 60 that beat you. Would it be correct that your chance of having the better hand is actually 39/99, not 40/100. I may be wrong, but just thought I'd write down what was going through my head.
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#16
07-11-2005, 06:04 PM
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Re: heads up theory
You mock him for being able to ante $1 million to play this game against you, but being unwilling to play Daniel Negreanu heads up at the Wynn. Then you check. He bets, you call, he shows you 39. Then Mason Malmuth pranks you with a tire iron in a back alley and takes back Sklansky's million and one.
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