Head Up Theory Question

[David Sklansky]

You and another player ante a dollar and both have unlimited money in front of you. You are both dealt one card from a deck where the cards are numbered from one to a million. You are dealt 999,999. You bet and get raised. How many times should you reraise, a dollar at a time before you just call against an expert? What about in Pot Limit?

[pheasant tail (no 18)]

21

[fnord_too]

Assuming that you bet or raise if you have a better hand than opponents average hand, you reraise 8 times. (when the opportunity to reraise time number 9 gets to you, his average hand is 999,998.1 without rounding.)

For pot limit, I would guess you bet the pot when you figure to be ahead of 66% of the hands he could have, since you are always offering him 2:1 (not sure about the first bet, probably still 500K or higher). That gets you to 5 reraises (all raises assumed to be full pot) before you stop if I did the math right.

In pot limit, though, I think you can make your bets more exactly, but I would really have to think about that and there are information considerations to not betting the size of the pot.

Edit - If your initial bet line is 666,667, it is still 5 reraises if I did the math correctly.

[brick]

499,998

[tipperdog]

You should reraise 9 times in the fixed limit game.

[Guruman]

Since I have unlimited money in front of me I do not fear the risk of ruin against my opponent, so I bet and raise until he calls.

Also, since we both have unlimited money the amount won or lost ends up being inconsequential anyway.

[bobbyi]

[ QUOTE ]
You and another player ante a dollar and both have unlimited money in front of you. You are both dealt one card from a deck where the cards are numbered from one to a million.

[/ QUOTE ]
Glad you have finally found the game to which you want to challenge Negreanu.

[RiverDood]

Just to keep it close, Daniel won't look at his cards

[felson]

In limit, I would put in fifteen bets (a bet and seven raises by me total) and call the sixteenth bet.

EDIT: actually, I think maybe I should put in 13 and call the 14th.

[fnord_too]

Actually, my answer is probably wrong since I did not take the initial pot into account correctly, and a propper strategy will definitely have some degree of bluffing in it. The only way my answers can be right is if you assume after a reraise or two that the liklihood of bluffing has been dimished to a negligible number. I am not sure though that, for instance, in the first case 500,000 is the line of demarkation to bet out with, so the average hand you reveal by betting might not be 750,000. In the end this wont impact the answer more than one reraise I am pretty sure, but it seems, nonetheless, important.