Head Up Theory Question

[threeonefour]

i never stop raising, if he has the nuts he will never stop raising either so there will never be a showdown. plus no matter how much i lose i still have an infinite amount left.

i'm rich! let's gambool

[Shoe]

I would be willing to wager about $900,000 on this, give or take a few thousand depending on if he is wearing sunglasses or not.

Please explain to me people why you would only be willing to raise 13 or 14 times when you only have a .000001 chance of being beat. I think you guys are playing scared. You have a huge edge here and need to push it to the max.

[GFunk911]

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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?

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Can I assume at the end, you call or fold with a game theoretically optimal frequency?

[uphigh_downlow]

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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.

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Assuming there is nobluffing

Are you basing your reply on limiting his range by a fraction every time he reraises.

When would you raise if your oppnent leads out (no bluffing) And when would you simply call?

This is what I made of it.

Worst case, you open with 500000, he raises with atleast 750,000, you raise with atleast 875,000, and so on.

Is this correct?

Do pot-odds matter at all here? Would the raising range get progressively smaller (more than half) since there is more money in the pot?

[9cao]

After the first bet I belive you should reraise 8 times, and you should fold to his/her reraise after your 8th reraise since you know he/she cannot be holding the 999,999th card. (edit: obvioulsy for fixed limit only).

[PairTheBoard]

If the answer is as few as 9 as fnord and tipperdog say it's a good lesson and I happen to have a story to illustrate the point.

The one time I played at a table with David was a 10-20 game at the Mirage years ago. I had KK and the guy next to David had AA. This may have been my first experience with KK vs AA. Unlimited raising heads up and I reraised the hell out of my KK - I'm sure I went way too far with them. When I finally just called I heard David on the other side of the table comment something like, "gee I wonder what they've got?"

With unlimited reraises, How many reraises should you put in preflop with KK?

PairTheBoard

[Shoe]

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With unlimited reraises, How many reraises should you put in preflop with KK?


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many less than with 999,999 vs. 1,000,000. Do you see why?

[chopchoi]

Normally, if he bets the pot, you figure he has a hand that is better than 50% of all possible hands. Of course, bluffing is possible early on, but if he doesn't have a legit hand, he will eventually grow tired of bluffing, and call or fold. If he continues to bet the pot, we must assume he has a hand.

My guess is, each time the pot is bet, you can narrow your opponents possible hands by half. So with his first bet, you can assume he has a hand higher than 500,000. When you re-raise, he can assume that you have a hand better than 750,000. Eventually, it will get to the point where he would not bet without the nuts. You call one bet before it gets to that point.

[bobbyi]

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My guess is, each time the pot is bet, you can narrow your opponents possible hands by half. So with his first bet, you can assume he has a hand higher than 500,000.

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So you think the right strategy is to open for a pot-sized bet with anything 500,000 or up? I'm not sure I see why that is right. When you bet there, you are offering your opponent 2-to-1 on a call. So he should call (or reraise) if his hand is good a third of the time. This means that if he think you will bet with anything, he should call (or reraise) with 333,333 or better.

This means that your bet would be a loser because more than half the hands in the range [333,333 - 1,000,000] beat your 500,000. Further, his hand range is probably stronger than that since he knows you hold better than a random card since you chose to bet. And you will sometimes be reraised and then have to either call and lose or fold and possibly get bluffed out. So it looks to me like opening for the pot with 500,000 or up can't be the right strategy and you should need a better hand than that.

[brick]

How many less?

If you are dealt #1,000,000 you're not going to be worried until you put $1,000,000 in the pot. Then you're going to be very worried and say "Did I miss a rule or something?"

With hand number #999,999 you're not worried until you put $999,999 then you're going to say "It's one in a million!"

anyway it seems I don't understand the concept.