Head Up Theory Question

[Shoe]

I agree with what you wrote, you basically put what I was thinking into better words than I could.

Unlike KK vs. AA, there is no flop to worry about here.

THIS IS BETTER THAN FLOPPING QUADS!!! It's also better than flopping a straight flush that could only lose to runner-runner royal (or whatever the worst beat possible is)! [img]/images/graemlins/grin.gif[/img]

I would definitely wager way more than $8 on this.

[nomofoshobro]

with unlimited money, isn't it possible that this game could be played infinitely?

i would say raise until he calls. what have you got to lose with unlimited money?

[Shoe]

[ 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. 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?


[/ QUOTE ]

Also, what if we reversed the situation. You are now playing "indian one to a million". High number wins. Each of you put a number on your forehead between one and a million. Your expert opponent has a 2 on his forehead. How many times would you re-raise him? The answer should be the same (i think, or maybe I'm just being dumb). Either way, it would be hard to get me to stop raising.

[IronUnkind]

In pot limit, I never stop reraising.

[Blackwolf]

Man if I had unlimited money I would hire a guy to sit and keep raising [img]/images/graemlins/tongue.gif[/img]

[brick]

[ QUOTE ]
In pot limit, I never stop reraising.

[/ QUOTE ]

what are you guys smoking? I want some.

[9cao]

I agree. I posted after that a mixed strategy of calling and folding after getting reraised the 8th time at a ratio of what the pot odds are offering (21:1 I think). This wouldn't allow your opponent any opportunity to exploit your strategy.

[David Sklansky]

I haven't made any attempt to figure out the exact answer. Just watching you guys.

[PairTheBoard]

[ QUOTE ]
[ QUOTE ]
Interesting. This is what i was thinking as well. Pot-odds certainly matter, and the way we halve the range seems to ignore any pot odds.

The first question, that noone really has answered is, "What is expert strategy here?"


[/ QUOTE ]

It would not be linear.

[/ QUOTE ]

My intuition this morning is telling me that as the pot odds go up, the Rate at which remaining Hand Ranges get reduced goes down. For example, the first bet cuts the Range of a Million in half. But his first raise cuts the remaining Half Million by only a Third say. Your reraise cuts the remaining Third by only 1/4 say, and so on. Maybe it works something like this.



PairTheBoard

[marv]

Also interesting would be answers for fewer cards. Assume no more than 1 million raises to make the game always terminate.

[Primarily to DS] What would your answers be for the cases with 10, 100 and 1000 cards, when we're dealt the second highest card as in your original post?

Marv