Head Up Theory Question

[BeerMoney]

I made a post and it was a unanimous vote that you play "HeadS up", not "Head Up"

[9cao]

Actually, I don't think it is nearly as simple as I thought. Even if you get raised after your 8th reraise you would have to mix your strategy to call 20/21 times and fold 1/21 times.

[reubenf]

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21

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That looks like log2 rather than log4.

Not that I'm saying log4 is the correct answer.

[NYCNative]

I would reraise indefinitely. I would probably do this as well if I was dealt 999,998 even though my opponent is now twice as likely to beat me. [img]/images/graemlins/smile.gif[/img]

Not sure about 999,997...

I think I see the point in this excersise though. At what point in the cards do you start to worry you're beat? Well, it's somewhere between 500,000 and 999,999, I suppose... But where?

[Shoe]

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Actually, I don't think it is nearly as simple as I thought. Even if you get raised after your 8th reraise you would have to mix your strategy to call 20/21 times and fold 1/21 times.

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Are you saying you would fold 999,999 1/21 times just to mix up your strategy? This is clearly wrong. But maybe I am misunderstanding your post. Also, an expert would not play so predictably in such a way that he/she would always have 1 million after raising 8 times.

[PairTheBoard]

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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?

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Of course, and exactly my point if the number for 999,999 vs 1,000,000 is as few as 9.

PairTheBoard

[Shoe]

I disagree that the number for 999,999 vs 1,000,000 is 9. I think that is way too weak-tight. I would put the number in the hundreds of thousands.

However, I anxiously await more info from David, explaining why (if no one gets the correct answer first).

[rwesty]

You should just call, to trick the other expert.

[raisins]

I don't know. This question is hard. It's a bit more advanced than anything in the [0,1] game although clearly related to it.

Optimally, we should bluff some small percentage of the time (a fraction of the worst hands). The bluff raise would be this same percentage of the bluffing set. And so on, each successive raise reducing the bluffing hands set from the previous raise by the same fraction. Assume we bluff with the first bet with the bottom 20% of our hands, a guess but I think a reasonable one. The reraise by an expert will be with the bottom 4% of hands. Obviously this series quickly approaches 0.

We call at the ratio of pot size over pot size +1 of our set of hands that can beat a bluff. So on the first bet if it is right for the opponent to bluff with 20% of his hands then 80% of our hands beat all his bluffs. 3 (pot size) / 4 (pot size +1) of 80% is 60% we call with 60% of our bluff beating hands. As with each succesive raise the set of bluffing hands gets smaller then the smaller the set of bluff catching hands. This applies to our opponent just as much. So how many times can we bet this hand for value?

A guess is 8 or 9. As the chances of bluffing descrease the number of calling hands gets smaller. Both of these happen fast.

With pot limit betting it happens even faster. I'm assuming the only bet size is the pot. In limit the ratio of bluff catching hands gets larger, but in pot limit it stays the same, 2/3. The number of bluffing hands is smaller because the rish reward ratio is worse. So the set of bluff catching calling hands is smaller and the group of value betting hands decreases as well. I'm thinking you can only bet it for value somewhere around 4 times.

Conclusion.

limit - 8 or 9 times
pot limit (must bet pot) - 4 times

regards,

raisins

[ClaytonN]

I think the answer is the quickest algorithm to find 999,999

IE start at 500,000 higher go to 750,000 higher go to 875,000

etc etc etc etc