Head Up Theory Question

[Gabe]

I think you should raise his ass three times, unless there's more to this than I see, and there probably is because you guys are all geniuses and everything. There are too many replies to read.

[chapstick]

Is the equivalent problem, but with a smaller decks, so much less interesting that they are not worth trying to "solve" first? Maybe we can we then extrapolate to put limits on the result with a million card deck. What if the deck had 5 cards, and you were dealt the 4. How many raises would you put in before you called?

[marv]

[ QUOTE ]
Is the equivalent problem, but with a smaller decks, so much less interesting that they are not worth trying to "solve" first? Maybe we can we then extrapolate to put limits on the result with a million card deck. What if the deck had 5 cards, and you were dealt the 4. How many raises would you put in before you called?

[/ QUOTE ]

With 5 cards and at most 45 bets/raises, one optimal solution does the following: you open the betting 13% of the time and fold 100% of the time if raised.

Marv

[xpsyuvz]

Marv,

What about when the deck has 100 cards. When does the 99-player call/fold?
It seems that after a point having more available raises in the game wouldn't change much for any optimal strategy.

For example: in the 100 card game, I would imagine the 99-player would never go beyond say the 5th raise.


How are you figuring this out? Do you have a program or something?

[chapstick]

Marv, your response is interesting, but you are proposing not to initially bet often. Sklansky's question states that you lay the first bet. How does your answer to the 5-card deck change if you force yourself to make the first bet?

Thanks

[Gabe]

I thought it was 999 out of 1000.

[marv]

[ QUOTE ]
Marv, your response is interesting, but you are proposing not to initially bet often. Sklansky's question states that you lay the first bet. How does your answer to the 5-card deck change if you force yourself to make the first bet?

Thanks

[/ QUOTE ]

If the first player must raise at his first action with a 4, then he should call a raise 72.5% of the time and fold 27.5% .

However this game is much worse than if he is allowed to check with a 4. It's value is -8.4% rather than -5.2% if he is allowed to check with a 4.

Marv

[marv]

[ QUOTE ]
Marv,

What about when the deck has 100 cards. When does the 99-player call/fold?
It seems that after a point having more available raises in the game wouldn't change much for any optimal strategy.

For example: in the 100 card game, I would imagine the 99-player would never go beyond say the 5th raise.


How are you figuring this out? Do you have a program or something?

[/ QUOTE ]

[I have a program for these sorts of games.]

With 100 cards (and at most 25 raises), an optimal strategy with a 99 is to open the betting 95% of the time and then call after the 4th bet/raise:

us them

bet raise
raise raise
call

Your intuition is right!

Marv

[chapstick]

[ QUOTE ]

[I have a program for these sorts of games.]

With 100 cards (and at most 25 raises), an optimal strategy with a 99 is to open the betting 95% of the time and then call after the 4th bet/raise:


[/ QUOTE ]

Marv, can your code do more than a 100-card deck? Could you do the series of decks: 10, 20, 40, 80, 160, 320 and see if there is a trend, to extrapolate to a million, as to when you should stop raising and call?

Thanks

[xpsyuvz]

Marv, cool, thanks for running that 100 card scenario for me.