Hypothetical Heads Up Gambling Situation

[Nichomacheo]

I was playing live today and I was thinking of offering my buddy this deal.

For $200, I will play this game with you:

We both get dealt two preflop cards. I will call your all in at any point preflop. You either go all in or fold. If you fold, we do this again, for ten total times. On the tenth hand, if you havent gone all in preflop, you are forced to play whatever hand you get.

If you are my buddy, what hand are you looking for preflop and how long do you wait to get it?

Have fun.
Nichomacheo

[roommate]

I would not take this bet... and neither should anyone else.

*****SPECIAL NEWS BULLETIN!!*****
NICHOMACHEO IS THE LARGEST LUCK-BOX IN THE WORLD

~rob

[XxPenguinxX]

AA-22, Ax, KQ, KJ, QJ, KTs, QTs, JTs
From hand 7, add in any two cards 9 or higher.

You?

[thechainsaw]

AA
KK
QQ
JJ
AK s
AQ s
TT
AK
AJ s
KQ s
99
AT s
AQ
KJ s
88
QJ s
KT s
AJ
A9 s
QT s
KQ

EDIT: this was my first reaction, though after a few minutes thought, im thinking a MUCH wider range is appropriate

[thechainsaw]

PS is there no blind structure? Otherwise I will play A8s

[thechainsaw]

I would play the above range first up, with the range increasing on each failure. On the final attempt, I would play any hand, on the penultimate, I would play any 50% hand.

EDIT: this is not true, since you are 50% at the end anyway, you must play only 50% hands

[thechainsaw]

[ QUOTE ]
AA-22, Ax, KQ, KJ, QJ, KTs, QTs, JTs
From hand 7, add in any two cards 9 or higher.

You?

[/ QUOTE ]

22 is a mistake, you will play against 2 overcards for a coin toss, imho

[thechainsaw]

Some analysis.

The expected median on n trials on the beta distribution is the top hand minus 1/n. So in 10 goes you normally expect the maximum to peak around 90% therefore playing one of these hands is a good idea.

As you play more your bet range increases so hat you aim to play more hands. On the last trial, anything about 50% is playable. On the penultimate, a hand in the top third, one before that a hand in the top quarter etc.

I cant prove it, but does that sound logical?

[Nichomacheo]

chainsaw,

I'm not sure you 100% understood. On the tenth hand you must play whatever hand you are dealt. Therefore, if you fold nine times, you are forced into a "coin flip" situation -- whoever wins the hand after five cards are dealt on the table. But along the way, you can decide "Hey, I want to wait a few hands because even though Q8o might be favorite against a random hand, I will probably get a better hand soon." The dilema is that the longer you wait for a good hand, the wider your calling range has to be. You might fold K3 on the first hand waiting for an ace, but eventually you have to call with K3 because thats favorite over when you can expect to get on the next two or three hands. You might go on a bad run -- 27, 39, T4 or something. OR you could get your AT. Gambool.

I'll add a twist when I get more initial responses.

[AK-47]

Wait for any top 49% hand and push. You'll be a more than 1-to-1 favorite on the pot, while the pot odds are always 1-to-1 (I don't consider blinds structure here).
This is enough to give you the edge.
The least favorable case is when you reach the 10th hand, but :
1) it is VERY VERY unlikely
2) it's a coin flip, you are not an underdog

So your buddy has a very favorable deal here...