Tournament Theory question

[storm_madden]

Without looking at the other answers I say E.

The other 40% of the time you dont make 20K by playing normally you could have nonzero amounts

Some of the sixty % of the times you make 20K you could have much more than 20K.

[storm_madden]

After reading the clarification I interpret it to mean 40% of the time you will go broke since David did not include a time frame. It's different I think if he were to say 60% chance of doubling up on the first day or a given time frame.

A hand like AcQh vs KcJd is a 63% to 37% matchup (Wins 62.8 ties 0.2). Would I call with it?

62.8% of the time I double up, which is better than the 60% if I just play normally. There is no reason why a big stack will hurt me in the future, it will probably help me. It's better to double up now than later at the same odds because the blinds rise.

This hand allows you to fast forward the tournament at better than expected odds. It's even better than a fast forward, more like a time warp where you go forward and back in time with your chips.

It's almost like asking would you like 20K in chips at the beginning of the first day or at the end. Do you want to be chip leader after first hand or another chump with a par stack of 20K at the end of day one?

There are no real hands in Holdem that are exactly 60% propositions. But is it a push? Well, I think I'm better off taking a 60% proposition immediately rather than spend all day slugging at it. Again, do you want your 20K now or at the end of day one? So I'll take a bit less than 60%.

I take B.

[Josh W]

But most (all) tourny pro's accept E as the correct answer, and its not close.

[TimTimSalabim]

Actually, most top pros would probably assess their chances of getting to 20k at much greater than 60%. But if it is indeed 60% as stated in the problem, why not take the chance now instead of later? You lose nothing, and in fact you gain a slight edge having the chips now. I'm sticking with "B".

[Bozeman]

This is what I hate about the questions posed by Sklansky here. He poses a question in a tone that the answer is obvious, but often incompletely specifies the conditions such that multiple answers are possible. Maybe he just likes to have multiple answers so that more back and forth goes on.

If he means that there is a 60% chance you will have 20K at the end of the first day (or even some time during the first day), E is the obvious answer.

If instead he means that you have a 60% chance that you largest stack achieved in the tournament is 20K or greater, then C seems to be the answer. B is also a possible answer since having a large stack now may give you more opportunities. Some would, however, say D because they overestimate the difference in chip values between small and large stacks.

Since the second alternative has more gray area, he must have meant the first, though the wording seems closer to the second.

Arghhhhhh,
Craig

[elysium]

hi mr. sklansky
i think you would need significantly greater than the 60%. the reason is that by playing normally in many, many non-all-ins, and spreading the risk over a wide area, you can reserve your all-in calls for times when you have significantly greater than the 60%.

if you have a 60% chance when playing normally in the non-all-ins, but then are forced to play 60% all-ins also, al-ins in which you have a 60% chance of winning, the odds of surviving go down to about 40%. and playing normally cannot include going all-in with a hand that you normally wouldn't go all-in with.

i think you would need to be about a 70% favorite, excluding the effect of blinds, in order to go all-in hot and cold.

[BB King's]

... B !
Allow me to ellaborate a little !
C is of course wrong. Call now - earn you 2k and use the rest of the day for futher improvent.

[Cosimo]

My first guess would have been E. Al Capone Jr makes a good point here. Mathematically, C is correct.

A timeframe for getting to 20k IS specified, implicitly: the whole tournament. I am choosing to ignore the chance of getting into the money without ever having broken 20k, because I think that is so low as to not affect the decision. It's a long tournament; I give it a 0% chance.

The correct conclusion is that you have a 40% chance of going broke before making it to 20k if you fold. Likewise, on this hand, you have a 40% chance of going broke before making it to 20k. The two options are a push, answer C.

Saying "if you make an infinite number of small bets then you are guaranteed to get to 20k because you have a 60% chance of winning" (or whatever) is incorrect. If your play after this hand gave you a greater than 60% chance of getting to 20k, then the problem would be "I estimate my chances of getting to 20k to be 100%." Whether you double up now or fold and go for it later does not matter; both ways you still have a 60% chance of getting to 20k before going broke.

It doesn't matter what "most pros" do--that's arguement from authority.

-Cosimo

[7stud]

Leonardo,

I like your analysis and your confidience, however as you must know, if the player folds, it is most likely that not a single one of the ensuing hands will ever be equal to a 60% coin flip. The player will have to play the future hands according to whether they are +EV or not--not wait and play only those hands where he has a 60% chance of winning the hand. Hands he plays will sometimes have a 30% chance of winning if the pot odds are right, and some other hands may have a 65% chance of winning. The good player will be able to extract some extra value for each hand he does play. If the player waited and only played those hands where he had a 60% chance of winning, his stack would get blinded away, and the tourney would end with him maybe never even having played a single hand.

In the end, having a 60% chance of getting to 20k is not the same thing as having a 60% chance of winning every hand, so the player cannot fold and then get many 60% coin flips instead.

[Deadbuddha]

Id go for d on this one, no point on risking what i can most likely get by playing normally.