Tournament Theory question

[David Sklansky]

is B. The four players who got it right explained it well. HOWEVER if the tournament was a short one the answer would be D. Why?

[Al_Capone_Junior]

"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."

If you definitely will go broke before reaching the money 40% of the time (after skipping this bet), then C must be the correct answer.

We COULD consider that he MIGHT NOT reach 20,000 but ALSO might not go broke, or that he might reach 20,000 but still not make the money... and consider lots of other "what-ifs" but I doubt that's what DS was looking for.

So it seems you and I are in agreement.

al

[7stud]

[img]/images/graemlins/frown.gif[/img]

[crockpot]

remind me to bribe the tournament director to get a good seat at your table, and push all in whenever i want to steal any money you've put into the pot.

i'm only kidding, of course, and i understand your tournament goal is to win pots without showing down hands, but i still don't see how you can turn down a free 70% increase in your tournament EV at this point.

[Rushmore]

Although I have already seen the fact that the answer is B, I think Tim makes a good point. Wouldn't almost anyone here at 2+2 consider himself better than 60% to double up eventually playing "normally?"

If so, wouldn't the answer have to be (as I had originally thought) to go with E, as opposed to B?

Or do I overestimate the edge the better players have when factoring in the dead money (of which there is obviously less than in most tourneys, as it's a "main event," yet still significant, as with all tournaments these days)?

[emanon]

Selecting B greatly increases your standard deviation.

In a long tournament, this is offset by the increased liklihood of making it into the money due to the advantage conferred by starting out with a large stack. ie, you are increasing your risk for a higher EV.

However, in a short tournament, there will be fewer opportunities to take advantage of your stack. Thus, you will not be appreciably increasing your chances of finishing in the money. Therefore, you will be increasing risk without increasing return.

Thus, in a short tournament D is the correct choice.

[TimTimSalabim]

If the tournament was short enough that you could conceivably make it into the money without reaching 20k, that would offset the advantage of having the chips now, because if you get knocked out now you have zero chance of making the money. So, the answer shifts to D.

[TimTimSalabim]

Actually, I said the "top pros" would gauge their chance to reach the first double-up at much greater than 60% in a typical tournament they enter. Of course, it's all relative, no matter who you are. I'm sure most 2+2'ers have entered tournaments where they had greater than 60% chance to reach that first doubleup, and other, tougher tourneys where it might have been less than 60%. This problem is a good illustration of how your strategy changes depending on how good you are relative to the rest of the field. The less skill advantage you have, the more you roll the dice. But given the parameters of the problem, the answer is always B.

[slavic]

In a short tourney having extra chip equity is not as valuable because the blinds increase too fast to allow you to properly pumel the small stacks. Thus your additional equity risk does not gain you as much making it improper to do.

[Copernicus]

On the surface it seems straightforward that anything above 60% on this hand gets you to 20k with greater probability than you would have gotten there. The "gotcha" in the question may be the suggestion that this is a "long" tournament, ie there are many players in it, and the ommission of any probabilties of advancing beyond 20k.

Doubling up instantly without significantly affecting the number of opponents (many minus one is still many) is equivalent to starting out with twice the TCs without investing anything further, and doubles your tournament equity instantly. That would imply that 33% is sufficient. However that is contradicted by "don't risk it all on one bet if you have an edge on future bets" so more than 33% but less than 60% is called for. Since getting to 20k "normally" is the sum of many wagers which have some small edge pushes my answer closer to 60% (would a casino rather risk all of its bankroll on one roll of the dice with a small edge, or many smaller wagers), but not all the way to 60% because of the tournament equity considerations.

[i]The above answer assumes I have intepreted the question correctly, and differently than some of the first few responses indicate. I assume the alternative to getting to 20k with 60% probability is 40% of going broke. If you dont get to 20k anything less is obviously not in the money because there are many players * 20k in TCs. [\q]