Tournament Theory question

[Piiop]

Magic Man makes good point that his chances of busting out are not 40%, rather he has a 60% chance of reaching 20k. That leaves the remaining 40% to mean that he can obtain anything from 0 to 19,999. And he could finish as high as 2nd place. Even if he does not make that 20k, he is still definitely alive in the tournament, though he may be at chip disadvantage, that doesn't really apply to the question.

So, back to the question, I think that I'm changing my answer to E. Unless the chance of me winning is very, very high, I'm folding. When I do fold where does it leave me? The same amount of chips as everyone else and I still have a good chance of continuing and possibly winning the tournament.

Just for fun I might call at 60% anyway [img]/images/graemlins/smile.gif[/img]

[slavic]

In a side game A would be the obvious answer, the one and done aspect of a NL Tourney makes A anything but correct in this aspect. Since you have a 60% chance of doubling up anyway, simply folding gives you a better shot of doubling up with a much lower variance than A, B, and C.

Now we add in that if you double up now and you are significantly better than you competition you can marshall yourself into the money a higher percentage of the time. So even though you add to your risk, you may very well out distance your average opponent so far as to minimize the luck factor of a large tournament. So the added gain pushes us back towards B or C. More to the point B.

I really don't like this answer and probably wouldn't push it in with anything less than 4.5 TO 1 but that's my tight early tourney play comming out. This would also be why your slider strategy seems to work so well.

[youtalkfunny]

[rayrns]

"player pushes all in in the SB and <b>unwittingly exposes</b> his cards to me in the big blind (no penalty)"
"And no other players."

At this point knowing what the player has, you should be 100% sure of a win or loss. Therefore why would you need more than a 50% chance of winning. I'll be different and vote for A.

[7stud]

The answer would be anything over 60% if when you folded you had a 40% chance of going bust. However, that's not necessarily the situation as magic man pointed out. If you play on, you also have chances of getting to 19k, 18k, 17k, .....4k, 3k, or 1k as well as 0 the other 40% of the time. If the probability of all those outcomes were equally likely, then the other 40% of the time, you would average a net gain or loss equal to 0 relative to your 10k now. Setting up some equations with that assumption in an attempt to quantify the difference in the expected value of calling versus folding:

x = probability of winning the current hand
y = probablilty of losing the current hand

EV(calling) = x(+10,000) + y(-10,000)
EV(of folding) = .6(+10,000) + .4(0)<---net change of 0
x + y = 1.0

Setting EV(calling) equal to EV(of folding):

10,000x - 10,000y = 6,000

Substituting in:

x = 1 -y

for x in the equation gives:

10,000(1-y) - 10,000y = 6,000
10,000 - 10,000y - 10,000y = 6,000
20,000y = 4,000
y = .20
=>
x= .80

How valid is the assumption that all the other outcomes below 20k are equally likely? It seems fairly reasonable, and in fact, just because you have a 60% chance of getting to 20k doesn't mean you have 0 chances of getting to 40k or 60k or even 100k the other 40% of the time, so the expected value of folding could be even higher.

I'll choose E.

[risen]

[ QUOTE ]
At this point knowing what the player has, you should be 100% sure of a win or loss. Therefore why would you need more than a 50% chance of winning. I'll be different and vote for A.

[/ QUOTE ]

Wow I can't think of any situation where you are a 100% favorite preflop. On the first day of a big money and what I hope to be a long tournament for me, I see no reason to ever be all in preflop. I'd muck AA vs a flashed 73o right here rather than go home with nothing to show for my entry fee but a bad beat story to post on RiveredAgain.com or somethin [img]/images/graemlins/grin.gif[/img] Doubling up this early is overrated anyway, you're not going to make it to the final table by default off of this win, and as you said you will more than likely get to 20K with your normal play. Put another way, would you put up the deed to your house and title to your car on a wager with a 40% chance of leaving you homeless?

[Leonardo]

I think its a very simple question. The answer is E, and I am 100% certain. If you have a 0.6 chance of getting to 20k, you are saying you have a 0.6 chance of doubling though. I will take that as a given that you always have a 0.6 chance of doubling up. So we are no longer playing cards, rather flipping coins(biased coins). You cant take a 0.6 chance for your whole stack. It would be much more prudent to take tonnes of 0.6 chances with small amounts. If the amounts were small enough, you are effectively guaranteed to win. The larger the amounts get, and in this case, 100% of your stack, the more you lose. I figure that taking this bet on the first hand with 60% chance of victory is taking a HUGE LOSS, way more than 10k, could be more than $1 Million. If you always have a 0.6 chance of doubling up, you would be mad to push your whole stack in (unless of course the blinds are huge, which you say they arent), with anything. Even AA may be better in the muck for the whole stack (am i taking this too far here?? [img]/images/graemlins/smile.gif[/img] )
regards
Leonardo

[ohnonotagain]

"I estimate my chances of getting to 20K by playing normally is 60%."

I understand this to mean that 60% is the chance of getting to 20K *before getting knocked out*. So it is meaningless to say that the statement implies a 40% chance of getting to some lesser amount: if you get a lesser amount you are still just on the way to trying to get 20K (or more, or to the money).

I think this is true because it is also fair to assume, in the context of a long 10K tournament, that the chances of having 20K (or less) being worth anything in itself is very small. The chances of getting into the money while *never* having had as much as 20K are very small indeed, although it does happen (note that many of the people who limp into the money with e.g. one chip left previously had a good deal more, and certainly twice the buy in). So you almost certainly have to get to 20K on the way to winning any money.

So I think DS's question really relates to the added value, if any, of having 20K (much) earlier than you "normally" would. if you have 20K after the first hand, I would say that is going to give you a significant period at the start of the tournament, when many other players are typically playing very tight, when you cannot go broke in a single hand, and everyone else (or at least many people) at your table can. In the terminology of DS's tournament book, "they're broke, they're done" holds good, but "you're broke, you're done" does not. This should allow you to steal a lot of chips.

If you have the skills to exploit this situation, then I would say that the value of having 20K earlier than "normal" is substantial. This leaves options "A" and "B" as possible answers. I do not know how to quantify the above advantage, but very much doubt if it is worth a 10% difference in your chance of reaching 20K. So I would answer "B".

Oh no!! Not again!

[Al_Capone_Junior]

I think that this situation should go on the principle that it's better to pass up a merely good bet now if losing that bet will prevent you from making an even better bet later. So if you have a 50.00001-59.99999% chance of doubling now, but losing would prevent you from getting a 60% chance of doubling later, then you should definitely fold.

Therefore the answer must be C. You should not pass up a better bet now if you doing so only allows you to make a worse bet later.

al

[Al_Capone_Junior]

I did not consider the possibility of NOT doubling, but also NOT going broke by passing up this bet. Since going broke is of course bad, I should have figured in the possibility of not going broke, but not doubling either, thus still having a chance to win anyway. Assuming this, I would accept that E) significantly more than 60% could be the best answer.

al