My hand against Chris Moneymaker

[prospector]

Before any further discussion of the effect of one hand on a player's chances, I believe we need to have a mutual understanding of the situation we are talking about. I think there are two cases. Case 1 (which I understood to be the case in your first post on 10%-20%) concerns an expert player in a large slow-moving tournament. This expert is much better than most of the field; so good that his initial chance of making the final table is 10%, even though there are a large number, say 500, players in the tournament. Case 2 (which you seemed to be describing in your first answer to my 10.1% post) is a ten player tournament where all are equally skilled.

Let's dispose of Case 2 immediately. I agree with you (and S&M). Doubling through in the first hand does nearly double our hero's chances.

In case 1, it's my intuitive belief that doubling through in the first hand does not have as large an effect on the expert's chance. His expert play in many, many hands will dilute the effect of that first hand. Of course, one might argue that an expert would never allow the chance that the first hand would knock him out of the tournament. But that is beside the point. We could set up artificial cases in which the expert (A)starts with the same number of chips as everyone else or (B)starts with twice as many as everyone else. How say you about case 1?

[microlimitaddict]

again, i consider myself to be something of a novice on these ideas....but i believe this is kind of like the corollary of Sklansky's tourney All-in principle.

and i would have to agree with Dutch that there is a big difference when we're talking about 5 day tourneys. there is virtually no point in trying to double up on the first hand in this situation.
i think Dutch said he had gone all-in just one time prior to his hand with Moneymaker (did i remember this correctly>> too lazy to confirm). if this is true then think about it....just one all-in in 4 days. if true, that means he built his stack by clawing his way along.

in one of the WSOP episodes I saw Lederer lay down a couple of hands where he was at the advantage and I think he sensed that he was at an advantage. but he would rather live to fight another day then to roll the dice there. i thought his lay-downs were impressve even though it probably didn't look that way to most viewers since he indeed had the best hand when he got pushed out.

of course you have to take risks in order to move up and make it to the final day....but if you take more than one 3:2 risk or more than three 2:1 risks (with all your chips on the line) in a single tourney, then you are letting luck take an even greater role in your tourney fate.

i believe the influence on the +EV of doubling up early is being greatly exaggerated here and would be very interested in Sklansky or Malmuth's opinion on this. in a 5 day tourney, i would suggest that doubling chips in the first hand certainly does not double your chances of making the final table.

regardless of your impressions of my novice observations
I have enjoyed reading the ideas presented in this thread.

[M.B.E.]

No, you totally misunderstand.

I was positing a case where the player is somewhat above average, having a 10% chance of finishing in the money (i.e. top 65) out of 800 players. I say that if this player doubles through on the first hand, his chance of finishing in the money will almost double: it will increase to something like 19%. Your "intuitive belief" that doubling your stack would only increase your chance of finishing in the money from 10% to 10.1% is ridiculous.

This thread is not concerned with what you call case 2, "a ten player tournament where all are equally skilled". I don't know why you brought that up. This thread is about how to play in the WSOP.

Your "case 1" concerned a player so skilled that he has a 10% probability of making the final table (i.e. top 10) of the WSOP. Well, nobody can be that skilled, unless they have X-ray vision so they always know what their opponents hold and what cards are coming.

On the other hand, it's pretty reasonable to suppose that someone who plays a little better than average has a 10% chance of finishing in the money (i.e. top 65).

[Daliman]

Well Dutch, with the small amount I have for context,I think it was a case of a couple excellent plays, preceded by a bad one. I like your thinking on what you want him to think, and also what you wanted to represent having. MM's call with the 33 was NOT lucky. He made a good, strong intuitive call. I agree that you may have been better served by more like a 300K raise, and think he may have possibly folded to it given that it represents a bet that wants to be called more, but that's my opinion. It annoys me severely when people say MM was lucky there. If he was lucky, please tell me where he was ever behind in the hand. The BAD play was him calling with 33 preflop, a hand in which you are always either a small favorite or big dog, plus, you never know exactly where you are with it. The play to make there is all-in with the 33, if you're going to play it at all. I think you took it pretty well overall, and may be one of the few people you understood your "chip tricks intimidation" was tongue in cheek, as well as most of your other interview talk. You're a young guy, having a great time, doing well in the biggest tourney in the world, period. Cocky? Maybe a little, but more of an affable cockiness. My question on the Pokerspot issue is: wouldn't you being 22 or so now put you at about 18 at the time of Pokerspot? How the hell did you end up running a fairly major(at the time) poker site, and do you feel your age and lack of experience had something to do with the ultimate downfall? PS died owing me about $900 (maybe more, maybe less, tuff to remember now), and, though I'd love to have you pay me that $$$, I kinda have to agree with your stance that those are corporate debts, sorta like if people invested in a company with a positive expectation yet never recieved their dividends, although I wouldn't place it anywhere near the level of smaller scale ENRON; I'd like to think it was mismanagement and poor business model that doomed PS, and not corporate malfeasance. Also, if you graduated law school at like 18, what the hell are you doing with your life now? I'd have to consider it a shame if someone of your intelligence and drive now just plays poker for a living, but hell, who am I to talk. I have a 151 IQ and sell tires for a living, (mainly).

[prospector]

If I may quote form a post in this thread by a self-acknowleged expert:

"It's well known that if all players are equally skilful, your probability of winning the tournament is precisely the number of tournament chips you have divided by the number of tournament chips in play. Double your chips and you double your probability of winning. Your probability of finishing 2nd, 3rd, 4th, etc. might not double but it would be close."

It was you, not I, who brought up this point. If my
position is so ridiculous, please refute it rather than insulting me and my posts.

[Daliman]

The AK vs. QJo discussion seems to boil doen pretty easy to me; Call. There are going to be very few instances where you are going to be able to make a bet all-in and be guaranteed a win. Tournament poker is all about pressing edges; if your edge is that you are of of the best players, maybe you might not want to make this call. If you have to playing edge, your edge is playing good cards, that's all. You will be outplayed otherwise, so get it all in there with an edge whenever possible. A corollary to this was posted a few moths ago in the probability section I belive by me which was brilliantly responded to by Bruce Z. I believe, where I put forth the hypothetical situation of myself vs. Johnny Chan where on the first hand of WSOP big event, I go all-in with 67s, show him my cards, and he has aces. I wondered whether or not he would be better off folding than taking a 25% chance at being knocked out of the tourney and Bruce Z said no, under any circumstances player-wise in this situation, Aces should call, and that the mathematical probability of doubling his stack FAR outweighed the possibility of being busted. And yes, doubling your stack effectively doubles your chance of cashing; it's just the exact chip-for-chip average of all things being equal that makes it so, in most any situation. For example: lets say 100 people are in a tourney, you go all in, double through, everyone else chops and has exactly what they started with. you have just gone from having 1% of all chips e.g. a 1 in 100 chance of winning(all things/players equal) to 2% of all chips, PLUS ONE LESS PLAYER TO HAVE TO BEAT, now making you more like a 2 in 99 shot, or 1 in 49.5!(a bit off, i'm sure, but only a bit) See, MORE than double. MAKE THAT CALL!
[img]/images/graemlins/grin.gif[/img]

[prospector]

O.K.M.B.E.. lets take your player and your formula and go a little further. Doubling his stack doubles his chances, right. So, he begins with a 10% chance of being in the money.In the first hand of the tournament, he doubles through and now has about a 20% chance, as you said. In the second hand of the tournament, he get two more players all in and doubles his stack again. Now he has about a 40% chance to get paid according to your formula. And in the third hand of the tournament four opponents bite the dust and he double up again. 80% chance, right. And in the fourth hand of the tournament,..... well, lets not go there, M.B.E. Lets leave him with his near 80% chance to be in the money. What do you think? Does he have an 80% chance?

[Bozeman]

No, but he probably has at least 50% chance (the corrections become significant, though not huge, as the stack gets larger and the probability approaches one), while you would say that he has 11%.

You really think even a great player hardly cares to double his stack?

Craig

[M.B.E.]

[ QUOTE ]
So, he begins with a 10% chance of being in the money.In the first hand of the tournament, he doubles through and now has about a 20% chance, as you said. In the second hand of the tournament, he get two more players all in and doubles his stack again. Now he has about a 40% chance to get paid according to your formula. And in the third hand of the tournament four opponents bite the dust and he double up again. 80% chance, right.

[/ QUOTE ]

I agree with Bozeman that the probability would be less than 80%, but still excellent -- easily over 50%.

If we were just looking at this player's probability of winning -- finishing first -- then having octupled his chips so early on his probability of winning would have close to octupled. If this player were exactly average in skill, i.e. he started off with a 1/800 probability of winning (assuming exactly 800 entrants), then yes I think if he somehow octupled his chips early on he would then have a 1/100 probability of winning the whole thing. But not precisely, because we've already had something like six or seven players eliminated, who probably were some of the weaker ones. That means that even though this player began the tournament with an average skill level, among the 793 remaining players he's a tiny bit below average. (On the other hand, his huge flukey early lead could have a psychological effect on other remaining players, which would increase his chances if he took advantage of it properly.)

If the player was a little above average in skill, let's say starting with a 1/600 probability of winning the whole thing, then octupling his chips should theoretically result in a probability of slightly less than 8/600 to win (but only very slightly less).

However when we're looking at the probability of finishing in the money (top 63 or so), even if every player in the tournament was equally skilled the probability would not exactly octuple when your chips octuple. It's because the increase in your probability of finishing first interferes with the probability of finishing 2nd, 3rd, 4th etc.

Prospector -- sorry if you were insulted by my earlier post; I might have gotten carried away with my sarcastic tone. I am enjoying this debate and have nothing against you personally. Also the confusion between "finishing in the money" and "making the final table" was partly my fault because I accidentally mixed them up in one of my own posts on this thread.

[prospector]

Apology accepted, M.B.E. I probably owe you one as well. I'm still perplexed about the mathematical foundation for your assertions. You state your conclusions, but don't demonstrate how you get from here to there.