% of time winner knocks out most players?

[StepBangin]

I tried this in the Probablity forum but figured I would get a more interesting discussion over here. Im not sure if it has been discussed before.

If we take a large sample, say 500,000 NLHE tournaments, what percent of the time do you think the winner of the tournament also knocked out the most amount of players?

I have no clue but thought it might strike up an interesting discussion.

Does your answer change for limit or pot limit?

What about other games like Omaha or Stud?

[valenzuela]

Depends on number of players in the tournaments ldo.

[valenzuela]

I have the following so far:
2 players --> 100%
3 players --> 66%

[VarlosZ]

3 players is also 100%, if you count ties.

[thylacine]

You need a sample of more like 500,000,000.

[Jcrew]

Unless you make some simplifying assumptions (i.e. person knocking out a player still remains equal probability of winning to everyone remaining), you have to Monte Carlo this.

[willie24]

hmm. the winner is always the favorite to knock out the most players, relative to the other places.

for example, 1st place on average might knock out 4.9 players. 2nd place 3.8, 3rd place 3.3 etc. in any format, 1st place is going to be highest relative to the other places, simply because he always knocks out 2nd place. fairly obvious.

however, more important for what you are asking is- who knocks out more players, 1st place, or the non-first place player from the tournament who knocked out the most players.

i would guess that in most very large tournaments, it is the non-first place player.

here's why: we know that the 1st place player gained A LOT of chips (on average) by knocking out 2nd place, and any other player he might have knocked out at the end of the tournament. but over the course of the tournament, most hands where a player was knocked out were for much smaller pots. there are usually some players who showdown allin a lot early, and a few of them get lucky and win a high number of times, resulting in a lot of "KOs" but a relatively small number of chips (compared to the chips that are changing hands at the final table). since showing down all-in a lot early is, in general, a -EV strategy, we would expect the player who does this to be a poor player, and would give him less of a shot of winning the tournament.

on the other hand, the strongest players tend to lay low when the stakes are low, but steal when the stakes are higher - resulting in a lot of chips being gained without a lot of showdowns. so they usually have fewer KOs than their chipstacks might suggest.

these factors would lead me to guess that the typical KO leader is someone who goes nuts early, gets hot and knocks out a bunch when the stakes are low...and then is lucky enough to knock out a few when the stakes get higher also. has a lower chance of taking 1st because he is not an excellent tournament player, and because he gained a relatively low # of chips from his KOs

[EvilSteve]

Yeah you'd need to run lots of simulations with semi-realistic computer AI tournaments, or have the data from a large sample of actual tournaments to find the answer. I tend to agree that often it wouldn't be the winner or even a high finisher who knocks out the most players, but instead a maniac who manages to go on a tear for a while before his luck runs out.

What I think would be an interesting gimmick is if a poker site kept a running total of the number of "scalps" collected by each player during the course of a tournament, and displayed it for everyone to see. So midway through a tournament a new player is moved to your table. If he has only 3 scalps you have reason to believe he's been laying low, and if he has 12 scalps you likely have a maniac on your hands. Also some players would get overly caught up in scalp collecting, which would make the play wilder than normal but those who properly adjusted for this tendency could benefit.

[VarlosZ]

[ QUOTE ]
What I think would be an interesting gimmick is if a poker site kept a running total of the number of "scalps" collected by each player during the course of a tournament, and displayed it for everyone to see. So midway through a tournament a new player is moved to your table. If he has only 3 scalps you have reason to believe he's been laying low, and if he has 12 scalps you likely have a maniac on your hands. Also some players would get overly caught up in scalp collecting, which would make the play wilder than normal but those who properly adjusted for this tendency could benefit.

[/ QUOTE ]

I love this idea.