Positive EV article - PLEASE HELP

[Bicycles_Biatch]

Please help me settle an argument.

About a year ago I read an article (I think it was by Mason Malmuth) regarding tournaments and +EV.

It basically outlined that in tournament poker... if you are better than 50% of the field... your return on investment was double the buy-in.

Is this TOTALLY out of line? Did I miss read the article?

Theory help please.

[jay_shark]

How do you define your roi on "being better than half the field " ?

You cannot say much about your win rate if you're marginally better than half the people but you get annihilated by the other 50% . This is too vague to give a definitive answer .

[JammyDodga]

Assuming the distribution of ROI was evenly spread over the field, and assuming an entry fee of 10%, if you are just better than half the people, you will have a negative ROI of 10%... I think.

[Sherman]

[ QUOTE ]
Assuming the distribution of ROI was evenly spread over the field, and assuming an entry fee of 10%, if you are just better than half the people, you will have a negative ROI of 10%... I think.

[/ QUOTE ]

I don't think so. Assuming you are better than 50% of the field by a significant amount and you aren't that much worse than the top 1/2 of the field, MTTs ought to be profitable for you.

Think of it this way...Does everyone who plays MTTs professionally only enter MTTs if they think they are the best player in the field? No. Absolutely not. There are plenty of donks who go around and increase the equity in the tournaments. Beyond that, by the end of the MTT when you run into the better players, much of their skill advantage is negated by stack to blind ratios.

[Cheetah]

[ QUOTE ]
How do you define your roi on "being better than half the field " ?

You cannot say much about your win rate if you're marginally better than half the people but you get annihilated by the other 50% . This is too vague to give a definitive answer .

[/ QUOTE ]

I agree. It is impossible to deduce a win rate even if somehow "better" could be defined. Here is an example to illustrate this point:

Say that in a MTT 50% of players fold all their hands, but say that Hero steals one BB per orbit, but otherwise folds like they do. Hero is definitely "better" than 50%, but Hero is still losing chips and will typically end up out of the money.

So being "better" than 50% can even result in losses [img]/images/graemlins/blush.gif[/img] In general, I don't think it is possible to make quantitative predictions based on "better" than X%.

[Bicycles_Biatch]

I agree that "better" is about as vague as it gets.

However, I'm just trying to quantify your positive EV if you feel you play "better" than 1/2 the field.

What I'm saying I guess is that if there was no fee and 100% of the buy-in went to the prize pool... over millions of tournaments... what would your positive EV be if you were ALWAYS better than at least half the field?

[Cheetah]

[ QUOTE ]
I agree that "better" is about as vague as it gets.

However, I'm just trying to quantify your positive EV if you feel you play "better" than 1/2 the field.

What I'm saying I guess is that if there was no fee and 100% of the buy-in went to the prize pool... over millions of tournaments... what would your positive EV be if you were ALWAYS better than at least half the field?

[/ QUOTE ]

It still cannot be quantified.

Let's say that 1,000 players play the same tournament 1,000 times. We can then use their winnings (or win rate) as a measure of "better".

Let's say that player Hero is better than 50% of the players according to that measure. Let's further assume that they are the worst possible players and they never win ANYTHING. (That would be the case if they just keep folding as in my previous example.) The net result would be that there would be TWICE as much money availble to be won. If the top 50% all had equal skill, then the win rate for Hero would be exactly 2 times that of the buy-in. On the other hand, if top 50% were all world champions except for player Hero, then Hero will be losing most of the time.

Another way to look at it is that bad players have the effect of "contributing" money (they give up some of their equity). That equity is up for grabs, but if Hero is only marginally better than 50%, Hero may not be able to even win their buy-in back. The latter implies that Hero is contributing equity to the better players. Basically to win, Hero should not give up equity and grab some of the equity that the players worse than Hero are losing.

In summary, what is relevant is not 50%, but rather how much equity are the players worse than you contributing, and how much better are the players better than you. If you have 25% terrible players, you are at 25% and the other 75% although better than you, they are not MUCH better, then you will be profitable. Alternatively, you can be better than 75%, but if the top 25% are very good, you may still be losing. So basically what we want in a tourney is as many terrible players as possible, and the players that are better than us should be only marginally better.

I hope this clarified it a bit [img]/images/graemlins/confused.gif[/img]

[Cheetah]

It turns out there is an upper limit of the win rate as a function of how many players are worse than you.

Let X be the % of people who are worse than you.
Let WR be the win rate (wins/buy-ins).
Then
0 <= WR <= 100/(100-X)

If X=50% then WR<=2
If X=75% then WR<=4

Regardless of X, WR can be less than 1(meaning we are losing). The only exception is if we are the best player (X=100).

Here is a quick way to see the validity of this upper limit for the win rate:

Say X=50%. Half of the players are worse than us. The worst they can be is to never ever win anything. This doubles the prize pool for the top 50%. On the other hand, the best we can ever be if we are at 50% is to have equal skill with the remaining top 50%. In that case we split equally which results in a maximum win rate of 2.

So to answer the original thread question, the win rate of 2 is a theortical upper limit if you beat 50% of the players.

Sorry for the bad news [img]/images/graemlins/frown.gif[/img]

[Bicycles_Biatch]

thanks for the info cheetah... that's exactly the type of information I was looking for...

Does anyone remember the article I was talking about in the OG post?