Theoretical limit for ROI

[gholizad]

Is it possible to show that there is a theoretical limit for achievable ROI ((over a large enough sample)) in single table sit and go? I have seen many good sit and go players have a very similar ROI ranges and was wondering if it is possible to prove it mathematically.

[creedofhubris]

prize for 1st place - entry fee

[jay_shark]

The more players in a tournament , the higher your ROI if we assume you're the best player . In other words , the better player you are , the more you would prefer players to join as long as they are inferior to you .

It's possible to sustain a ROI of about 100% but this would only apply to mtt's and good tournament selection . On the other hand , the higher your stakes , the lower your ROI becomes .

At a 9 player sng , your ROI drops significantly . It does become mostly a crapshoot but you may still derive profits from it .

[pzhon]

You aren't going to be able to prove a reasonable mathematical estimate that explains the ROI of good players. Poker is too complicated for that. The amount a good player wins depends on the way bad players play, which you have to determine from actual data, not predict it mathematically.

The SNG FAQ suggests some ROI values for turbo SNGs on Stars. These seem quite low to me. I have played hundreds of turbo SNGs on Stars, and can statistically reject having a ROI that low. I think the reason is that many winning players prefer to play 4 times as many tables rather than doubling their ROI. If that is their choice, then they win more money, at least in the short run, but they are not maximizing their ROI. So, even if you come up with a good mathematical model for the bad players, you still won't explain the results of the good players.

The common advice to play only premium hands in early levels while the maniacs knock each other out is bad. It might help you to play 16 tables at the same time, but you miss most of the value from playing against really bad players. It is much easier to accumulate chips by playing against bad players than playing against good players, and this is still extremely valuable, even though survival is more important in SNGs than in normal tournaments.

[jogsxyz]

[ QUOTE ]
You aren't going to be able to prove a reasonable mathematical estimate that explains the ROI of good players. Poker is too complicated for that.

[/ QUOTE ]

It's more due to there's too much luck in poker.
Skill is measured in inches. Luck in SnGs is
measured in feet. Luck in large MTTs is measured
in yards.
The aggregate standard deviation of a 10 player
SnG is 1.67 buy-ins. The aggregate s.d. of a 500
player MTT is nearly 9 buy-ins.
It takes around a thousand of MTTs before one gets
a nice tight confidence interval for the estimate
of expected ROI. And that assumes your relative
ROI remains constant thruout the sample.
If only if it were possible to obtain Hellmuth's
complete tournament records. Then it would be
possible to make an educated estimate.

[pzhon]

[ QUOTE ]
[ QUOTE ]
You aren't going to be able to prove a reasonable mathematical estimate that explains the ROI of good players. Poker is too complicated for that.

[/ QUOTE ]

It's more due to there's too much luck in poker.

[/ QUOTE ]
No, that's completely irrelevant. It is easier to determine the edge in some games with a much lower advantage relative to the variance, e.g., blackjack. The problem with poker is not that there is luck, but that poker is too complicated. You can't model the mistakes made by weaker players a priori because players at different levels and in different games make different mistakes. Since the win rate of a winning player depends on mistakes made by others, you can't get a useful upper bound on the best possible results.

[ QUOTE ]

The aggregate standard deviation of a 10 player
SnG is 1.67 buy-ins. The aggregate s.d. of a 500
player MTT is nearly 9 buy-ins.


[/ QUOTE ]
So, what? I've posted calculations like that several times. They have nothing to do with the expected return. Many players have enough SNG data to determine their ROIs quite accurately. As I stated, I can statistically reject having a ROI as low as what the SNG FAQ says is achievable in turbo SNGs. I have enough data despite the noise. (I think the explanation is that many regular SNG players play like crap, and are ok with that because they can play 16 tables. They aren't interested in anything that requires thought while playing, so I don't read the STT forum.)

I tried to get people to pool ROI data in the MTT forum years ago, since as a group we should easily have enough to get a meaningful average, but that thread sank like a stone. I guess people aren't really interested in finding out what ROIs are achievable in MTTs when they can talk about AA getting cracked again. Still, the win rates are much higher, so the acceptable confidence intervals are larger. If you play limit, a difference in win rates of 1 BB/100 makes a huge difference, but in NL it's not as important. Similarly, while a difference of 10% ROI makes a big difference in SNGs, it's not as important for MTTs. So, although the standard deviation is larger, you don't need as much more data as it may appear at first.

[jogsxyz]

[ QUOTE ]


[ QUOTE ]

The aggregate standard deviation of a 10 player
SnG is 1.67 buy-ins. The aggregate s.d. of a 500
player MTT is nearly 9 buy-ins.


[/ QUOTE ]
So, what? I've posted calculations like that several times. They have nothing to do with the expected return.

[/ QUOTE ]

It has everything to do with the confidence interval of
the expected return.

[ QUOTE ]
Many players have enough SNG data to determine their ROIs quite accurately. As I stated, I can statistically reject having a ROI as low as what the SNG FAQ says is achievable in turbo SNGs. I have enough data despite the noise. (I think the explanation is that many regular SNG players play like crap, and are ok with that because they can play 16 tables. They aren't interested in anything that requires thought while playing, so I don't read the STT forum.)


[/ QUOTE ]

Yes, it's even easy for players playing only one STT at
a time to succeed in creating a large data sample for
good estimates of ROI.

But live MTTs of $1,000 or higher is a different
matter. Only Hellmuth, Men 'the master' and TJ
Cloutier have any chances of playing over 1000
in their lifetime.

And the large MTTs needs about 25 times the sample
size to have the same confidence interval as a
STT sample.

[pzhon]

[ QUOTE ]
[ QUOTE ]


[ QUOTE ]

The aggregate standard deviation of a 10 player
SnG is 1.67 buy-ins. The aggregate s.d. of a 500
player MTT is nearly 9 buy-ins.


[/ QUOTE ]
So, what? I've posted calculations like that several times. They have nothing to do with the expected return.

[/ QUOTE ]

It has everything to do with the confidence interval of
the expected return.

[/ QUOTE ]
Reread the OP. The question was not about confidence intervals. It was about finding a theoretical bound on the maximum possible expected return. This has nothing to do with confidence intervals.

[ QUOTE ]
[ QUOTE ]
Many players have enough SNG data to determine their ROIs quite accurately.

[/ QUOTE ]

Yes, it's even easy for players playing only one STT at
a time to succeed in creating a large data sample for
good estimates of ROI.

[/ QUOTE ]
So, why did you bring it up?

[ QUOTE ]
But live MTTs of $1,000 or higher is a different
matter. Only Hellmuth, Men 'the master' and TJ
Cloutier have any chances of playing over 1000
in their lifetime.

[/ QUOTE ]
First, are you serious? There are a lot more large tournaments than you seem to think there are. It looks like you can play more than 100 such tournaments per year at the Bellagio alone. My first live tournament (elsewhere) had a $5000+$150 buy-in. Was it a once per year WSOP event, or on the WPT? No, it was called, "the Saturday tournament." AFAIK, they do it every Saturday. There seemed to be a lot of unnamed professional players there (including at least two other 2+2 posters).

Second, the OP was clearly asking about STTs when he said, "Is it possible to show that there is a theoretical limit for achievable ROI ((over a large enough sample)) in single table sit and go?"

[gholizad]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You aren't going to be able to prove a reasonable mathematical estimate that explains the ROI of good players. Poker is too complicated for that.

[/ QUOTE ]

It's more due to there's too much luck in poker.

[/ QUOTE ]
No, that's completely irrelevant. It is easier to determine the edge in some games with a much lower advantage relative to the variance, e.g., blackjack. The problem with poker is not that there is luck, but that poker is too complicated. You can't model the mistakes made by weaker players a priori because players at different levels and in different games make different mistakes. Since the win rate of a winning player depends on mistakes made by others, you can't get a useful upper bound on the best possible results.

[ QUOTE ]

The aggregate standard deviation of a 10 player
SnG is 1.67 buy-ins. The aggregate s.d. of a 500
player MTT is nearly 9 buy-ins.


[/ QUOTE ]
So, what? I've posted calculations like that several times. They have nothing to do with the expected return. Many players have enough SNG data to determine their ROIs quite accurately. As I stated, I can statistically reject having a ROI as low as what the SNG FAQ says is achievable in turbo SNGs. I have enough data despite the noise. (I think the explanation is that many regular SNG players play like crap, and are ok with that because they can play 16 tables. They aren't interested in anything that requires thought while playing, so I don't read the STT forum.)

I tried to get people to pool ROI data in the MTT forum years ago, since as a group we should easily have enough to get a meaningful average, but that thread sank like a stone. I guess people aren't really interested in finding out what ROIs are achievable in MTTs when they can talk about AA getting cracked again. Still, the win rates are much higher, so the acceptable confidence intervals are larger. If you play limit, a difference in win rates of 1 BB/100 makes a huge difference, but in NL it's not as important. Similarly, while a difference of 10% ROI makes a big difference in SNGs, it's not as important for MTTs. So, although the standard deviation is larger, you don't need as much more data as it may appear at first.

[/ QUOTE ]

nice post. I totally agree that poker is too complicated to model but statistically speaking, you can never find anyone with 50% ROI in STT over 1000 games. That got me thinking that maybe it is theoretically impossible to achieve that ROI no matter how well you play.

One thing that came to my mind was that you usually have to win at least 2 showdowns (usually preflop all ins) to make the money and probably 3 more to win the sit and go. So that sorts of suggests that even if you get it in with 4-1 favorite every time, you can only make the money about 50% of the time. So that could set a limit for ROI for example. It's definitely much more complicated for MTT, especially if it is relatively deep stacked.