singe table vs. multitable tournaments - sample sizes for average ROI

[eastbay]

If it takes 200 single table (10 player) tournaments to have an 'acceptable' average ROI, how many 1000 player tournaments would give the same confidence level in the average ROI of those?

Make any assumptions that seem reasonable.

eastbay

[Hiding]

Wouldn't you still need 200 multitable results to get the same confidence level on your ROI? I am no statistician, but isnt one game just one game, whether it be against 2 players or 2000? And if it did change, how many 9 player SnG would you have to play to get the same confidence level?

[eastbay]

[ QUOTE ]
Wouldn't you still need 200 multitable results to get the same confidence level on your ROI? I am no statistician, but isnt one game just one game, whether it be against 2 players or 2000? And if it did change, how many 9 player SnG would you have to play to get the same confidence level?

[/ QUOTE ]

I think the answer to that is certainly no. Think about this way:

Let's say everyone in every tourney is evenly matched. Then it becomes equivalent to rolling an n-sided die to pick the winner.

So take that to an extreme: consider coin flips vs. rolling a 1000-sided die.

How many coin flips does it take before you start averaging out pretty close to 1/2? Not many. Try it.

Now think about how many 1000-sided die rolls it would take before you averaged out close to 1/1000. It would take you 1,000 rolls just to hit your number once, on average. But you'd have to roll it at least a few multiples of 1000 to smooth out the average.

No, it certainly takes more. How many more is a harder question.

eastbay

[Outsidefun]

Eastbay is correct... the variance has a lot to do with confidence(staticstial significance) I'm not sure how to determine the variance of a 1000 player "game" but it is clearly far greater than the 10 player sng. I don't think you will likely play enough 1000 player games in years of playing to really have a high confidence factor... I do like the dice analogy.

[Bozeman]

Let's do some ballpark estimates:

Suppose an n player winner take all tournament with no vig, and you win an average amount.

SD1=sqrt(1/n*(n-1)^2+(n-1)/n*1^2)=sqrt(n-1) (units of buyins/sqrt(tourneys))

Statistical certainty, after m tourneys your ROI will be accurate (with 95% certainty) to 20% if 20%=2*SD1*sqrt(m)/m => sqrt(m)=10*SD1 => m=100*(n-1).

Thus for n=10, m=900, for n=1000, m=99900. In general, variance will scale approximately as number of players. For bigger winners, variance will increase, almost linearly with probability of first.

Now, for proportional payout tournaments, particularly deep and relatively flat payouts, these numbers will be reduced considerably, but very few situations have lower variance than a standard SNG (many (30%) places paid, relatively flat payout). In particular, if the additional places paid as number of players go up mostly pay approximately your buyin, variance will increase even faster than linear with more players.

Craig