ROI in Heads up Sit and go

[mb6tour]

how u came up with those numbers jay?

[ChicagoRy]

[ QUOTE ]
After 400 games , you can only determine that you're likely to be within 5 % of your true win-rate . So if you've won 60% , then your true win rate is anywhere from 55% to 65% .

If you want to be within 3% of your true win-rate , then you would need about 1,111 games . So if after 1111 games , your sample win-rate is 60% , then your true win-rate is anywhere from 57% to 63% .

[/ QUOTE ]

Isn't it true that the higher your winrate the less sample you need to accurately know your true winrate?

Your statement above does not seem to account for that.

[jay_shark]

You may want to check this post for more details .

http://forumserver.twoplustwo.com/sh...;Main=11851416

[pokercurious]

[ QUOTE ]
Isn't it true that the higher your winrate the less sample you need to accurately know your true winrate?

[/ QUOTE ]

I'm pretty sure this is not true. It is true that the higher your winrate, the less sample you need to know you're not a losing player, because if you're winning 75% (extreme, I know), then even if your true winrate is only within 20% (55%-95%), you're still guaranteed to be at worst around breakeven. And that you can know at relatively small sample sizes.

But sample size is THE factor in determining your true winrate with accuracy.

Think about it this way, which is more intuitive:
<ul type="square">[*]You win 6/10: as we all know, this tells you very little about somebody's winrate[*]You win 60/100: it's much more likely that you're a decent player now, but you could be terrible and on a heater, or [censored] amazing and not catching cards[*]You win 600/1000: cards even out by now, your winrate is almost certainly in the vicinity of 60%[*]You win 600000/1000000: anybody arguing that this player doesn't win pretty much exactly 60% of his games in the long run?[/list]Now replace 6 with any other digit. The basic idea holds whether it's 6, 8, or 2.

[HokieGreg]

So, in conclusion, my 60.5% winrate over 500 33's could actually be 75% in the long run.

You just brightened my day...

or it could be 45% too....

[Scansion]

[ QUOTE ]
You may want to check this post for more details .

http://forumserver.twoplustwo.com/sh...;Main=11851416

[/ QUOTE ]

Read most of it; what about cash games? How many hands before your HU winrate is accurate to within 1/10BB of your BB/100?

[LordMushroom2]

[ QUOTE ]
[ QUOTE ]
Isn't it true that the higher your winrate the less sample you need to accurately know your true winrate?

[/ QUOTE ]

Yes, because the standard deviation is smaller the further your winrate is from 50%. The difference in sample required is small, though.

[jay_shark]

[ QUOTE ]
[ QUOTE ]
You may want to check this post for more details .

http://forumserver.twoplustwo.com/sh...;Main=11851416

[/ QUOTE ]

Read most of it; what about cash games? How many hands before your HU winrate is accurate to within 1/10BB of your BB/100?

[/ QUOTE ]

Let x be the number of hands needed to be within 1bb/100 of your hypothetical win rate . So if we believe that we win 10bb/100 hands and our standard deviation is 110bb/100 hands , then the number of hands needed at 2 standard deviations is :

10+-2*(110/sqrt(x/100))
So we want 2*(110/sqrt(x/100)) =1
sqrt(x/100)=+-2*110
sqrtx=+-2*110*10
x=4 840 000

This means that even after 4 840 000 hands , you are 95% confident that you're within 1 bb/100 of your true win rate . This is one of the reasons why nobody really knows their true win rate because they usually change limits before they can draw any conclusions from it .

You can imagine how many more hands you would need to play to be within (1/10bb)/100 hands.

[SwingVelvet]

[ QUOTE ]
You may want to check this post for more details .

http://forumserver.twoplustwo.com/sh...;Main=11851416

[/ QUOTE ]

Jay, already ready this thread. I was actually coming to 2p2 to ask the following question:

Can you use the same table of confidence intervals for ROI?

I use sharkscope, which only gives ROI, not winrate. How do we translate?

Thanks!

[jay_shark]

You can translate your ROI to win-rate .

i.e., If your win-rate is x % (written in decimals) and your ROI is y% then we solve for :

(2*x-1.05)/1.05 = y Or x =[1.05y +1.05]/2

so if Y=15% , then x is about 60% .

In laymen's terms :

Roi = [2* win-rate - buy-in ]/ (buy-in)

Win-rate= [buy-in* Roi + buy-in ]/2

================================================== =========

Or we may make the assumption that your standard deviation is ~ 1 which applies to a wide range of win-rates .

So if after 500 sng's , your sample roi is 15% , then our confidence interval at two standard deviations from the mean becomes :

0.15 +-2*1/sqrt(500) which implies that our true win rate(z=2) is anywhere between [0.15 - 0.089, 0.15 + 0.089] or [6%, 23.9%]

After 2000 games , it is [ 10.5% , 19.47%]

Hope that helps