Not sure who wrote this.
I've noticed many threads, comments, discussions on poker messageboards about variance in relation to turbos and normal speed SNGs. There is a pervasive misconception that variance is greater when playing turbos than normal tables. It isn't. Even Jennifear (who I respect more than any other writer of online poker articles
) gets this one wrong in her article on whether you should play turbos or normal speed tournaments by saying it's slightly higher in turbos.
After seeing yet another discussion on this subject on another messageboard I thought I'd attempt to do my best to clear up the confusion.
Turbos have negligable impact on variance but can have a major impact on ROI.
Here's an example. Assume someone plays both normal and turbo 5$ 6-seater SNGs on Cereus. The stake and buy-in is $5.50, winner gets $21 and second $9. The ROI for winning is 281.8% and for second is 63.6% and for 3-6th is -100%.
Lets assume a good player on the Normals wins 25% of the time and comes second 25% of the time.
Their ROI is 31.34% with a mean variance per game of 248
Lets assume the same player on Turbos wins 23% of the time (it's lower as they become more random more quickly) and comes second 23% of the time.
Their ROI on the turbos is 20.2% with a mean variance of 242.
So the variance is very similar (as it's basically determined by the pay-out structure which is identical for normals and turbos).
Good players will actually have slightly lower variance but the negative effects on their ROI will be much greater.
Bad players (ROI of less than -10%) will actually have slightly higher variance and also a higher ROI on turbos.
Players with an ROI of -10% will have an identical variance as they will have an identical pattern of finishes in both. Their ROI will not differ.
The bottom line is variance should never be an issue when choosing to play turbos or normals. It is ROI solely that should determine that decision. The rule is very simple. Assuming Normal tables take twice as long as a turbo, then your ROI on Normal tables must be at least twice that on Turbos to make Normals more profitable to play on.
P.S. If you are interested in knowing how to calculate variance and 95% confidence intervals on your ROI here's how you can do it using just Excel.
First you need to know your finishing positions for a particular type of tournament. I use sharkscope
to get mine.
As an example I'll use my fictitious poker player on Cereus and their ability on Normal $5+0.5 6-seaters. Lets assume they have played 100 games with 25 1sts and 25 seconds.
You need to know the ROI for each type of finish. This is the profit over the stake and buy in.
So for 1st it's 15.5/5.5 = 281.8
For 2nd it's 3.5/5.5 = 63.6
For non-cashes it's -100.
You now have to enter all your finishes into a single column in Excel. So you want 25 rows of 281.8 followed by 25 rows of 63.6 then 50 rows of -100.
In the next row type =(VAR(A1:A100)/100)
This will calculate your variance. It is important that the last two numbers are equal to your number of rows. So if you have played 657 tables of one type then row 658 of your table should be =(VAR(A1:A657)/657)
In the next row type =(AVERAGE(A1:A100))
Again where I've put 100 you must put your number of tables played e.g.
This will give you your ROI.
In the next row type =((STDEV(A1:A100))/(SQRT(COUNT(A1:A100)))/1.96)
Again where I've put 100 you must put your number of tables e.g.
This will give you the 95% confidence interval on your ROI.
In my example you should get a variance of 247.9, an ROI of 31.34% and a CI of 30.86%
So your ROI is 31.34+-30.86%. The confidence intervals are large as 100 games is not very many. You need to play many 1000s of tables to get your ROI within a percentage point or two. Also the greater the variance in table type the greater the CI will be. So ROIs are most accurate for HU and DoNs which have the least variance and much less accurate for those that play large MTTs.