[x]

## Variance in Turbos v Normal Speed - a common misconception

1. <title>Enter text here.</title><title>Enter text here.</title>*Thread added to Strategy Archives* Sit & Gos

Hello,

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. First off I should point out I'm a statistician.

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.

=(AVERAGE(A1:A657))

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.

=((STDEV(A1:A657))/(SQRT(COUNT(A1:A657)))*1.96)

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.

Cheers

Landsbanki

Please visit my blog on sharkscopers.com
http://www.sharkscopers.com/blog/landsbanki
2. Having a properly adjusted game at turbos and regulars should yield the same ROI. Turbos do have more variance because your roll swings harder. Variance is commonly used to just mean negative downswings, but also applies to positive upswings, and this is where the misconception comes into play. Playing regulars your ROI deviates less from your average, and turbos will cause greater deviations.
over the long run, with a properly adjusted game your ROIs should be roughly the same at any given level.
3.
##### Originally Posted by iatetheredcrayon

Having a properly adjusted game at turbos and regulars should yield the same ROI. Turbos do have more variance because your roll swings harder. Variance is commonly used to just mean negative downswings, but also applies to positive upswings, and this is where the misconception comes into play. Playing regulars your ROI deviates less from your average, and turbos will cause greater deviations.
over the long run, with a properly adjusted game your ROIs should be roughly the same at any given level.

In the long run you can't maintain the same ROI on turbo as you can on Regulars. In the same way you can't maintain the same ROI on superturbos as turbos.

Here's the evidence:

This data is the average profit for the player at the top of each of the sharkscope leaderboards for for turbos and non-turbos for 5-6seaters

\$5 Regular \$2.18 Turbo \$1.70
\$15 Regular \$5.71 Turbo \$4.67
\$35 Regular \$12.54 Turbo \$11.24
\$100 Regular \$23.34 Turbo \$21.27
\$300 Regular \$51.16 Turbo \$41.80

For every category the ROI for the Regular is about 10-20% higher than the ROI for the Turbo equivalent.

You are correct that the extent of downswings and upswings are determined by variance. But it is a myth that upswings and downswings are greater with turbos. They are not. In fact for a player with a +ROI it will be slightly less. It is only more for weak players.
4. I think the main reason you can't maintain the same ROI in turbos is that all players are forced to get your chips in more often. At regular speed you will see good ROI players exploit too tight/passive players all the time but in turbos there's less room for it as the tight/passive ones are forced to act more often. This even out the advantages somewhat and results in lower ROI figures.

5. In an optimally adjusted turbo game swings will be greater, because you are having to take smaller edges because you don't have time to wait for huge ones.  In the regulars you have the opportunity to pass up some small edges that may bust you, because there is equity in remaining in the tourney. Likewise in the turbos if you aren't taking more of the edges this is recipe for lower ROI, because you have a limited number of chances in comparison to a regular. So the fact ct that you are having to exploit smaller edges more frequently in the turbos will lead to higher variance. For sake of argument say that when you get all in in a regular you will be an average of 65/35 to win the hand, but in a turbo with small edges you may only be averaging 55/45. Having a percentage closer to 50 is going to lead to more frequent and more extended streaks of losing than the regulars.  IE: at a 55/45 edge it may not be that uncommon to lose 5-8 "flips" in a row. Although possible at 65/35, the average loss streak should be lower, maybe 3-6. Even when you go on heater streaks on the turbos you will be less likely to go deep, because you are still more likely to follow that heater with a loss than if you are getting 65/35.
I guess in trying to explain why turbos will have more variance I have killed my previous point of ROI being the same because of the percentage and hot/cold streaks. Basically when you stack on a streak in a regular you are more likely to go deep, because you still avoid those small edge opportunities.
6.
##### Originally Posted by iatetheredcrayon

In an optimally adjusted turbo game swings will be greater, because you are having to take smaller edges because you don't have time to wait for huge ones. In the regulars you have the opportunity to pass up some small edges that may bust you, because there is equity in remaining in the tourney. Likewise in the turbos if you aren't taking more of the edges this is recipe for lower ROI, because you have a limited number of chances in comparison to a regular. So the fact ct that you are having to exploit smaller edges more frequently in the turbos will lead to higher variance. For sake of argument say that when you get all in in a regular you will be an average of 65/35 to win the hand, but in a turbo with small edges you may only be averaging 55/45. Having a percentage closer to 50 is going to lead to more frequent and more extended streaks of losing than the regulars. IE: at a 55/45 edge it may not be that uncommon to lose 5-8 "flips" in a row. Although possible at 65/35, the average loss streak should be lower, maybe 3-6. Even when you go on heater streaks on the turbos you will be less likely to go deep, because you are still more likely to follow that heater with a loss than if you are getting 65/35.
I guess in trying to explain why turbos will have more variance I have killed my previous point of ROI being the same because of the percentage and hot/cold streaks. Basically when you stack on a streak in a regular you are more likely to go deep, because you still avoid those small edge opportunities.

Very well explained!!!

7.
##### Originally Posted by iatetheredcrayon

In an optimally adjusted turbo game swings will be greater, because you are having to take smaller edges because you don't have time to wait for huge ones. In the regulars you have the opportunity to pass up some small edges that may bust you, because there is equity in remaining in the tourney. Likewise in the turbos if you aren't taking more of the edges this is recipe for lower ROI, because you have a limited number of chances in comparison to a regular. So the fact ct that you are having to exploit smaller edges more frequently in the turbos will lead to higher variance. For sake of argument say that when you get all in in a regular you will be an average of 65/35 to win the hand, but in a turbo with small edges you may only be averaging 55/45. Having a percentage closer to 50 is going to lead to more frequent and more extended streaks of losing than the regulars. IE: at a 55/45 edge it may not be that uncommon to lose 5-8 "flips" in a row. Although possible at 65/35, the average loss streak should be lower, maybe 3-6. Even when you go on heater streaks on the turbos you will be less likely to go deep, because you are still more likely to follow that heater with a loss than if you are getting 65/35.
I guess in trying to explain why turbos will have more variance I have killed my previous point of ROI being the same because of the percentage and hot/cold streaks. Basically when you stack on a streak in a regular you are more likely to go deep, because you still avoid those small edge opportunities.

I agree with every word you've said about differences in play. I disagree about the consequences of the different styles of play though. Taking more risks in turbos will substantially reduce your ROI but hardly affect your variance. You will simply get fewer cashes but the order that those cashes happens won't be affected. Downswings will simply seem worse as the baseline ROI is lower and thus there will be longer periods where you'll be down but the actually variance i.e. the amplitude of those swings really won't vary much at all between turbos and regulars.

I think the misconception a lot of people have is confusing variance with the length of downswings. Variance is the amount of variation away from your norn i.e. the slope and height of the peaks and troughs on your profit graph, not how long those peaks and troughs last.
8. Landsbanki, thank you very much for this analysis. Do you recommend not playing super turbos as they might lower ROI so much that they are borderline unprofitable?
9. OP: Excellent post. It's really nice to see someone with an actual statistical background posting about these things; I swear half the people on here who talk for hours about variance don't even actually have a good grasp of what it means (std dev squared, and what std dev even means). Those results are definitely counter to what I would expect, but the numbers don't lie. I'll definitely have to be reconsidering my game selection.
10.
##### Originally Posted by iSweatMoney

Landsbanki, thank you very much for this analysis. Do you recommend not playing super turbos as they might lower ROI so much that they are borderline unprofitable?

Here's the superturbo stats from sharkscope compared to turbos

\$5 Superturbo \$0.91 Turbo \$1.70
\$15 Superturbo \$2.25 Turbo \$4.67
\$35 Superturbo \$5.55 Turbo \$11.24
\$100 Superturbo \$13.77 Turbo \$21.27
\$300 Superturbo \$25.72 Turbo \$41.80

Assuming a superturbo is twice the speed of a turbo then the same half the ROI rule applies.

Looking at the data it seems really good players have profit levels on superturbos that are about half (may be more at higher stakes) that of a turbo. Including the rakeback from superturbos they might just be better. Personally, however I don't like them.
11. First off I should point out I'm a statistician.

Turbos have negligable impact on variance but can have a major impact on ROI.

Define the variables used in your variance calculations. it seems your analyzing finishes, when poker players refer to variance they are referencing bankroll swings or card variance, not pure numerical finishes.

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.

Please explain the logic used to get to this. I believe I understand what your saying but the explanation will help.

Their ROI on the turbos is 20.2% with a mean variance of 242.

Mean variance of what sample?

Good players will actually have slightly lower variance but the negative effects on their ROI will be much greater.

Since all humans are bound by the measurement of time, you can't truly compare turbo and "normal" poker without factoring it in. ROI means nothing in choosing a game, your profit is what matters, measured in units of time of course. ROI is excellent for tracking your progress in games as they get tougher\easier and as a way to compare your results to others meeting the same criteria.

The bottom line is variance should never be an issue when choosing to play turbos or normals.

If you see less hands in an "event" (game) then it is more likely you will be forced to take marginal spots more often, resulting in a smaller "success" margin. There's a theory called "one dimensional random walk" that deals with the probability of two equally likely defined outcomes occurring in succession. When you adjust the theory to include the larger skill edge a good player will likely receive over time you greatly decrease the odds of successive non-cash's.

For example if you compare two all ins one where we are 50/50 and one where we are 75/25 then in basic event terms your going to win 2 of 4 and 3 of 4. the odds of losing show the key to it, when you calculate the odds of losing x times in a row over multiple trials (say x=three) you get 64:1 (75/25) and 8:1 (50/50). OBV my numbers are for demonstration only but I believe its commonly held that your skill edge is more pronounced as the sample size of hands per game increase.

Bankroll variance refers to the probability of a defined number of games played without the events that cause profit (cashing, Final table, winning, etc.) not the overall distribution of finishes in a random sample size.

I apologize if I have mislabeled something, I'm am simply an accountant who enjoys statistics! good discussions tho!
12. Somebody run my ROI on \$12/180 on pokerstars from sharkscope and post.

Pretty good sample size of a high ROI% on the TURBO's

I would like to see my stats and it backs up OP idea.
13.
##### Originally Posted by StoneColdNz

Somebody run my ROI on \$12/180 on pokerstars from sharkscope and post.

Pretty good sample size of a high ROI% on the TURBO's

I would like to see my stats and it backs up OP idea.

<TABLE class=sortTable id=t1 border=1><THEAD> <TR class=sortTable><TH class=sortTableasc width=140>Username</TH><TH class=sortTable>Games Played</TH><TH class=sortTable width=45>Av. Profit</TH><TH class=sortTable width=45>Av. Stake</TH><TH class=sortTable width=45>Av. ROI</TH><TH class=sortTable width=50>Total Profit</TH><TH class=sortTable>Form</TH><TH class=sortTable>Ability /100</TH><TH class=sortTable>Network</TH><TH class=sortTable width=50>Filter</TH></TR></THEAD> <TBODY id=tablerows><TR class=sortTable id="csnyder16#pokerstars& E180-180 S10-15 G=H NoLim Spd=T SNG Only"><TD class=sortTable id="csnyder16#pokerstars& E180-180 S10-15 G=H NoLim Spd=T SNG Only0" align=middle>csnyder16<INPUT onclick=showpreferences(); type=image height=16 width=16 src="http://www.sharkscope.com/images/shark3.gif"></TD><TD class=sortTable align=middle>519</TD><TD class=sortTable title="The Av. Profit is the Average Profit Per Game after rake has been subtracted." align=right>\$9 </TD><TD class=sortTable title="The Av. Stake is the average tournament buy-in amount." align=right>\$11 </TD><TD class=sortTable title="The Av. ROI is the Average of each game’s Return On Investment. It is the average of each (Payout-(Stake+Rake))/(Stake+Rake). This is not the same as total ROI which is (Total Payouts-(Total Rake+Total Stakes))/(Total Stakes+Total Rake)." align=middle>76%</TD><TD class=sortTable title="The Total Profit is the net profit for this player (and includes rake)." align=right>\$4,735 </TD><TD class=sortTable title="W = Win. P = Payout. L = Loss." align=middle>WLLLLLLL</TD><TD class=sortTable title="The ability rating is a number up to 100 that shows a players ability based on combining all the statistical measures we have for that player." align=middle>N/A</TD><TD class=sortTable align=middle>PokerStars</TD><TD class=sortTable align=middle>E180-180 S10-15 G=H NoLim Spd=T SNG Only </TD><TD class=sortTable>x</TD></TR></TBODY></TABLE>
14. i don't really feel like arguing with every point right now, but your calculations aren't really accurate.

the person that talked about passing up edges is basically correct.

honestly tho, you can't possible believe that playing a tourney where the average stack is 7bb has the same swings as one where the average is like idk 20-30bb?

Gags30 is an instructor at PocketFives Training . To get more of his advice and to watch his training videos, click here.

15.
##### Originally Posted by iatetheredcrayon

Having a properly adjusted game at turbos and regulars should yield the same ROI. Turbos do have more variance because your roll swings harder. Variance is commonly used to just mean negative downswings, but also applies to positive upswings, and this is where the misconception comes into play. Playing regulars your ROI deviates less from your average, and turbos will cause greater deviations.
over the long run, with a properly adjusted game your ROIs should be roughly the same at any given level.

lol your ROI would be the same in a turbo vs non turbo longterm? that makes no sense. the deeper the structure and slower blind levels allows deeper stacked play thus more skill being involved. obviously if you take a pro player vs a novice at 100 bbs deep vs the same scenario at 10 bbs deep, the pro is going to show more profit with the deeper stacked play.

bottom line is faster structures/shorter stacks = more variance and less of an edge.
16. there are a couple of other factors, such as IMO the slower the structure the more reg's so the field gets tougher. Also many players fail to adjust to the turbo structure and there's some EV to pick up as a result.
17.
##### Originally Posted by dgillis

Define the variables used in your variance calculations. it seems your analyzing finishes, when poker players refer to variance they are referencing bankroll swings or card variance, not pure numerical finishes.

I think this right here is the crux of the issue. Variance in statistical terms is a measure of the amount of variation within the values of a given variable. As used in the poker community, variance is not well defined. We seem to use it as a general catchall phrase for the forces at work that cause bankroll swings, bad beats, etc. When your AA gets beat aipf by 27, we call it variance, which isn't really accurate. That situation can and does cause variance in your ROI, which is really where variance is a useful statistic. The OP throughout his post is referring to statistical variance in your ROI, which is why he is able to only analyze finishes: they're all that is relevant to ROI calculations. Variance in your ROI is also what accounts for the bankroll swings you mentioned, which is why it's relatively accurate when we all use variance to describe swings. Your ROI as typically represented on sharkscope/opr/etc is your mean ROI over x number of tournaments, variance is a calculation of the variation in that ROI from tournament to tournament.

Hope that helps clear things up a bit, I'm just on my lunch break or I would have tried to go into a bit more detail. And as a disclaimer, I'm also an accountant who enjoys statistics, so I'm by no means an authority ;)
18. When most poker players refer to variance, it is in the bankroll sense, and they are referring to the range of their bankroll over the sample. In the OP's example, the variance of finishes is measured, which is different. The variance of two samples can be approximately the same but the ranges can be significantly different.

I haven't done the calculations, but I guarantee that the range, calculated as max profit (or min loss) minus min profit (or max loss) is going to be larger in turbos. Thus, from a poker players perspective, the bankroll swings are going to be larger, hence "variance", albeit not the true statistical kind.
19. Get outta here with your "statistics." Of course we mean short term variance is higher. Over the long haul it is no higher.

All I know is I have never had a 1k game break even in regs, or a 140 bi downswing, and I have in turbos.
20.
##### Originally Posted by TiltinShoes

Get outta here with your "statistics."

That seems like an extremely rash thing to say as someone who wagers any amount of money in a game that is governed entirely by statistics.

And no, the difference here is not short term versus long term. Tyson is correct, the difference is between variance and range, as evidenced by your example of a "140 bi downswing." That isn't variance, that's range, which is an entirely different statistic, though again I think Tyson is probably right that most players are talking about range when they say variance. They're both useful statistics, but they are very different ones.
21. "Define the variables used in your variance calculations. it seems your analyzing finishes, when poker players refer to variance they are referencing bankroll swings or card variance, not pure numerical finishes."

I am analysing ROI. It is the variance on your ROI that determines your bankroll swings. I'm not talking about card variance.
"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.
Please explain the logic used to get to this. I believe I understand what your saying but the explanation will help. "

As other posters have already explained, you have to take bigger risks earlier in turbos. This will obviously affect you ROI. So I have simply assumed you get less 1sts and 2nd. An argument could be made that your proportion of 1sts to 2nss will also drop.This would actually lower your variance. I didn't assume that but it would add strength to my argument that variance does not increase.

Mean variance of what sample? 100 games, it wasn't a randon sample I assumed 25 1st, 25 2nds for regular and 23 1sts and 23 2nds for turbo. The mean variance is adjusted by the number of tournaments and won't change much over time.

If you see less hands in an "event" (game) then it is more likely you will be forced to take marginal spots more often, resulting in a smaller "success" margin. There's a theory called "one dimensional random walk" that deals with the probability of two equally likely defined outcomes occurring in succession. When you adjust the theory to include the larger skill edge a good player will likely receive over time you greatly decrease the odds of successive non-cash's.

For example if you compare two all ins one where we are 50/50 and one where we are 75/25 then in basic event terms your going to win 2 of 4 and 3 of 4. the odds of losing show the key to it, when you calculate the odds of losing x times in a row over multiple trials (say x=three) you get 64:1 (75/25) and 8:1 (50/50). OBV my numbers are for demonstration only but I believe its commonly held that your skill edge is more pronounced as the sample size of hands per game increase.

This is all true but I'm not talking about variance between hands. All this adjustment of playing style will simply reduce your ROI in turbos. It won't affect ROI (or bankroll variance) as you call. It will all be reflected in your ROI at regulars and turbos. So you don't need to consider hand variance when choosing between regulars and turbos as it will be seen in your two ROIs (which is equivalent to profit as I'm talking about comparing turbos and regulars with identical buy-in/payout structure. Different people will adjust with different success rates so each player should workout their ROI on regulars and turbos.

Bankroll variance refers to the probability of a defined number of games played without the events that cause profit (cashing, Final table, winning, etc.) not the overall distribution of finishes in a random sample size.

Er, no it doesn't. Bankroll variance is exactly the same as ROI variance when you only consider tournaments with the same buy-in. You shouldn't compare across buy-in levels, so they are identical. Bankroll variance is not a probability but a description of the amount of variability in your ROI (or average profit).
22.
##### Originally Posted by Gags30

i don't really feel like arguing with every point right now, but your calculations aren't really accurate.

honestly tho, you can't possible believe that playing a tourney where the average stack is 7bb has the same swings as one where the average is like idk 20-30bb?

I would like to know if my calculations aren't accurate, so I could correct them. But if you don't feel like telling how they aren't accurate it's difficult to respond.

The swings in turbos really are not substantially different to the swings in regulars. This is the misconception I'm talking about. The only difference is in ROI. In order for the varaince in turbos to be greater you would have to get more extreme outcomes. A good player actually has less extreme outcomes. The most extreme outcome (those that increase variance the most) are victories. These deviate the furthest from the mean and thus make the biggest contribution to variance. Good players will have fewer victories in turbos so their swings will be very slightly reduced. Donks will have more victories and as a consequence have slightly greater swings.
23. lol your ROI would be the same in a turbo vs non turbo longterm? that makes no sense. the deeper the structure and slower blind levels allows deeper stacked play thus more skill being involved. obviously if you take a pro player vs a novice at 100 bbs deep vs the same scenario at 10 bbs deep, the pro is going to show more profit with the deeper stacked play.

Spot on.

bottom line is faster structures/shorter stacks = more variance and less of an edge.
lol, no, the same misconception rears its ugly head again.

Faster structure, YES, less of an egde, YES, more variance NO!
24.
##### Originally Posted by Faded TV

I think this right here is the crux of the issue. Variance in statistical terms is a measure of the amount of variation within the values of a given variable. As used in the poker community, variance is not well defined. We seem to use it as a general catchall phrase for the forces at work that cause bankroll swings, bad beats, etc. When your AA gets beat aipf by 27, we call it variance, which isn't really accurate. That situation can and does cause variance in your ROI, which is really where variance is a useful statistic. The OP throughout his post is referring to statistical variance in your ROI, which is why he is able to only analyze finishes: they're all that is relevant to ROI calculations. Variance in your ROI is also what accounts for the bankroll swings you mentioned, which is why it's relatively accurate when we all use variance to describe swings. Your ROI as typically represented on sharkscope/opr/etc is your mean ROI over x number of tournaments, variance is a calculation of the variation in that ROI from tournament to tournament.

Hope that helps clear things up a bit, I'm just on my lunch break or I would have tried to go into a bit more detail. And as a disclaimer, I'm also an accountant who enjoys statistics, so I'm by no means an authority ;)

Exactly and very eloquently written.
25. I think I agree with the statistical approach taken here; it looks solid.

One thing though - the example used in this (the Cereus SNGs) has identical buyin/rake structures for the normals and turbos. Given that, on stars for example, turbo SNGs often have lower relative rake, the ROI% of 1st/2nd is higher in these games, than in their closest-equivalent normals.

At that point, there's a factor increasing turbo ROI% (known, quantified by prize structure), and a factor decreasing it (known, but not quantifiable) relative to the normals. That makes it hard to say what the overall effect would be; the empirical evidence from the leaderboards may be influenced by something other than the nature of the games (nature of players, moving of better players to normals vs. turbos, etc.)

Thinking further, that should also be a force for higher variance, because the outcomes are further apart (the Stars reset is stopping me looking at it for 6-man, but the 9-man comparisons (\$5 vs \$6) are: Normal - +309%, +145%, +64%, -100%; turbo - +315%, +149%, +66%, -100%.
26.
##### Originally Posted by tyson219

When most poker players refer to variance, it is in the bankroll sense, and they are referring to the range of their bankroll over the sample. In the OP's example, the variance of finishes is measured, which is different. The variance of two samples can be approximately the same but the ranges can be significantly different.

I haven't done the calculations, but I guarantee that the range, calculated as max profit (or min loss) minus min profit (or max loss) is going to be larger in turbos. Thus, from a poker players perspective, the bankroll swings are going to be larger, hence "variance", albeit not the true statistical kind.

I have done the calculations and I guarantee the range will not really differ between regulars and turbos. This is again the same misconception about variance.

The bankroll swings will be the same but simply with starting point in turbos. In statistical terms the mean (ROI) will differ but the variance (swings) around that mean won't substanitally differ.

In my example over 100 games someone with a mean ROI of 31% will achieve an ROI with +-30% with 95% confidence. So with 95% confidence it will be somewhere between 61% and 1%.

For the turbos the mean ROI is 20% due to having to take more risks but the variance and standard errors are basically the same (very slightly lower in fact). So after 100 games the 95% confidence on your ROI is 20%+-30% so someone with a true playing ability with an ROI of 20% on the turbos will over 100 games with 95% certainty acheive an ROI of between 50% and -10%.

In bankroll terms for the normals with 95% confidence you would win somewhere between \$336 and \$6. For the turbos you would win somewhere between \$275 profit to a \$55 loss. The potential swing/range is the same but it's simply shifted downwards in the turbos.

This means that you should adjust you bankroll management in turbos as the dips below zero will be greater NOT because of greater variance but because of a lower mean ROI i.e. one that is nearer zero in the first place. So the same amount of variance makes you dip below zero more often on turbos than regulars. But a downswing is not a consequence of variance. It is the steepness of the swings that is a consequence of variance i.e. how far they move away from your mean ROI/average profit. The steepness of the swings in turbos and regulars will be about the same.
27. "I think I agree with the statistical approach taken here; it looks solid.

One thing though - the example used in this (the Cereus SNGs) has identical buyin/rake structures for the normals and turbos. Given that, on stars for example, turbo SNGs often have lower relative rake, the ROI% of 1st/2nd is higher in these games, than in their closest-equivalent normals.

At that point, there's a factor increasing turbo ROI% (known, quantified by prize structure), and a factor decreasing it (known, but not quantifiable) relative to the normals. That makes it hard to say what the overall effect would be; the empirical evidence from the leaderboards may be influenced by something other than the nature of the games (nature of players, moving of better players to normals vs. turbos, etc.)"

I completely agree. Where the rake is lower for a turbo it will increase ROI and indeed variance but only by a couple of %. This actually adds to my argument that ROI in turbos is lower as even with the additional advantage on turbos people still do better on normals.

This difference will come out in peoples individual ROIs which is what I suggest people directly compare.
28.
##### Originally Posted by Landsbanki

This actually adds to my argument that ROI in turbos is lower as even with the additional advantage on turbos people still do better on normals.

Ah, good point, didn't think of it like that.
29.
##### Originally Posted by TiltinShoes

Get outta here with your "statistics." Of course we mean short term variance is higher. Over the long haul it is no higher.

All I know is I have never had a 1k game break even in regs, or a 140 bi downswing, and I have in turbos.

Is there a buy-in & table structure at which you've played 100s of tournaments at both regular and turbo speed?

Does anyone else have a large sample of both on the same type of table with the same buy in. I'd like to actually work out the variance on two datasets from the same player? If so and you don't mind your stats being analysed could you tell me your alias, pokersite and tournament type.

Unfortunately I don't have a good enough sample for my own data as I usually play turbos and the one table type I play at a normal speed has no turbo equivalent on stars. I think doing the calculations on real peoples data is the only way to get a definitive answer.
30.
##### Originally Posted by z06fanatic

lol your ROI would be the same in a turbo vs non turbo longterm? that makes no sense. the deeper the structure and slower blind levels allows deeper stacked play thus more skill being involved. obviously if you take a pro player vs a novice at 100 bbs deep vs the same scenario at 10 bbs deep, the pro is going to show more profit with the deeper stacked play.

bottom line is faster structures/shorter stacks = more variance and less of an edge.

Good job at reading my follow up post. As it stands you sure did own me tho.