Variance in SnGs vs. cash games

[alphatmw]

is it greater, lesser, or about the same? it seems to me that it would be less variance in SnGs.. if you get kings vs. aces here you just lose your buy in. if you get kings vs. aces in a cash game, your whole stack is in danger.

[Apathy]

your reasoning makes no sense but your conclusions are fairly accurate.

[FatalError]

Variance is way less, playing 50 SnG's a day i hardly ever post a loss, i very rarely post a huge (over my ROI) win either, it makes it easier to pay the rent and car though

[DonButtons]

but you run very good

[Karak567]

[ QUOTE ]
Variance is way less, playing 50 SnG's a day i hardly ever post a loss, i very rarely post a huge (over my ROI) win either, it makes it easier to pay the rent and car though

[/ QUOTE ]

Ever have a 22 buy-in drop?

They make me want to slice my eyeballs out and eat them.

[Ogre]

[ QUOTE ]
but you run very good

[/ QUOTE ]

i just had my first losing session in over a month at the 100s

[Karak567]

[ QUOTE ]
[ QUOTE ]
but you run very good

[/ QUOTE ]

i just had my first losing session in over a month at the 100s

[/ QUOTE ]

What do you define as a "session?" How many SNGs? Just curious...

[Ogre]

12-16 usually
Today I lost 6/6 coinflips so I lost 6 buyins.

[igotBlackJak]

6 is nothin...

word

[mosdef]

i think is a silly question. the degree of variance in your results is totally up to you. you can choose to play SNGs with more or less variance in results than cash games, or vice versa. your expected winnings and variance in winnings is dictated by your play, its not an intrinsic property of the game.

[NYCNative]

I'd say the variance varies...

[Matt R.]

[ QUOTE ]
its not an intrinsic property of the game.

[/ QUOTE ]

Yes it is. Your style of play can change how much variance you experience in each individual type of game you play, but given a style of play your variance will be different depending on the game. Take large multi-table tournaments for instance. You can be a great great player and have a huge positive EV for a tourney, but at the same time you could play in hundreds of these and never win (or even a long stretch without cashing). A player that is equally good at cash games won't go as long without booking a profit, so the variance is smaller by definition. The same is true for single table tourneys and cash games, just to a lesser degree. Just to note, I'm not saying STT's have more variance (I'm not really sure which style of game does), but I think the difference in variance between STT's and cash games is much less than MTT's and cash games.

[mosdef]

[ QUOTE ]
A player that is equally good at cash games won't go as long without booking a profit, so the variance is smaller by definition.

[/ QUOTE ]

no it isn't. the definition of variance is not the probability of "not booking a profit".

and your idea of someone "equally good" at cash games doensn't sit well with me. what do you mean?

and also, i agree that if you play all your hands the same way in a cash game and a SNG then your variance will be different. so will your expected profit. but my point is that you can control both your expected profit and your variance with your style of play, so you can't declare SNGs as "higher variance" or "lower variance" than cash games without a bunch of qualifying statements.

back to your MTT idea, these are also not "higher variance" games. you can go all-in every hand starting with the first hand and your variance would be almost zero because you would lose almost every time. of course it would be stupid to do so, but it's clear that as you become less stupid your variance goes up and you expected return goes up as well. its up to the player to determine what expected return and variance they will have.

[Matt R.]

A player with an expectation of, say, $35,000 in a tournament with a buy-in of $10,000 can easily play for a long, long time without showing a profit. They stand to show a profit that is equal to their expectation over a very long period of time. If they can go a very long period without even cashing, then their variance must be high by definition. Also, a really bad tournament player can get lucky and win, showing a huge profit despite a really negative expecation. This is clearly a high variance way of playing poker.

Similarly, when I say someone who is "equally good" at cash games, I mean someone with an equal positive expectation. It is much less likely that this player will go as long without showing a profit. Therefore, his variance must be smaller. Do you understand my point now?

[mosdef]

i understand your point, but i still disagree.

you seem to be defining variance as Maximum Possible Winnings - Maximum Possible Losses. This is not right. It needs to be weighted with the probabilities of the max winnings, max losses, and everything in between.

and your definition of equally skilled players is still too vague. lets say someone plays a MTT with 10k buyin and expected return of 35K. so expected long term return is 25K. what is an equally skilled cash player? someone who wins 25K in the same average time it takes him to finish one MTT? if so, i am not at all convinced that the variance is smaller. that just isn't necessarily true.

and your example of a "high variance" bad player who once-in-a-while flukes into a tourney win is just wrong. if he finished out of the money 99% of the time and first 1% of the time, that's a LOW variance return distribution because he almost always has the same result.

[Matt R.]

[ QUOTE ]
you seem to be defining variance as Maximum Possible Winnings - Maximum Possible Losses.

[/ QUOTE ]

I'm not. I don't really see how you're getting this.


[ QUOTE ]
someone who wins 25K *on average*, over the long term, in the same average time it takes him to finish one MTT

[/ QUOTE ]

Added a little bit, but basically yes, since the only constraint on a cash game is the length of time in which you play, you have to compare it to an MTT by using the length of time it takes you to play an MTT. As far as not being convinced, I still think my reasoning given based on my example should make it clear.

[ QUOTE ]
and your example of a "high variance" bad player who once-in-a-while flukes into a tourney win is just wrong. if he finished out of the money 99% of the time and first 1% of the time, that's a LOW variance return distribution because he almost always has the same result

[/ QUOTE ]

I didn't say he is playing said tourney more than one time. If he keeps playing in the tournament multiple times, his profits will converge to expected returns. If he only plays in it once, gets lucky, and wins, his results will *VARY* greatly with what is expected. This is why it is high variance.

[Apathy]

[ QUOTE ]
[ QUOTE ]
its not an intrinsic property of the game.

[/ QUOTE ]

Yes it is. Your style of play can change how much variance you experience in each individual type of game you play, but given a style of play your variance will be different depending on the game. Take large multi-table tournaments for instance. You can be a great great player and have a huge positive EV for a tourney, but at the same time you could play in hundreds of these and never win (or even a long stretch without cashing). A player that is equally good at cash games won't go as long without booking a profit, so the variance is smaller by definition. The same is true for single table tourneys and cash games, just to a lesser degree. Just to note, I'm not saying STT's have more variance (I'm not really sure which style of game does), but I think the difference in variance between STT's and cash games is much less than MTT's and cash games.

[/ QUOTE ]

In short, the higher your roi is the lower "variance" will be.

[mosdef]

[quote If he only plays in it once, gets lucky, and wins, his results will *VARY* greatly with what is expected. This is why it is high variance.

[/ QUOTE ]

you continue to ignore the fact that he almost never actually does win. you say that it's high variance because the difference between his result when he wins and his expected result is high. but he ALMOST ALWAYS comes very close to his expectation.

here are two players: tell me which one has the higher variance in SNG results:

Player A: Finishes 1st 1% of the time, out of the money 99% of the time.

Player B: Average player, finishes 1st 10% of the time, 2nd 10% of the time, 3rd 10% of the time, and out of the money 70% of the time.

[mosdef]

[ QUOTE ]
In short, the higher your roi is the lower "variance" will be.

[/ QUOTE ]

this statement is 100% totally and completely wrong.

[valenzuela]

[ QUOTE ]
i think is a silly question. the degree of variance in your results is totally up to you. you can choose to play SNGs with more or less variance in results than cash games, or vice versa.

[/ QUOTE ]
OMG!!!plz tell me how do I reduce variance!!!!plz I must know!!

[mosdef]

if you fold on the bubble over and over again your variance will go down. you'll end up with a lower ROI and a lot of 3rds and 4ths, but your variance will be lower.

[freemoney]

if you are aiming to minimize variance you will not always be making the max EV play.

[eastbay]

[ QUOTE ]
[ QUOTE ]
i think is a silly question. the degree of variance in your results is totally up to you. you can choose to play SNGs with more or less variance in results than cash games, or vice versa.

[/ QUOTE ]
OMG!!!plz tell me how do I reduce variance!!!!plz I must know!!

[/ QUOTE ]

I will now reveal the closely held secret to guaranteed minimum variance style of play:

Fold. Repeat.

eastbay

[mosdef]

good god, man! do you actually understand what i'm saying?

that makes 2 of us so far...

[valenzuela]

[ QUOTE ]
if you fold on the bubble over and over again your variance will go down. you'll end up with a lower ROI and a lot of 3rds and 4ths, but your variance will be lower.

[/ QUOTE ]
/images/graemlins/mad.gif, well if I go all-in every hand I can reduce variance a lot. Anyway Sngs have less variance than ring games and thats it, I was just making fun of someone who failed to identify a very legitamate question.

[Apathy]

[ QUOTE ]
[ QUOTE ]
In short, the higher your roi is the lower "variance" will be.

[/ QUOTE ]

this statement is 100% totally and completely wrong.

[/ QUOTE ]

Assuming you are using the term 'variance' to mean the negative swings that can be taken by playing, then I am not worng at all, of course if you mean "The range of monetary swings total you can take (+ and -)" then as eastbay says, just lose every single tourney, 0 variance right there.

[valenzuela]

[ QUOTE ]
if you are aiming to minimize variance you will not always be making the max EV play.

[/ QUOTE ]
where is citanul when u need him???????? /images/graemlins/mad.gif, dude I was being sarcastic...anyway I put u on ignore but once again Im reading ur post, I have no selfcontrol I just cant put ppl on ignore /images/graemlins/frown.gif

[Apathy]

[ QUOTE ]
if you fold on the bubble over and over again your variance will go down. you'll end up with a lower ROI and a lot of 3rds and 4ths, but your variance will be lower.

[/ QUOTE ]

once again you might have a slightly smaller range of monetary swings doing this, but you would lose a pile of money, and your down swings doing this would be MUCH greater then playing optimally.

[freemoney]

if you are referring to on the bubble this will surely not reduce variance, and it is not true that sng's clearly have more variance.

[valenzuela]

clearly have less variance...it was a typo

[freemoney]

no, thats wrong.

[mosdef]

this is what i'm trying to get at. variance is not bad. it's a necessary consequence of positive expected return.

but some people may want to play with a lower variance and be willing to accept lower return. the same way people will buy bonds instead of stocks if they don't want to take on the risk. each player defines their own expected return and variance combination with their play. and you can choose a higher or lower variance in cash game OR a SNG. it's not as if one naturally has a higher variance than the other no matter what you do.

[freemoney]

well said.

[pzhon]

On a site called Two Plus Two, I expect to see more numbers.

There are many ways to try to compare the variance of one game with another. One way is to look at the win rate you can safely obtain with the same bankroll and the same level of safety. For scalable games, the Kelly Criterion recommends playing so that your bankroll equals SD^2/Edge. Your comfort level might be described by the multiple of this bankroll you have. (Most people prefer to have at least 2-4 times the bankroll recommended by the Kelly Criterion.)

The standard deviation per SNG is about 1.7 buy-ins. The ROI depends on the level. At low levels, some winning players expect a ROI of 30%.

The standard deviation for a NL ring game depends on many factors including your playing style and how long you stay at a table if you accumulate multiple buy-ins. Many SSNL players report a standard deviation of about 40-50 PTBB/100. Up to NL $100 or so, many people report a win rate of about 10 PTBB/100.

For a low stakes limit ring game, many people win 2 BB/100 with a standard deviation of about 15 BB/100.

If you play $20+2 SNGs with a ROI of 30%, and each SNG averages 40 minutes, the Kelly Criterion recommends that you have a bankroll of $211 to get that $6.60 per SNG, or $10/table-hour.

If you play $50 NL, the Kelly Criterion recommends that you have a bankroll of about 250 PTBB = 500 big blinds = $250 for the ~$7/table hour you win.

If you win 2 BB/100 at $2-$4, the Kelly Criterion recommends that you have $450 for the ~$6/table hour you win.

So, if these win rates match yours, you can safely win more with a smaller bankroll by playing SNGs than ring games. The advantage over NL ring games is slight.

[mosdef]

that's not true. even if you are playing with a higher expected ROI, if your variance per tournament is higher than the probability of large downswings is higher.

[beeyjay]

If your sample size is longer than a week I think you're lying.

[Matt R.]

[ QUOTE ]
you continue to ignore the fact that he almost never actually does win

[/ QUOTE ]

I'm not ignoring this at all. Variance is defined as the square of the difference between the expectation of a random variable and it's known mean. If a good player enters a large tournament and has a large positive expectation, but very few spots pay out, there's a high probability that he WILL NOT CASH ONCE over a long period of time. Therefore, the difference between his expectation and his known mean is large -- and his variance is large. Take a player of equal skill in a cash game (same positive expectation as the tournament player). It is very unlikely that he will go broke every single session he plays in over that same period of time. This could happen to the MTT player. Based on the definition for variance, the cash game player's variance is lower.

[ QUOTE ]
ALMOST ALWAYS comes very close to his expectation

[/ QUOTE ]

This simply isn't true for a tournament player who plays in tourneys of large fields with typical payout structures (see above) when compared to a cash player. STT's are a different story and are much lower variance, but that wasn't my point.

And as for the question you asked, Player A has a much lower variance. His expectation is essentially zero though (edit -- meant to say it's essentially 0% of the prize pool, so E(x) would be negative and the actual value would depend on the buy-in), so I don't see your point. One of the qualifiers in my original argument was that the cash game player and tourney player were of equal skill in their respective game, and hence had equal expectations.

[pzhon]

[ QUOTE ]
and you can choose a higher or lower variance in cash game OR a SNG.

[/ QUOTE ]
Of course you can affect the variance slightly. However, everyone reports a very similar standard deviation for SNGs, roughly 1.7 buy-ins. Some people say that you can affect the variance in a SNG by a lot, but I believe that has been refuted by the data.

You can affect the variance in a limit ring game a bit more, but again, everyone seems to report a standard deviation of about 15 BB/100. I don't recall any claims outside 12-20 BB/100.

There is much more control over variance in a NL ring game, since you can choose your stack size and you can still win while playing extremely tightly.

[ QUOTE ]
it's not as if one naturally has a higher variance than the other no matter what you do.

[/ QUOTE ]
Actually, that's how it looks to me. Do you have new data?

[dhende3]

Well as an example, I was playing with a $1300 bankroll 2 weeks ago at the 11s. I dropped 30 buyins to go down to around $1k. Then, being the smart gambler I am, moved up and started playing the 22s and have since gone up about 60 buyins to around $2300. That is about as swingy a stretch as I have experienced in about 1k SnGs.

[Apathy]

[ QUOTE ]
that's not true. even if you are playing with a higher expected ROI, if your variance per tournament is higher than the probability of large downswings is higher.

[/ QUOTE ]

How does one calculate "variance per tournament"?

The thing is, the argument you are trying to make may appeear to make intuitive sense, but is incorrect, I would love to be shown otherwise though.

For one the AM spreadsheets required Bankroll for x% ROR calculations would strongly disagree with your assertations.

[mosdef]

Let X equal your winnings per tournament. X is a random variable, it's variance is your variance per tournament. Let's say that the expected value of X is E[X] and variance of X equal Var[X].

Let Y equal your cumulative winnings over n tournaments.
E[Y]=nE[X] (for the most part - if you're a person who goes on tilt then your tournament by tournament results will not be indepedent, for example). Similarly, Var[Y]=nVar[X].

Let's take a look at two players. For the sake of argument, let's say that these are 10+1 players.

Player A: Weak-tight grinder with the following distribution of finishes.

1st: 9%
2nd: 16%
3rd: 17%
4th-10th: 58%

Player A has an expected return of E[X_A]=1.7 and variance of Var[X_A]=275.71.

Player B: More aggressive player who "plays-for-first" more often.

1st: 18%
2nd: 7%
3rd: 10%
4th-10th: 65%

Do the math, we get E[X_B]=2.1 and Var[X_B]=381.39.

No surprises yet: most of us would agree that aggression and shooting for first helps your ROI - you can see that here.

Now, suppose our players are both about to embark on a 100 tourament session. We can ask interesting questions, like: what are the relative chances that A or B will hit a bad downswing? More specificallly, lets ask: what are the relative probabilities of A or B ending up down 20 buy-ins at the end of their sessions.

Define Y_A and Y_B as the cumulative winnings of A and B, respectively after 100 tourneys. We can accurately approximate Y_A and Y_B with normal distributions with mean and variance as follows:

Y_A ~ N(170,27571)
Y_B ~ N(210,38139)

Prob(Y_A < -220) = 0.84%
Prob(Y_B < -220) = 1.39%.

So, for these 2 particular players, the guy with the higher ROI also has a higher prob of a downswing (downswing defined as 20 buy-in drop).

So what have I proven? Not a heck of alot. For starters, there are player finish distributions with higher ROI and lower probabilities of multi-buyin drops. But, it is not ALWAYS the case that a higher ROI means lower probabilities of multi-buyin drops (the dreaded downswings).

One last comment: In my comment that Apathy challenged, I was sloppy in my statement. What I should have said is that as your variance goes up, the likelihood of downswings goes up IF you consider downswings to be underperformance relative to your expected performance. Of course, if your expected performance is increasing along with your variance, then its anyones guess as to whether or not your probability of a multi-buyin drop is higher or lower.

In conclusion, your playing style dictates your expected return and variance. As your variance goes up, your likelihood of underperforming your expectation goes up. So there's a balancing act going on, where you need figure out if the additional variance is being compensated by sufficient added return. Of course, the ultimate way to improve is to add expected return and lower variance at the same time.

What a long post. First one to finish gets a prize.

[bluefeet]

is blood oosing from your tear ducts normal?

[raptor517]

[ QUOTE ]
Variance is way less, playing 50 SnG's a day i hardly ever post a loss, i very rarely post a huge (over my ROI) win either, it makes it easier to pay the rent and car though

[/ QUOTE ]

what is yer sample size? 2 weeks?

holla

[raptor517]

[ QUOTE ]
Ever have a 22 buy-in drop?

They make me want to slice my eyeballs out and eat them.

[/ QUOTE ]

try 22 ootms in a row. then you might wanna die foreal. holla

[raptor517]

[ QUOTE ]
In short, the higher your roi is the lower "variance" will be.

[/ QUOTE ]

well, TECHNICALLY this isnt the case, though generally it is. if you have 28% 1s, 0% 2s, 0% 3s, and 72% ootms, you will be a VERY high roi player, but will have HUGE swings. you could EASILY go 20+ sngs without cashing. but whatever, im just tired and nit picky. holla

[raptor517]

in 15-30, the BEST players in the world have talked abuot 400+ BB downswings. thats 12k+. in the 215s, the BEST players have talked about 60+ buyin downswings. thats 12.9k+. so basically, to play these levels, you need a pretty solid bankroll. in EITHER case, there can be quite a bit of variance. this topic has been brought up time and time again, with great points being made on each side of the debate.

in NL cash games, variance will be rather low, even if you are playing in the bigger games. i think the LOWEST variance form of poker for the super solid online players is the NL cash games. if you EVER drop 10 buyins in a 400 max game online, you are likely making some HUGE errors in judgement.

im really tired right now, so i dont want to get into all of the numbers, but sng variance is a LOT more than what most casual players expect. once you get to start playing full time, multitabling like a mad man, you will start to see some crazy swings. EVERYONE has. period. its not all that hard to be on a super heater for 3k sngs. its really not.

holla

[SNOWBALL138]

If you want, you can almost completely avoid downswings in cash games. By adjusting your play solely for that purpose, you would gravely injure your winrate though.