Variance in SnGs vs. cash games

[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.