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# Introduction

• How high is the variance?
• Four examples of variance

Variance is an expression often used in relation to downswings. It's a synonym for the longer-term appearance of the improbable, the apparent deviation from the probabilities.

Especially with SnG's, you often hear the question: How high is the variance? This is the question with which the following article will deal. As benchmark, we'll use the ROI (Return on Investment). It shows in four definite examples what kind of variance you could be faced with, while having a given ROI and sample size.

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#1 mouse89, 10 Nov 08 16:15

ok

#2 Bedoze, 22 Nov 08 03:02

It is interesting to see the numbers but there should be some explanation along for the ones that don't like numbers that much.

I see that a bigger volume is surely the best for the profitable players! For the ones breaking even not so good.. so they should work on their game.

#3 danutz123, 24 Jun 09 11:45

WHAT ABOUT DON S&Gs? Certainly lower variance, nicht wahr?

#4 Tim64, 19 Oct 09 23:56

The only issue I see is that we don't know which case we fall into. We don't know whether we're a 10% ROI player or 13% or whatever. We only know this once we've played 3000 sngs or so. And if we've played that many we already will have experienced variance. If we haven't, we won't know if we're in a variance period if we are doing badly or if we are just a player with a low ROI...

#5 oFISHnCHIPSo, 26 Oct 09 21:47

Want to see variance: look me up: Syko_21 on Stars!

#6 oFISHnCHIPSo, 26 Oct 09 21:49

April thru June - awesome!
July thru October - about as bad as it possibly could get, considering my finishing positions and Top Shark Rating.

#7 oFISHnCHIPSo, 26 Oct 09 21:50

Look at May, and then look at October, hahaha

#8 excelgeo, 11 Nov 09 13:57

so you should be aiming for win more than being ITM

#9 stevegold87, 25 Dec 09 02:59

#10 paukuk, 15 Jan 10 15:01

I agree with PPL. An explanation would be pretty handy in here.

#11 Koshburger, 10 Feb 10 02:31

ok

#12 Arthibald1, 05 May 10 17:17

WHAT VARIANCE SHOULD A PLAYER EXPECT WITH 3,000 SnG's?

"37% probability that his ROI is negative.
36% probability that his ROI is positive."

There is only a tiny chance that ROI is exactly even, not 27% as this suggests.
This is just WRONG!!!!!

#13 SkamanVN, 08 May 10 09:33

How do they calculate that? is there a method to do it?
I am at 13.8% ROI with 12%#1, 15%#2, 13%#3 after 250 SNG.
What would be the variance for 500 SNG, for 1,000 SNG??
Also, how to take into account the improvment of the game? we surely/hopefully don't play the same after 200 SNG and after 1,000.

#14 shakin65, 10 May 10 12:11

Not sure if it still exists, but I used a prog from a well respected 2+2 poster to run those calculations: RVGs ROI Simulator.

And it does not calculate any improvements of heros game.

#15 laimvai, 11 Jun 10 15:25

You need atleast 20K games to know your estimate ROI.

#16 MikeAK47, 13 Sep 10 23:27

Yep, 20K for sure, guys posting on Forum saying, wow my ROI is 40% after 200 SNGs, should I turn pro?

Hahaha they make me chuckle so much.

#17 CRI4BRA, 29 Dec 10 18:22

by "probability that his lowest bankroll balance will be 15 buy-ins down or worse"

you meab that if he roll on 100 buy in, the stat shows the probability that
a) he will be at 85 buy ins at some point - lowest

b )he will have only 15 buy ins starting from 100 buy ins at some point

thanks

#18 Malamir, 31 Jan 11 18:34

I recently experience 7 out of the money SNG's and I hurt like hell. I see you are referring to 14 OOTM SNG's. Why you chose 14?

#19 DouglasQuaid, 05 Apr 11 00:04

Great article! I was not suspecting that variance is that great over a course of 500-1000 games... That basically means if you play 8 hours a day, and multitabling that even with good ROIs you could expect loosing money at the end of the month with relevant probability.
I was kinda sure that 100 games was a good indicator for SNGs...

#20 outspan, 24 May 11 09:40

Something doesn't add up. In case 1, for a \$11 sng (I assume \$10+\$1), the ROI is said to be 9%, but the EV is:

0.12*3.5 + 0.12*1.7 + 0.12*0.8 - 1*(1-0.36) - 0.1 = -0.02

so the ROI on this sample should be -2%, or 8% without counting the rake (which would be wrong).

(Hero wins 3.5, 1.7 or 0.8 BI each in 12% of cases and loses 1 BI in the other cases. The final -0.1 accounts for the rake, measured in BI).

The calculations are wrong for the other cases as well.

#21 307th, 09 Jun 11 05:13

@#17: pretty sure it means a), which is actually pretty encouraging. 14 buyins down isn't too bad.

@#18: because even if you're a winning player, having 7 OOTM sng's is actually very likely over 500-1000 tournaments, as much as it sucks. They picked 14 because it is unlikely but can still happen.

@ #20: the article's calculations are fine. In a \$10 + \$1 9-man tournament you get \$45 for first place. That's a bit over 4 buyins, but you have 1st place at 3.5 buyins. So that's why your calculations aren't matching the article's - you've got the payouts wrong.

#22 outspan, 17 Jun 11 11:44

@#21: no, I already subtracted the buy-in. If the placements in 1st, 2nd and 3rd are 12%/12%/12%, then you gain:

3.5 BI (4.5-1) in 12% of cases
1.7 BI (2.7-1) in 12% of cases
0.8 BI (1.8-1) in 12% of cases

and you lose 1 BI in all other cases (100-12-12-12)% = 64%

and then you have to account for 0.1 BI in rake (\$1 over \$10). So the EV is

0.12*3.5 + 0.12*1.7 + 0.12*0.8 - 1*(1-0.36) - 0.1 = -0.02

and the ROI is -2%.

#23 bankrollmanagment, 21 Jun 11 11:55

#24 307th, 17 Jul 11 13:52

@22: Oops, I'm wrong and you're right. Yeah, it looks like the article forgot to include rake or assumed they were 10man sng's or something.

#25 TheGuyFromCIA, 04 Oct 11 19:12

the variance is too damn high!

#26 C0WB0Y, 18 Sep 12 00:17

I have to agree that these numbers are meaningless without explaination! Did you pull these numbers out of your asterisk? Please to explain where these numbers come from. If 20k sng's is the measure than why are you using such a small sample of 1000 or 500 why not show the numbers for 20k games?