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#1
06-12-2005, 02:20 PM
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A simulation of Variance (Long)
Having read all about variance on these forums and witnessed first hand the highs and lows I decided to simulate the results for a winning SNG player over a number of games played. First off I decided that the player would exclusively play $20+$2 tables and that they would place: 1st - 14% 2nd - 12% 3rd - 14% This results in a winning player ITM = 40% and ROI = 21.8%. So not the worlds best player but a solid winning player nonetheless. I then decided that the player has decided to hammer party on 4 tables playing 50 in a day, 250 in a week, 1,000 a month and 12,000 a year. THE RESULTS FOR A DAY (50 SNG's) So I ran the simulation 10,000 times each time generating the result of playing a block of 50 SNGs. The very worst day our player lost $580 and their best day resulted in a $1,400 win - but these are extreme results as on average our player won $240. The interesting bit is that 10% of days resulted in losing $80 or MORE. 20% (including the previous 10%) of days played resulted in only winning $20 or less. On the flip side our player went on a tear and won $580 or more 10% of the time and $460 or more 20% of the time. However to me the interesting part was that 20% of the time this player would play all day and end up roughly breaking even or worse (and sometimes much worse). The other point to make here is that this player is absolutely immune from tilt i.e. the result of their next game is in no way affected by any of the previous results. So to reiterate this player will play 50 SNGs and 20% of the time they will breakeven or lose - and this pure variance and is never due to tilt induced bad play. THE RESULTS FOR A WEEK (250 SNG's) Once again the simulation was run for 10,000 blocks of 250 SNG's. The extreme results for the week were losing $1020 and winning $3280 on average our player made $1180. So our player witnessed a 46 buy in downswing over 250 SNG's - which kind of make me wince even though this was only one result in 10,000. However the good news is that as you might expect some of the variance seen in the days results is being ironed out by the larger volume of SNGS played. Now the player only breaks even or loses about 3% of the time - so maybe one or two weeks per year our player breaks even or worse. Again there is upside with 10% of the weeks being $1940 or better and 20% being $1680 or better. THE RESULTS FOR A MONTH (1000 SNG's) Once again the simulation was run for 10,000 blocks of 1000 SNG's. The good news here is that in 10,000 months (833 years!) of results our player never had a losing month with their worst result being a win of $1060. On average our player won $4800. 90% of the months fell within a band starting at $2920 and ending in $6700. So I guess a fair spread of results but I would feel a lot happier never posting a negative month as this really would be awful! THE RESULTS FOR A YEAR (12000 SNG's) Once again the simulation was run for 10,000 blocks of 12,000 SNG's. If you played this in real time finishing around now then you might have bumped in to Jesus having by then completed 80% of the years! Anyhow over a years worth of SNG's our players very worst year was 'only' winning $42,860. On average they won $57,540 which would have bought quite a lot back then! 90% of years fell between winning $51,100 and $64,460. Anyway I thought that I would share this info as I know that it will help me the next time I break even over 50 SNG's and ponder whether I should have stopped after the first 4 when I was $52 up. Next time this happens I will know that due to sheer randomness this result will happen about 20% of the time and that it is not some conspiracy due to cashing out or Party being bent. Take a step back and see the larger picture. 
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#3
06-12-2005, 02:26 PM
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Re: A simulation of Variance (Long)
[ QUOTE ]
1st - 14% 2nd - 12% 3rd - 14% This results in a winning player ITM = 40% and ROI = 21.8%. So not the worlds best player but a solid winning player nonetheless. [/ QUOTE ] Those stats are for a player better than most will assume. Sure he/she is not world class....but I would say if those are long term metrics, then this player is better than 'solid.' Even in the $22s....22% ROI is certainly not trivial by any means. I'd be curious to see what your numbers say for 5% or 10% ROI (or even a player who just beats teh rake). I think far more 'winning' players play at these levels than most 2+2ers assume after reading this board. Yugoslav
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#4
06-12-2005, 02:29 PM
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Re: A simulation of Variance (Long)
Great work, and killer first post.
If you do the same for a 10% player at the $109s I will love you forever, and as an added bonus I'll convince Yugo to sleep with you. Welcome to the forum!
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#5
06-12-2005, 02:36 PM
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Re: A simulation of Variance (Long)
[ QUOTE ]
I'd be curious to see what your numbers say for 5% or 10% ROI (or even a player who just beats teh rake). I think far more 'winning' players play at these levels than most 2+2ers assume after reading this board. [/ QUOTE ] Yeah. This information is great, but the best info would be a comparison of these same numbers between players of different ROIs. With something like this, players can decide whether moving from a 15% ROI player at the 100s to a 8% ROI player at the 200s is really worth the added variance. Great first post.
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#6
06-12-2005, 02:39 PM
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Re: A simulation of Variance (Long)
"players can decide whether moving from a 15% ROI player at the 100s to a 8% ROI player at the 200s is really worth the added variance."
Yeh it'd be great to see a comparo of that. I know in EV terms that if you can only get half the ROI at the $109s as you can at the $55s it is still worth the move up (the extra rakeback), but the variance issue would be nice to look at.
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#7
06-12-2005, 02:29 PM
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Re: A simulation of Variance (Long)
Wow -- excellent post!
I agree an almost 22% ROI player is quite good, better that mearly a solid winning player. I, too would be interested in results for something a bit lower like 15% or so.
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