A simulation of Variance (Long)

[AgentSp]

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.

[Kama45]

Nice!

The lack of losing months surprises me a little.

[The Yugoslavian]

[ 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

[AliasMrJones]

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.

[Unarmed]

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!

[Freudian]

If you have the energy please do it with a ROI of 5/10/15. I think we will see pretty big losing streaks now and then.

[morello]

Very nice post. As others have mentioned, I'd love to see the results for someone with an ROI around 10%.

[Jman28]

[ 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.

[Mr_J]

" 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"

God damn I love sngs sometimes...

[Mr_J]

"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.

[lastchance]

Very, very nice post. Interesting.

[FieryJustice]

Imagine the hell I have been going through over the last 1500 games with only a tiny roi.The swings happen much more often and are for many more buyins than listed for the 20% guy. I have only done 2 months worth, but I had a losing streach of 500 games, which really sucks. Variance is not for the weak.

[Eihli]

Thanks for this post. How did you do this sim? Excel?

[Ryendal]

I can't figure out how you can make a simulation of variance without choose an arbitrary variable ...

Nevertheless it's some funny and nice work .

[AgentSp]

I'll post the results as best I can below for other ROI players. The results are in a table generated in excel where the left hand column are percentiles which hopefully are clear.

The 9% player sometimes has losing months which has got to hurt!


OK here are the results for a (1st=13%,2nd=12%,3rd=13%) = 15.5%ROI player again for the $20+2 SNG's

1 DAY=50 SNGs
MIN -$620
0.01 -$380
0.05 -$240
0.1 -$140
0.15 -$100
0.2 -$40
0.25 $0
0.3 $20
0.35 $60
0.4 $100
0.45 $120
0.5 $160
0.55 $180
0.6 $220
0.65 $260
0.7 $300
0.75 $340
0.8 $380
0.85 $440
0.9 $500
0.95 $600
0.99 $780
MAX $1,260

1 WEEK = 250 SNGs

MIN -$1,220
0.01 -$500
0.05 -$80
0.1 $120
0.15 $260
0.2 $380
0.25 $460
0.3 $554
0.35 $620
0.4 $700
0.45 $760
0.5 $840
0.55 $900
0.6 $960
0.65 $1,040
0.7 $1,140
0.75 $1,220
0.8 $1,320
0.85 $1,420
0.9 $1,560
0.95 $1,800
0.99 $2,220
MAX $3,420

1 month - 100SNGs

MIN -$580
0.01 $780
0.05 $1,560
0.1 $1,980
0.15 $2,260
0.2 $2,460
0.25 $2,640
0.3 $2,820
0.35 $2,960
0.4 $3,120
0.45 $3,260
0.5 $3,400
0.55 $3,540
0.6 $3,680
0.65 $3,820
0.7 $3,980
0.75 $4,140
0.8 $4,340
0.85 $4,580
0.9 $4,860
0.95 $5,280
0.99 $6,020
MAX $7,840


1 year = 12,000 SNGs

MIN $26,120
0.01 $31,780
0.05 $34,400
0.1 $35,820
0.15 $36,780
0.2 $37,520
0.25 $38,180
0.3 $38,740
0.35 $39,253
0.4 $39,740
0.45 $40,220
0.5 $40,700
0.55 $41,140
0.6 $41,680
0.65 $42,220
0.7 $42,820
0.75 $43,420
0.8 $44,080
0.85 $44,880
0.9 $45,900
0.95 $47,561
0.99 $50,360
MAX $58,060

Here are the results for a (1st=12%,2nd=12%,3rd=12%) = 9.1%ROI player again for the $20+2 SNG's

1 day=50SNG

MIN -$780
0.01 -$460
0.05 -$300
0.1 -$220
0.15 -$160
0.2 -$100
0.25 -$60
0.3 -$40
0.35 $0
0.4 $40
0.45 $60
0.5 $100
0.55 $120
0.6 $160
0.65 $200
0.7 $220
0.75 $260
0.8 $320
0.85 $360
0.9 $440
0.95 $540
0.99 $720
MAX $1,140

1 WEEK = 250SNG

MIN -$1,540
0.01 -$800
0.05 -$400
0.1 -$220
0.15 -$80
0.2 $20
0.25 $120
0.3 $200
0.35 $280
0.4 $340
0.45 $420
0.5 $500
0.55 $560
0.6 $640
0.65 $700
0.7 $780
0.75 $860
0.8 $960
0.85 $1,060
0.9 $1,200
0.95 $1,440
0.99 $1,800
MAX $3,080

1 Month=1000SNG

MIN -$2,280
0.01 -$520
0.05 $200
0.1 $580
0.15 $840
0.2 $1,040
0.25 $1,240
0.3 $1,400
0.35 $1,560
0.4 $1,700
0.45 $1,840
0.5 $1,980
0.55 $2,120
0.6 $2,280
0.65 $2,420
0.7 $2,580
0.75 $2,760
0.8 $2,940
0.85 $3,160
0.9 $3,420
0.95 $3,840
0.99 $4,620
MAX $6,240

1 year = 12,000 SNG

MIN $9,180
0.01 $14,960
0.05 $17,739
0.1 $19,120
0.15 $20,040
0.2 $20,740
0.25 $21,340
0.3 $21,940
0.35 $22,493
0.4 $22,960
0.45 $23,480
0.5 $23,980
0.55 $24,440
0.6 $24,920
0.65 $25,400
0.7 $25,940
0.75 $26,540
0.8 $27,180
0.85 $28,000
0.9 $29,080
0.95 $30,561
0.99 $33,340
MAX $39,300

[pergesu]

I thought AleoMagus did something like this a while back, made a spreadsheet simulating a winning player. It was used to show that even a solid player could have some brutal runs...numerous 500-game stretches at breakeven or worse, 50-60 buyin drops, etc.

In one of the bazillion "Am I running bad or do I suck?" threads, raptor said he frequently has losing days or weeks, and I think it was Yugo who said you can expect a 30 buyin drop every month or two. Then there's Irie's thread on running bad.

Why are these results so different from what everyone else has said?

[4T25Q85]

w000000t!!!! sweet post!!

I think im gonna start playing more SnGs /images/graemlins/cool.gif

[OrcaDK]

Way cool first post, and very cool stats!

As others did, i got curious about the variance of other players.

I have made a very quick little app that simulates the variance in the same fashion yours does. This is not an attempt to copycat you, simply my own interest taking over, and why not share it. The full credit goes to the OP, let there be no doubt!

You can download it from http://www.improve.dk/sngtest.rar. It requires the .NET framework to run, and it requires WinRar to unpack.

If you're afraid of keyloggers, spyware, whatever, and you don't trust me on my word, please don't use the app. But i can assure you that it's clean.

It has a feature to export to a tab delimited text file, that way you can import the data into Excel and create graphs as you like.

[raptor517]

very excellent first post. (you will rarely hear me say that). holla

[Sabrazack]

This program would truly rock if you could make the results show in some kind of structured manner like in the OP. Also if you could input a decimal placing value, like 14.5% 1:st.
This program could give me some serious comfort when im running horrid.

[lehighguy]

Thank for the post. I've only been playing part time for a month or so at the 50s. When I watch my ROI go from 18% to 10% in like 2 days or go up 2000 and give it all back it really effect me. Eastbay's program is the only thing that keeps me sane and lets me keep pushing. So far over 423 tournies I only have an ROI of 9% + rakeback. I'll keep trying to analyze my game and play more tournies.

[Karak567]

AWESOME first post. TYVM!!!

[OrcaDK]

[ QUOTE ]
This program would truly rock if you could make the results show in some kind of structured manner like in the OP. Also if you could input a decimal placing value, like 14.5% 1:st.
This program could give me some serious comfort when im running horrid.

[/ QUOTE ]

Sure thing, i'll work a bit more on it, gotta win this party $500k first /images/graemlins/smile.gif

[MrTrik]

My post count would indicate what a newb I am here, but for what it's worth, the original post has made my favorites list. Nice work.

[SuitedSixes]

Here is a similar post (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Board=singletable&Number=169 1666&Forum=All_Forums&Words=variance&Searchpage=0& Limit=25&Main=1691666&Search=true&where=sub&Name=1 0938&daterange=1&newerval=1&newertype=y&olderval=& oldertype=&bodyprev=#Post1691666) with instructions on how to simulate this using Excel. In the same thread AM created a link to a better Excel way of doing it, I have no idea if it is still up.

[treeofwisdom7]

my BR is 400$ right now. i started with half like raptor said. im starting to think 400 might not be a bigenuf bankroll altho im not sure what my roi is but in the past 150 games i have a roi of about 15% ..
anyway my question is b4 i start taking some money out of my account how much should i leave in?/??

500 , 600 , 800.. for psychological reasons too.

[OrcaDK]

I've made a lot of improvements to the app now. There's more settings, a whole lot of new stats and some UI improvements. Please tell me if there's more stats you'd like /images/graemlins/smile.gif

www.improve.dk/sngtest.rar (http://www.improve.dk/sngtest.rar)

[OrcaDK]

Forgot average win, app updated.

[SuitedSixes]

I live out of my BR, so my answer may be different, but I just take out 90% of what I made that week as long as it is above what my AM spreadsheet says I need for a 0.0% ROR, which for me is just over 50 Buy-ins.

[1C5]

[ QUOTE ]
my BR is 400$ right now. i started with half like raptor said. im starting to think 400 might not be a bigenuf bankroll altho im not sure what my roi is but in the past 150 games i have a roi of about 15% ..
anyway my question is b4 i start taking some money out of my account how much should i leave in?/??

500 , 600 , 800.. for psychological reasons too.

[/ QUOTE ]


I used to leave everything in my poker account which I liked. It was nice playing the 11s and 22s with $6000+ in my accounts. I could lose and not even notice how much I lost.

Now I keep most in Neteller so I only have $500 which I hate. I had to reload after a $500 downswing. Very annoying.

Probably caused tilt looking at my shrinking account every bad beat.

So my advice is keep a little more than you need. Now I am at around $1000 for the 22s which seems fine.

[raptor517]

[ QUOTE ]
I live out of my BR, so my answer may be different, but I just take out 90% of what I made that week as long as it is above what my AM spreadsheet says I need for a 0.0% ROR, which for me is just over 50 Buy-ins.

[/ QUOTE ]

for me its like 273 buyins. yay. holla

[Nottom]

This is a nice post and all, but frankly I'm shocked that so many posters haven't already run simulations of their own.

They can be pretty easily done without any programming skill just using excel.

Here (http://forumserver.twoplustwo.com/showthreaded.php?Cat=&Number=1711139&page=&view=&s b=5&o=&vc=1) is just one of the previous posts on how to do so.

[FieryJustice]

OK...I feel like a total idiot asking this...but would someone run the numbers for me, assuming 15% for 1st, 11% for 2nd and 12% for 3rd? So, 7% roi and 35% itm. I basically would like to know how many buyins i need for my ror to be 0 and the size of the biggest downswing I may encounter. I GREATLY appreciate it. I hate computers.

[OrcaDK]

[ QUOTE ]
OK...I feel like a total idiot asking this...but would someone run the numbers for me, assuming 15% for 1st, 11% for 2nd and 12% for 3rd? So, 7% roi and 35% itm. I basically would like to know how many buyins i need for my ror to be 0 and the size of the biggest downswing I may encounter. I GREATLY appreciate it. I hate computers.

[/ QUOTE ]

I've contacted my spirits, and they came up with these results for your next 1000 SnG's (you didn't write buyin, so i'm assuming $20's, won't make a difference anyhow).

http://www.improve.dk/variance.jpg

During this rollercoaster your biggest OOTM streak was 13 in a row, and you got ITM 7 in a row. Your biggest downswing was about 28 buyins.

EDIT: According to my simulation, your actual ROI should be around 25% with those numbers, and your ITM should be around 39%.

[FieryJustice]

Thanks a lot. I greatly appreciate it. I'm not too sure how you came up with the 20% roi though, as I have had about 7% roi over the last 2K games with 35% itm.

[Nottom]

[ QUOTE ]
Thanks a lot. I greatly appreciate it. I'm not too sure how you came up with the 20% roi though, as I have had about 7% roi over the last 2K games with 35% itm.

[/ QUOTE ]

From your first post -
15% - 1st
11% - 2nd
12% - 3rd

15+11+12 = 38% ITM

((.15*3.9)+(.11*1.9)+(.12*0.9)+(.62*(-1.1)))/1.1 = 20% ROI

Either you are calculating stuff wrong or your numbers are wrong.

[FieryJustice]

I meant 12% for 1st, not 15%....I am such an idiot....mind running the numbers again? I love you people

[OrcaDK]

http://www.improve.dk/variance2.jpg

During this rollercoaster your biggest OOTM streak was 12 in a row, and you got ITM 5 in a row. Your biggest downswing was about 27 buyins.

Your ROI now stands at around 11% for the simulation, ITM 36%.

[FieryJustice]

That seems much more correct. Sorry for not making sure my forst post was right. Do you have any clue how many buyins i needed to have a ror of close to 0?

[OrcaDK]

I can't do the math for it, but i can tell you that over a streak of 1.000.000 simulated SnG's with your stats, your largest downswing was a whopping 103 buyins! - Now THAT's a downswing able to hospitalize even the most experienced players. All in all, i'd say 50 buyins and you should be safe /images/graemlins/smile.gif

[Madd]

Hi,

I also made an excel-sheet with a simulation over 2000 sitngos and in your case with 12% 1st, 11% 2nd and 12% 3rd (ROI 6.4%) you will encounter dramatic swings. It's not at all unusual to drop more than 100 buy-ins and losing streaks can last more than 1k tournies.
That's why I prefer to play at a lower limit with a higher ROI.

[FieryJustice]

I keep 150 online for a reason /images/graemlins/smile.gif From what I can tell over my first 2000 sngs, the swings are brutal...

[AgentSp]

I agree with the post that says they are surprised at how few people have tried this kind of simulation. I got the idea from a post a long time ago where EastBay mentioned how this is a simple task to perform.

The reason that I posted was that I thought the results were interesting - not so much the process involved.

However the reason that I started the simulation at all was to confirm to myself that after a large number of games the results achieved would form a normal curve. I know that this has caused some controversy in the past with it being counter intuitive as results from a single game are clearly not a smooth normal distribution.

If you don’t believe that this is the case then stop reading here. I checked the results predicted by the stats Vs my simulation and the results are close – really close for larger number of games involved.

I don’t recommend using this for any less than 50 games and preferably over 100. Open a fresh Excel sheet and :

In Cell A1 input the number of games played.

In Cell A2 input the buy in (including rake)

In Cell A3 input your ROI in decimal form (i.e if you have an ROI of 20% then input 0.2)

In Cell A4 input your target.

In Cell A5 (or anywhere in fact) input

=NORMDIST(A4/A1,A3*A2,(1.8*A2)/(A1^(0.5)),1)

Format this cell to be a percentage and viola this is the % chance of NOT achieving your target figure.