More fun with variance - monte carlo results

[fnord_too]

Ok, I whipped up a little monte carlo simulation in java that does the following:

Given the total cost of an STT, payout structure, and %chance of finishing in each of the paid spots, it runs a player through 10,000 STTs. I wrote the program to run 10,000 players through 10,000 STT's and save the data to run stats on. I can easily change any of the variables and re-run it. For the first go round I used:

Entry fee: $55
Normal pay outs (250, 150, 100)
12% chance for finishing 1, 2, or 3 (so 36% ITM)
This comes out to $5/S&G, or 1/11 (.0909...%) ROI.

So, for 10k players playing 10k tournies each, here is what I got.

Net Profit:
Mean: $49,962 (E is 50K)
SD of Net: $8,789
Max Profit: $83,600
Min Profit: $17,100

ROI
Mean: 9.08%
SD: 1.60%
Max: 15.20%
Min: 3.11%

Max Loss (Before going positive for good)
Mean: $709 (just under 13 buy ins)
SD: $747
Max: $7,140 (just under 130 buy ins!)
Min: $0 (duh)

Last STT where player was negative
Mean: 291 (!!!)
SD: 422
Max: 3,755 (!!!)
Min: 0 (again, duh.)

As I said, easy enough to change the values and see how different assumptions change things. I probably wont move this to my home computer until tomorrow, but if there are specific runs people want me to do, it takes like 2 min all told to do the run and post process the data. (It takes longer to type it in here. Maybe I will add the stats to the program and have it spit out cut and pastable results.)

[A_PLUS]

I'd be really interested to see the longest streaks a losing player can have a +ROI.

[1C5]

Cool,
can you do a 20% ROIer for the $22s?

[Kama45]

nt

[Kama45]

[ QUOTE ]
I'd be really interested to see the longest streaks a losing player can have a +ROI.

[/ QUOTE ]

Maybe start off with a player 10% 1st, 10% 2nd, 10% 3rd?

[AbelM]

I would be real interested in these with a sample of 1000 STT's.

[fnord_too]

To everyone who is interested in seeing some particular run, give me:
Level (or buy in and payout structure if it is not a party stt)
win, place and show percentages
number of STT's each "player" plays (I did 10k for this since that is reasonably into "the long run". There is little danger at that point of a player with 1/11 ROI ever being negative or close enough to zero to worry about it.)
number of players you want run through (again, 10K gives a lot of good statitics, and you will see about the worst you can expect. even if you wanted to see short runs of STT's, a lot of players taking those short runs will give you a better understanding of the deviation.)

If there is any other data you would like to see, let me know. I whipped this program up in short order just to get my bearings on generic MTT tool. (those of you who have read poker, gaming and life by DS will recognize that he had an MTT chapter that did some monte carlo analysis. That made me think about building a tool to explore things a little more than he did. I will actually do design work on that tool, which will be able to do STT's, too, but in the mean time it is trivial to change the parameters on the monte carlo simulation I have.)

[Nottom]

[ QUOTE ]
[ QUOTE ]
I'd be really interested to see the longest streaks a losing player can have a +ROI.

[/ QUOTE ]

Maybe start off with a player 10% 1st, 10% 2nd, 10% 3rd?

[/ QUOTE ]

I don't have a robust program for this, but I threw some numbers into an excel spreadsheet I have that does this sort of sim and after about 30 refreshes I got an "average" player to be a winner after 3318 SNGs (I never got anything else greater than 1600 in another 50 tries or so). Most of them were positive at some point in the 300-500 range.

[tshort]

I think these are really interesting results. After 10,000 tournaments, the player could be 95% confident his profit will be between 67,540 and 32,384. I wouldn't have guessed the standard deviation would be so high after 10,000 tournaments.

The mean drop of 13 buy-ins before going positive confirms past discussions about expected drops.

I don't know how you are storing the data your generating, but I think some scatter plots would be interesting.

I think simulations are pretty cool, too, so a while back I had written a simulator that does some of this same stuff and a few other things as well. Same idea as OP, basically... for a given finish distribution, the simulator compiles a few statistics and prints out the probability distribution for Total Profit, Longest OTM Streak, and Lowest Profit (think lowest point on a profit graph). The info below is from a simulation of 10,000 players playing 1,000 SNG's each ($50 + 5). The finish distribution I used was 1st=13%, 2nd=12%, 3rd=10%.

The most interesting thing I've taken from these sims is how drastically finish distribution can affect the other distributions, so let me know if you want to see the stats / charts for other distributions.

FYI on the charts, the number in () is the number of players falling in that particular bucket and the number in the [] is the percentile for the upper end of the bucket. The number after the bracket is the value of the point in the distribution (or the upper end of the bracket, in the case of the profit charts).

Hope you find this useful somehow...



avg profit: 5470.81 , avg ROI: 0.0994692727272727
profit per game: 5.47081
longest otm streak: 34
avg longest otm per trial: 14.4373

Consecutive OTM: ____________________
|# (5) : [ 0.1% ] 8
|## (57) : [ 0.6% ] 9
|########### (349) : [ 4.1% ] 10
|############################ (891) : [ 13.0% ] 11
|########################################### (1394) : [ 27.0% ] 12
|################################################# # (1624) : [ 43.2% ] 13
|############################################# (1446) : [ 57.7% ] 14
|######################################### (1302) : [ 70.7% ] 15
|############################ (901) : [ 79.7% ] 16
|##################### (655) : [ 86.2% ] 17
|############## (434) : [ 90.6% ] 18
|########### (326) : [ 93.8% ] 19
|####### (225) : [ 96.1% ] 20
|#### (125) : [ 97.3% ] 21
|#### (113) : [ 98.5% ] 22
|## (57) : [ 99.0% ] 23
|## (40) : [ 99.4% ] 24
|# (26) : [ 99.7% ] 25
|# (10) : [ 99.8% ] 26
|# (7) : [ 99.9% ] 27
|# (9) : [ 100.0% ] 28
|# (1) : [ 100.0% ] 29
|# (1) : [ 100.0% ] 30
| (0) : [ 100.0% ] 31
|# (1) : [ 100.0% ] 32
| (0) : [ 100.0% ] 33
| (0) : [ 100.0% ] 33
|# (1) : [ 100.0% ] 34


Profit: ____________________
|# (5) : [ 0.1% ] $-3877 -7.0% ROI
|# (14) : [ 0.2% ] $-2805 -5.1% ROI
|## (30) : [ 0.5% ] $-1732 -3.1% ROI
|#### (91) : [ 1.4% ] $-660 -1.2% ROI
|######## (221) : [ 3.6% ] $412 0.8% ROI
|############### (436) : [ 8.0% ] $1485 2.7% ROI
|######################### (719) : [ 15.2% ] $2557 4.7% ROI
|###################################### (1091) : [ 26.1% ] $3630 6.6% ROI
|################################################# (1405) : [ 40.1% ] $4702 8.6% ROI
|################################################# # (1463) : [ 54.8% ] $5775 10.5% ROI
|################################################ (1398) : [ 68.7% ] $6847 12.4% ROI
|######################################### (1195) : [ 80.7% ] $7920 14.4% ROI
|############################# (834) : [ 89.0% ] $8992 16.4% ROI
|#################### (561) : [ 94.6% ] $10065 18.3% ROI
|########## (285) : [ 97.5% ] $11137 20.2% ROI
|###### (151) : [ 99.0% ] $12210 22.2% ROI
|### (68) : [ 99.7% ] $13282 24.1% ROI
|# (22) : [ 99.9% ] $14355 26.1% ROI
|# (7) : [ 100.0% ] $15427 28.1% ROI
|# (4) : [ 100.0% ] $16500 30.0% ROI

Profit Low: ____________________
|# (2) : [ 0.0% ] -5581
|# (3) : [ 0.1% ] -5287
|# (3) : [ 0.1% ] -4993
|# (8) : [ 0.2% ] -4700
|# (1) : [ 0.2% ] -4406
|# (12) : [ 0.3% ] -4112
|# (12) : [ 0.4% ] -3818
|# (22) : [ 0.6% ] -3525
|# (22) : [ 0.8% ] -3231
|# (47) : [ 1.3% ] -2937
|# (60) : [ 1.9% ] -2643
|## (114) : [ 3.1% ] -2350
|### (176) : [ 4.8% ] -2056
|#### (249) : [ 7.3% ] -1762
|###### (419) : [ 11.5% ] -1468
|########## (645) : [ 17.9% ] -1175
|############## (941) : [ 27.4% ] -881
|###################### (1521) : [ 42.6% ] -587
|############################### (2183) : [ 64.4% ] -293
|################################################# # (3560) : [ 100.0% ] 0

[AbelM]

215's
1/2/3 - 12.2%/12.25%/10.3%
1000 STT's
10k

Is it also possible to put out some graphs?

Thanks /images/graemlins/cool.gif

[fnord_too]

[ QUOTE ]
215's
1/2/3 - 12.2%/12.25%/10.3%
1000 STT's
10k

Is it also possible to put out some graphs?

Thanks /images/graemlins/cool.gif

[/ QUOTE ]

E = +$21.70/STT = $21,700 for 1K STT's

Net Profit:
Mean: $21,720
SD of Net: $11,255
Max Profit: $64,800
Min Profit: $-20,400

ROI
Mean: 10.10%
SD: 5.23%
Max: 30.14%
Min: -9.49%

Max Loss (Before going positive for good)
Mean: $2,620
SD: $2697
Max: $26,910
Min: $0

Last STT where player was negative
Mean: 226
SD: 270
Max: 1000
Min: 0

I'll think about graphs in a little while, just got into work and I have a meeting in a few. What's shocking is that the average person with these stats doesn't get positive for good until 226 STT's. wow.

[AbelM]

Thanks a lot!