More fun with variance - monte carlo results

[AbelM]

Thanks a lot!

[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