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.

[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?

[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.

[1C5]

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

[Kama45]

nt

[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.)

[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 [img]/images/graemlins/cool.gif[/img]

[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 [img]/images/graemlins/cool.gif[/img]

[/ 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.