Simulation of Floating bankroll needed

[Nicholasp27]

I wrote a quick function to see how low a br could dip from the starting point...this would mean if u have that many buy-ins + 1, then u could feel pretty confident about withdrawing the extra money any time your account hit above that initial amount...

i did it for the wiki's roi/itm for 11/22s, which is 42% itm, 30% roi...so i did a dist of 15% 1sts, 14% 2nds, 13% 3rds...if someone wants to suggest a different ratio, then i can run it again

anyway, i had it do 10,000 sngs and any time it hit the lowest point it had ever been, it recorded that and at the end gave me back that lowest point...i then had it run that function 10,000 times and return the lowest it ever got in any of the 10,000 trials of 10,000 sngs...that number: -30


so if u have a 15/14/13 dist, then you can be pretty confident that u won't go broke (at least any time soon) if u deposit 31 buyins ($341 for 10s, $682 for 20s) and then ANY time your account shows more than that amount, u can withdraw that extra for bills/fun/etc

i'll post my code in the next post to make sure that i didn't make any mistakes

[Nicholasp27]

Public Function getLowestBR() As Integer

Dim randVar As Integer, intCount As Integer, lowestBR As Integer, currBR As Integer
intCount = 0
lowestBR = 0
currBR = 0

Do
randVar = Int((100 * Rnd) + 1)
currBR = currBR - 1
If (randVar < 16) Then currBR = currBR + 4.5454
If (randVar > 15 And randVar < 30) Then currBR = currBR + 2.7272
If (randVar > 29 And randVar < 43) Then currBR = 1.8181
If (currBR < lowestBR) Then lowestBR = currBR
intCount = intCount + 1
Loop While intCount < 10000

getLowestBR = lowestBR

End Function


Public Function testBR()
Dim totalLowest As Integer, currLowest As Integer, intCount As Integer

intCount = 0
totalLowest = getLowestBR()

Do
currLowest = getLowestBR()
If (currLowest < totalLowest) Then totalLowest = currLowest
intCount = intCount + 1
Loop While intCount < 10000


MsgBox totalLowest

End Function

[Nicholasp27]

if i ran it for 100 sims of 10k sngs at a time instead of 10000 sims, it returned 21-23 every time...so it does dip to 30 after 10,000 sims of 10k sngs, but i think u could be pretty safe with 25 buy-ins and still remove the extra $$$

[gildwulf]

I guess determining adequate bankroll sizes is the new 'folding QQ preflop':P

This is great stuff, by the way.

[Slim Pickens]

It gets really interesting once you start tracking the largest downswing as a function of finish distribution. Nice work.

EDIT: ...because the concept of an unreplenishable bankroll is much more important to players at higher levels where 42/30 is a little too high... maybe 38/15 for a donk like me.

[Nicholasp27]

yeah, but this isn't the same question as "what br is needed"...this is a question of how much do i need so that i can constantly withdraw the extra...the standard question assumes u don't withdraw from the br...


u can also look at it like this: if your profit graph ever dips -30 buy-ins, then you are not playing poker at a 42/30 clip (at least with that dist)...so u can see when u are on tilt or just not good enough, as opposed to thinking it's variance and bad luck

[Nicholasp27]

yeah, i just ran it for a 20/9/8 dist...which is also 30%, but where u are more aggressive so higher variance...

-38 after only 1k trials of 10k...

u know a quick way to get all possible sets of {1sts, 2nds, 3rds} that = 30% roi? if i have that, i can run it for all of those and graph them so any 30% roi player can see where they stand

[Slim Pickens]

I wouldn't worry about funky finish distributions like 20/9/8. What's more important is to look at how ROI affects the max drop. The finsh distribution itself is a much smaller effect in reality since (long-term anyway) most players have fairly flat 1/2/3 distributions. To reduce it to a simple 2D plot, I think you should do all the x/x/x distributions, where 5%<x<20%.

SlimP

PS: Anyone who hijacks this thread with a "my finish distribution is nowhere close to flat" will get a "sample size snob" response unless you're raptor or FieryJustice or someone else who has at least 10,000 finishes in each place.

[Slim Pickens]

Oh, and AleoMagus is right. This is just a longer, less elegant, less precise way of getting the same results as the empirical ROR equations.

[viennagreen]

I don't think you need to run all possible sets of distributions.... in any case though--- in order to solve the question you asked:

for SNGs where tournament fee = 10% of buy-in:

f(x,y,z)= x (3.5455)+ y (1.7273)+ z (.8182) - (100 - (x+y+z))

where x= % first place, y = % second, z = % third

set f(x,y,z) to whatever ROI you want, in this case 30..

you'll see that you have a lot of answers to this function.