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.

[Nicholasp27]

i don't think 20/9/8 is that funky...people who are more aggressive tend to get more 1sts and 4/5ths than 2/3 places

people who are less aggressive may have tons of 3rds and a higher itm than 42%, but lower roi as a result as they enter itm extremely short stacked

[Nicholasp27]

which equations?
on his spreadsheet, he gives ror% and bankroll needed for that, etc, but that's assuming u never withdraw any money

this question is basically: what's the largest dip u can expect to have to be able to withstand at any point...so u can be safe withdrawing anything above that point from your account whenever you feel like it

is there an equation known for what i was calculating, and if so, where can i find it?

[viennagreen]

since you seem to like simulating-- and if you really want to solve this---

i would recommend a brute force guess-and-test, with x,y,z being random INTEGERS between 0 and 50, and a 10% or 20% leeway on the ROI (that is, variables satisfying the equation for a 30 ROI would give a result 29.8 < f(x,y,z) < 30.2 or something like that)...

It would be interesting to see the results of this program with a dist of:

1 - 10%
2 - 10%
3 - 10%

Which is what could be referred to as the "average" player.

[Nicholasp27]

10,000 sims of 10,000 sngs and the biggest downswing was...

-55

Thank you.

What language was the programmed in? Looks like basic?

[Nicholasp27]

yeah, vb in an Access module

[Benholio]

[ QUOTE ]
It would be interesting to see the results of this program with a dist of:

1 - 10%
2 - 10%
3 - 10%

Which is what could be referred to as the "average" player.

[/ QUOTE ]

This player would go broke pretty quick every time, since he is losing a buy-in every 10 tourneys on average.

[Nicholasp27]

that's why he's the 'average' player

however, i wonder why -55 is the lowest for that player, considering he should be 'expected' to lose 1000 buy-ins in 10,000 games

maybe i messed something up there

[Nicholasp27]

oh wow, i just realized that i had the line

If (randVar > 20 And randVar < 31) Then currBR = 1.8181

so every time it got 3rd it reset the br back to 1.81...so that means u could go down to -30 with getting no 3rds...ouch

i'll rerun the numbers now

[Nicholasp27]

it was resetting my br back to 1.81 every time it got 3rd place, regardless of what the real br was...so i fixed that and reran it and got...

-32

not much diff from the original distribution

[Slim Pickens]

Check AM's recent posts. He just reposted it in another thread. Risk of ruin given x buy-ins as a bankroll is the same as asking what is the risk of an x buy-in downswing starting with the next game... I think.

[Nicholasp27]

risk of ruin is based on u winning, tho

mine is based on u never ever going above point zero

i don't think they are the same, but i'm open to that possibility if someone can explain why

[Slim Pickens]

Here's AleoMagus' response from the other thread.
[ QUOTE ]
The actual calculations to determine a specific bankroll requirement or a specific ROR are:

B=-(SD^2/2W)LN(R)

r=EXP(-2WB/SD^2)

where,
W is your average profit per tourney ($)
SD is your standard deviation per tournament ($)
R is your desired risk of ruin
B is your bankroll ($)

These calculations assume that a player will continue to play at a certain level, and will not cash out profits. This is, of course, a foolish assumption. In reality, we will sometimes cash out profits, and we will sometimes move up or down in stakes.

Assuming we want a 1% ROR, and we have a SD of 1.7 buy-ins, this looks something like this:

ROI - Buy-ins required

5% - 133.1
10% - 66.5
15% - 44.4
20% - 33.3
25% - 26.6
30% - 22.2
35% - 19.0

Really, the old 30 buy-in rule comes from smaller buy-in players who can get 25%+ ROI. All the higher limit players then notoriously chime in that 30 is way too little. This is obviously just because at the limits they play they are far more likely to get 5-10% ROI and thus, require a lot more.

[/ QUOTE ]

By changing the distribution, you're changing SD. That's all.

...and don't make me flame you about the distribution, sample size, and so on.

[Nicholasp27]

he says that those calculations assume u will not withdraw the profits

so it's different calculations and different problem entirely

[Slim Pickens]

OK. I missed that point. Here's a thought on something you could do. Throw some variation into the finish distribution Monte Carlo-style. Instead of using a single finish distribution for the entire run of 10k (or however many) tournaments, for each simulated tournament have it first pick a random finish distribution from a normally-distributed distribution of distributions. Yeah, you heard me. What I think this does is include some epistemic uncertainty in your simulation. Bah. If this makes sense do it. Otherwise, just ignore mme.

[AleoMagus]

Yes, and it is an interesting question.

There is this (quoted from Bozeman in an old thread), though it is not exact calculations:

[ QUOTE ]
The cashing out correction can be dealt with very simply: when your bankroll changes (because of a win, a loss or a cashout), your risk of ruin, from that point, changes. So, if you cash out any excess whenever bankroll is larger than B(r), you will have r probability of going broke after each cashout. Those times your BR falls below B(r) your risk of ruin, calculated at that time, will be larger.

While 1% risk of ruin doesn't sound like much, it can be significant over many opportunities for ruin, since if you play with this RoR always (never less), your risk of going broke sometime will increase linearly (~1%*NumberofSNG's/25). Playing 400 SNG's like this is more dangerous than playing with a bankroll 2/5 as big that you never touch.


[/ QUOTE ]

This is a good approximation (well, actually, I don't know, but I trust Bozeman's opinion on these kinds of things).

I suppose it's a kind of justice that right after I express my frustration about sim guys not bothering with math, a problem arises that I don't have an immediate and more exact answer to.

I can't imagine this will be too hard to figure out though.

I will say this much. The real answer is that a floating bankroll has a 100% ROR. You will go broke. (It only becomes interesting if we ask this over a given sample size).

Regards
Brad S

[Nicholasp27]

yeah, i prefer math over sims, but didn't know how to

and yeah, if u play infinite tournies, u eventually will go have a -X buy-in downswing where X can be any number you want

but i can live with 31 buy-ins if 10,000 sims of 10,000 sngs say that 30 is the worst i can expect (so long as it's accurate)...worst case and it does happen to you after 10k sngs, or even earlier, is that u have to reload with another 31 buy-ins, since u expect to win 3000 buy-ins over those 10k tournies

for now i'm not cashing out cause i'm building a bankroll to move up to the 30s/50s...but once i hit the level that i'm gonna stay at, i'll run the sim for my 1/2/3 ratios and then keep that buy-in amount and withdraw any excess to invest, etc