Simulation of Floating bankroll needed

[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