Bases for Bankroll Recommendations?

[pzhon]

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Could you show what happens to the RoR if you drop down a limit once your effective BR drops to 50% of starting strength? Rather than playing that limit until busto.

Assume you're playing 2000NL with a 1BB/100 WR and 20BB/100 SD. You can drop to 1000NL where you're 2BB/100, and if you drop to 50% of that roll, on to 500NL with a 4BB/100 WR (no drop down from here, win or you bust).

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First, that SD/100 is quite low for NL.
Second, with those stats, you are winning the same $/hand at each level, so you should normally play in the game with the least variance. Of course, you might expect that your win rate would rise faster in the tougher game.

To determine the actual risk of ruin, you need to determine your plan for moving back up, if any.

Case 1: You never move back up.
Case 2: If you move down to NL $1k, then double up to your original bankroll, you return to NL $2k. If you move down to NL $500 and double up to half of your original bankroll, you move back to NL $1k.

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Roughly the percentages of hitting the floor of each limit multiplied by one another, no? Except that your BR for the higher two limits is halved in the calculation?

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Yes, for Case 1.

Let ROR_n(x) be the risk of ruin if you play at level n forever with a starting bankroll of x.

Then your risk of ruin with this strategy is

ROR_2k(BR/2) * ROR_1k(BR/4) * ROR_500(BR/4)

~ ROR_2k(BR/2) * ROR_2k(BR) * ROR_2k(4 BR)
~ ROR_2k(5.5 BR)
~ ROR_2k(BR)^5.5

So, this strategy has the effect of increasing your bankroll by a factor of 5.5, or raises the risk of ruin to the power 5.5. Just playing at NL $500 in the first place would be a factor of 16 rather than 5.5, since your bankroll is 4 times as many buy-ins, and your win rate is 4 times as great.

Case 2 is more complicated.

What is the probability that you lose everything before reaching n times your initial bankroll? The probability of going to infinity is both 1-ROR(BR), and probability of making it to n*BR, and then failing to bust out.

(1-ROR(BR)) = P(BR->nBR)(1-ROR(n BR))
P(BR->nBR) = (1-ROR(BR))/(1-ROR(n BR))

You can use this to set up a solvable system of equations for the risk of ruin with BR, BR/2, and BR/4, but the answer I get is not worth typing. Returning to the higher stakes games increases your ROR relative to Case 1.

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Cue the chimpanzee to scream

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what's up with you and screaming chimpanzees

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They don't like me? It's hard to tell, since it seems to be a different one each time. I write that so that someone who seriously disagrees will take more effort to distinguish himself from a screaming chimpanzee than is sadly typical, or will look like a joke.

In another forum, someone posted a poll, A or B. It turns out he really wanted people to answer A. I alone voted B, and posted the results of a mathematical model supporting B, and gave some qualitative arguments about why B is better. The responses? "Kill yourself." "Intuition always beats mathematics." I hope we can do better in the 2+2 forums.

[Gonso]

Thanks, no my numbers aren't right, I just needed to see how that works. I'm trying to move up to a limit I haven't beat in a couple tries yet. When I gave example numbers I didn't consider the $/he was all the same - of course in that case lowest variance makes for the best game.

[Paul2432]

A couple of additional points to consider:

1) The 300BB rule assumes you bankroll accumulates. If you consistantly cash down to 300BB you will eventually go broke. Think of flipping coins and counting tails as down swings. If you flip a coin 100 times, 10 tails in a row would be unusual. If you flip a coin one million times, you would expect multiple runs of 15 tails or more. The effect of growing your bankroll is that by the time the larger downswings come, you'll have the bankroll to withstand them.

2) Another point is that you risk of ruin only depends on your current bankroll (assuming win rate and standard deviation stay the same). If you start with 300BB and lose 100BB, you have exactly the same risk of ruin as if you started with 100BB and won 100BB. The consequence of this is that if you want to play with a certain risk of ruin, you need more than you think unless you plan to quit as soon as your bankroll drops.

Paul

[facepull]

an excellent discussion on this in print is in mark blades book. but that really is for limit. the problem i have is what exactly does BUY-IN mean? is it the max buy-in for a capped no-limit game? dont you control that buy-in? is it the minimum buy-in? also when you guys say no-limit$200 or no-limit$500 what the hell does that mean? I know its used for internet games.

[EGO]

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what exactly does BUY-IN mean? is it the max buy-in for a capped no-limit game?

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Yes. A buy-in in NL is the max buy-in for a table.

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also when you guys say no-limit$200 or no-limit$500 what the hell does that mean? I know its used for internet games.

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NL200 means the max buy-in is $200. If you think you need 20 buy-ins to play NL200, you'll need $4000 in your bankroll.

Pzhon is very correct, though. Your bankroll requirements are exactly that. Your bankroll requirements. Before anyone decides how much they need to play at a certain limit/stakes, they should answer a few questions.

- Will I move down if I lose a bunch? (yes - smaller BR)
- Will I be withdrawing from my bankroll? (yes - bigger BR)
- Am I trying to move up to the next level? (yes - bigger BR)
- How good am I at this level? (one of the best - smaller BR)

Each of these questions (and quite a few others) affect how much you want to have in your bankroll.

Edit: I'm currently building a bankroll, and playing with the intent of moving up with around 200-300BB for the limit I'm playing. I don't withdraw (smaller bankroll), consider myself better than the majority of my competition (smaller bankroll), amy trying to move up in stakes (bigger BR), and can move down if I go on a long losing streak (smaller BR).

However, when I reach my target limit, I'm going to want a much larger bankroll than I'd need, because I might not be in the top 10% or so of the field, I'll be withdrawing regularly, I won't be actively attempting to move up in stakes, and moving down will really hurt. At this point, I'll probably want 1000+ big bets in my roll.

Determine your motives for playing, and you can use that information to derive your appropriate bankroll.