bankroll concepts - risk of ruin

[ryanj247]

if i assume a given win rate and standard deviation, then the larger my bankroll, the lower my risk of ruin, correct?

by the same token, if i require a y% risk of ruin, then I need a $x bankroll.

now, let's say i run the calculation and fund a BR with the required $x for a y% risk of ruin, and head to the tables. suppose i lose money in the first month: is my risk of ruin now higher than it was when i started?

if so, then isn't a BR formula basically saying "you need a $x bankroll to have a y% RoR (given the WR and SD), unless you ever (i.e., initially) run bad enough that your BR drops below $x"? that is, if you lose in the first month, you should be prepared to replenish your bankroll to the starting amount to maintain a y% RoR going forward?

i'm having a hard time matching that line of thought to the idea that a BR calculation gives a definitive, "one time" amount that should be enough to withstand swings and avoid going broke all but y% of the time.

[AaronBrown]

Your reasoning is correct, but you're putting too much faith in the calculation.

If you always replenish your bankroll to $x, then your risk of ruin is zero (unless you lose all $x before replenishment). The risk of ruin calculation says when you have $x, if you keep playing regardless of bankroll, there is y% chance that you will go broke. Every time you win or lose any money, your risk of ruin changes.

Most people use this as a theoretical result only. If your bankroll is large enough that your risk of ruin is, say, 1%, most people can play comfortably without worrying about bankroll. For most people, that means they can play their best poker and enjoy life. If the risk of ruin gets up to, say, 25%, you take some remedial action: move to lower stakes, play more conservatively or get some more money.

In that case, your risk of ruin never was 1%, because you never planned to play without adjustment all the way to ruin. But the number gave you the confidence to ignore bankroll for a while. Similarly, the 25% wasn’t real either, it was just an alarm signal to say, “start worrying about your bankroll.” You then adjusted your play to reduce the risk of ruin to an acceptable level again.

The reason people do this kind of thing is to avoid thinking about bankroll every day and in every poker decision. You establish a comfort zone for risk of ruin, then live and play as if the risk of ruin is zero. When you get outside your comfort zone, you fix things to get back in. Worrying about bankroll every day isn’t fun, and worrying about bankroll in a poker decision hurts your play

[DrVanNostrin]

[ QUOTE ]
let's say i run the calculation and fund a BR with the required $x for a y% risk of ruin, and head to the tables. suppose i lose money in the first month: is my risk of ruin now higher than it was when i started?

[/ QUOTE ]
Team X was on the books as a 2:1 favorite over team Y. At halftime team Y is ahead by a lot. Is team X a 2:1 favorite now?

[ryanj247]

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In that case, your risk of ruin never was 1%, because you never planned to play without adjustment all the way to ruin. But the number gave you the confidence to ignore bankroll for a while. Similarly, the 25% wasn’t real either, it was just an alarm signal to say, “start worrying about your bankroll.” You then adjusted your play to reduce the risk of ruin to an acceptable level again.


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thanks for the reply. that really helped to clarify things for me.

one question: is 25% a reasonable point to "start worrying about your bankroll"? i wasn't sure if you were using that number as a sort of established standard, or just threw it out there.

the basic dilemma for me is this: once i decide on a reasonable size bankroll for the game i intend to play, at what point should i *really* be concerned that i'm no longer properly bankrolled for that game if i start off in the new game with a downswing.

just as an example: when i run my BR calculation for 10/20, given my expected WR and SD I find that i should have a $5300 BR for 10/20 @ 1% RoR. i wouldn't hit the 25% RoR mark until i was down to $1600. if i'm down $2500-3000 in the first few weeks, should i still feel comfortable playing as if my RoR was zero?

[BillC]

Your risk of ruin is approximated by a function of your bankroll, expectation and variance. Therefore as you bank changes, so does your risk of ruin. There is no "once and for all" number.

If your risk of ruin exceeds 13%, then if you can move down in stakes, you certainly should. Probably you want to keep your ROR under 1%. These numbers all come from fractional Kelly betting theory.
For more on this topic see bjmath.com, especially the risk formula paper by BillC and Marc Ingenoso.

[alThor]

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If your risk of ruin exceeds 13%, then if you can move down in stakes, you certainly should.

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I think this is too strong of a statement.

I know where it's coming from: (1) If you are currently playing at full Kelly, and will never resize bets (i.e. change stakes), then your ROR is around 13% (or 13.5%, whatever). (2) If you are resizing your stakes/bets as your bankroll changes, then you don't want to bet more than full Kelly (to max your growth).

I think you are using (2) and (1) together to make your statement that "ROR above 13% is always bad". But note that the two statements apply to different scenarios: whether or not you resize.

A person who wants high EV and is less concerned about ruin may very well have a ROR above 13%. I don't think it's common, nor would I advise anyone to do this in most situations. Nevertheless, I don't think we should proclaim 13% ROR as the highest permissible one, absolutely.

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Probably you want to keep your ROR under 1%.

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This is very conservative for people who can replenish their bankrolls. It would often be better to set a higher ROR, but then resize (change stakes) if your bankroll drops significantly. In this case, your true ROR is lower than the the ROR you originally calculated, but your EV is going to be much higher.

If one is a retiree who plays to supplement his income, then a conservative ROR is certainly appropriate.

[ QUOTE ]
These numbers all come from fractional Kelly betting theory.
For more on this topic see bjmath.com, especially the risk formula paper by BillC and Marc Ingenoso.

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Am I correct that you are a different BillC?

[KurtSF]

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just as an example: when i run my BR calculation for 10/20, given my expected WR and SD I find that i should have a $5300 BR for 10/20 @ 1% RoR. i wouldn't hit the 25% RoR mark until i was down to $1600. if i'm down $2500-3000 in the first few weeks, should i still feel comfortable playing as if my RoR was zero?

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If you're down 150BBs in the first few weeks of playing that level I would suggest that you reevealuate your expected win rate, as well as BR, when calculating RoR.

[BillC]

I am making some assumptions to invoke Kelly of course. Some fool might want to bet his whole BR on a coin flip, but Kelly is optimal in well-known senses, which one can read about.

Bankrolls can't be replenished by definition. The replenishment would be included in the initial BR. If I am going to inherit a million dollars in 30 years, I would include the present value in my BR.
The 1% rule is in line with the usual 300-500 big bet bankroll often recommended for limit holdem for a "skilled player".

You are incorrect--I am the same BillC

[AaronBrown]

I agree with KurtSF that if you lose you should worry more about your expected win rate than your risk of ruin. After all, if your original ROR was 1%, only 4% of the time should you ever see it balloon to 25%. Therefore, even a confident player should take a hard look at her game.

I don't buy the Kelly logic in this situation for several reasons. One is that, as BillC says, it defines bankroll as everything you could get over your life, not just your cash in hand today. Second, as alThor says, it assumes you don't change your variance as a percentage of bankroll. Finally, it assumes everything is scalable, that you can bet as little or much as you like without cost.

In poker, you can't easily adjust your stake. Moving down in limit may not improve your ratio of win rate to standard deviation, and it may have costs to your reputation, or giving up accumulated knowledge about players. Playing more hands may mean playing more poker than you want, and your level of play might suffer. Turning down close bets hurts your win rate.

I personally think 25% ROR is a reasonable level to reassess, but reasonable people can differ. It will depend on your circumstances and personality. The point is to escape constant adjustment, to concentrate on poker and not on bankroll.

[ryanj247]

thank you for the replies, this has been a very helpful thread for me.

let's assume that we have enough experience to feel confident that our estimate of winrate is accurate for the game we're going to be playing. i understand that true winrate is not something that is easy to be confident in. suppose we've played, i dunno, 1 million hands in this game and we're using our results over those hands to estimate our winrate.

messing around with the RoR calculation i find that i would need to lose 200BB for my RoR to go from 1% to 25%. is a 200BB downswing really enough to start questioning a winrate that has been established over a very large number of hands?

i can definitely see this being a good trigger point to start considering my course of action given my smallish bankroll. but it seems like my main concern at this point would be my high RoR, moreso than doubt about my estimate of winrate... this seems even more true for a 150BB downswing.

now, when moving to a new game, it seems much more reasonable to start questioning your estimated winrate if you have a bad start. in this circumstance, my question is this: is 150-200BB too much to lose before revising your estimated winrate in a new game? if so, what size of loss (in BB) would be a reasonable "trigger point" for readjusting your winrate assumptions/estimations when making RoR calculations? also, suppose that 100BB is a reasonable trigger point. isn't this much moreso the case if the 100BB is lost in 2000 hands than if it takes 10,000+ hands to accumulate that loss?

now that i think about it i think i've seen some forumlas for this type of thing (i.e., "your 100BB loss means that your winrate is between x and y with z margin of error"). i'll start searching for that now, but if you have any links and/or additional thoughts for me i'd much appreciate it. =)