bankroll concepts - risk of ruin

[KurtSF]

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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?

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Probably not. If you've played a million hands at this level, then in the next 10k hands lose 200BB, that is a blip on the radar. I wouldn't think twice about losing that much with as much confidence as 1000k hands sample will give you.

OTOH, very few people have that kind of sample to base their expectations on. Especially because when they "get serious" they will often rack up a number of hands that dwarfs whatever sample they were basing their expectations on. The key is the "one long session" idea. As long as you didn't change games, or improve, or otherwise change the "assumptions", everything should be considered together... don't split it up. If you play 20k hands at 1BB/100, then the next 1K hands you lose 200BB, you are not a winner with a losing streak. You are aparently a break even player, but don't really know. If you play 100K hands at 2BB/100 and then 200k at -1BB/100, again, you are apparently a break even player but don't really know.

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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.

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That risk of ruin calculator is nifty, but you you really should know that the number you are plugging in for winrate is an estimate. How confident are you? How many hands?

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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?

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I would consider both amount and time. If you lose 100BB in 1k hands, who cares. Lose 20BB over 100k hands and the lossrate is tiny, but its much more likly to be real. If you do something that can potentially have a big impact on your rate like move to a new game, you should keep close tabs on your bankroll, etc. Big swings can hurt.

This is very prescient example for me. I beat a game to the tune of 5BB/100 over 100k hands. Moved up in levels and over the next 15k hands lost 500BB. Whoops! Guess I wasn't as good as I thought I was!

As a "rule of thumb", I would say you should start being aware around 200BB. Any less is pretty standard, but around there is where it starts becoming pretty unlikly for a winning player to have a sustained losing streak.

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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. =)

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You should do that for sure, to give yourself an idea of where you stand. Anyone can have a 200BB losing streak. Easily. But its definitly worth reevaluating your expected win rate if you do. No links, sorry.

Good luck.

[ryanj247]

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This is very prescient example for me. I beat a game to the tune of 5BB/100 over 100k hands. Moved up in levels and over the next 15k hands lost 500BB. Whoops! Guess I wasn't as good as I thought I was!

As a "rule of thumb", I would say you should start being aware around 200BB. Any less is pretty standard, but around there is where it starts becoming pretty unlikly for a winning player to have a sustained losing streak.


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ok, thanks!

yeah i mean, when you're unsure of your winrate estimate in a new game, it really sucks to get to -200BB, start questioning your assumptions at that point, and keep going until you get to -3,4,500BB before you say "yep, guess i'm not a 2BB/100 winner in this game" lol.

seems like maybe somewhere between -100-200BB is the time to just stop, move back to the game you're a winner in, replenish the roll and work on improving anything you think might have been your weakness before giving the new game another shot....

[BillC]

1. You must take into account future bankroll supplements when discussing risk of ruin. If you do not, any discussion seems absurd. If you have an alternate bankroll model you will just have to end up converting it to the traditional notion - I think. If you have another way to do it, I'd love to hear it.

2. Kelly model is a good continuous approximation to discrete reality. You readjust your betting levels in stages, approximating Kelly or fraction thereof. The approximation is very good in practical terms.

I think it is best to start with a Kelly model for bankroll and factor other considerations in. I mean, what are you going to do otherwise? Just use seat-of-the-pants numbers like 25%?

If you cannot drop down in stakes, at some point you might be well-advised to stop playing. The cardinal sin of the Kelly criterion is to overbet you bankroll. Betting twice kelly (ROR=1/e) or more leads to negative bankroll growth.

Of course having confidence you are winning is of paramount importance. Obviously most are losers.
People complain about all this splitting of hairs over bankroll, when they should be talking about poker. But some of us split hairs for a living.

[ryanj247]

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If you cannot drop down in stakes, at some point you might be well-advised to stop playing. The cardinal sin of the Kelly criterion is to overbet you bankroll. Betting twice kelly (ROR=1/e) or more leads to negative bankroll growth.


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i need to do some reading on the kelly stuff. but there's one thing that's hard for me to grasp about RoR as it applies to poker:

suppose i run the calculation given my WR and SD and find that a 250BB BR = 1% RoR. well, when i only have 25BB on the table and i'm betting in increments of 1BB, my RoR is 0%. if i lose all those chips, then my BR is now smaller and my RoR is higher when i start my next session.

so when you talk about "betting twice kelly or more", how does that really apply to poker, when in poker we're not really "betting" much at all (relative to BR)?

[BillC]

If you are engaged in an activity that say gives you a certain win rate r and variance v per unit of time (or e.g. 100 hands), betting k times Kelly translates into having a bankroll of v/(kr). The attendant risk of ruin given k is exp(-2/k).

So if your v/r is 100 big bets, betting Kelly means having 100 big bets as a BR. Twice Kelly would be a BR of 50 units. You certainly want to readjust before getting below the 50 unit mark, and probably before going below the 100 unit mark.

You see, Kelly betting applies to a macro game, which averages over whatever goes on from hand to hand at the table. It is a continuous approximation which only depends on win rate and SD. There is a way to apply Kelly theory to micro decisions such as drawing and pot odds, and blackjack playing indices, but that is for another thread.