bankroll concepts - risk of ruin

[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.


[/ QUOTE ]

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.