bankroll growth question (kelly experts wanted)

Guruman · #1 01-11-2007, 01:12 AM

After some research it’s become apparent that the Kelly criterion really can't apply to poker because of how specific one has to be in the analysis of the edge. Since poker advantages and disadvantages are forever in flux, Kelly can't apply.

With that said, surely there must be a more optimized way to grow my poker bankroll than the method that I am currently using. My poker situation is as follows:

My entire roll is devoted solely to limit poker. I add all rakeback and bonuses to my poker roll and use those along with my winnings to push me into the highest games I can afford (without regard for skill level). I do not have to withdraw from my poker roll at any time for living expenses, and can sustain swings that cause me to move down in levels with only bruises to my ego. My goal is to grow my bankroll and my stakes as efficiently as possible.

I currently use a linear, stepped bankroll management system that works as follows: move up at 600 bb, move down at 200 bb, withdraw a max of 20bb on moveup and buy toys.

This system has served me well for many thousands of hands and many different levels of play. It generally assures me of always playing for meaningful stakes while providing a mechanism to diffuse the risk of ruin. The one glaring hole though, is the fact that for any given bankroll I could be playing at one of two different limits, depending on whether or not my last move was up or down. For example, my threshold to move up into the 1/2 game from the .5/1 game is $600 (600 * 1bb). I’ll stay at the 1/2 game until I reach a bankroll of $1200 and then move up into 2/4. If I then lose until my roll decreases to $800, I’ll have reached my movedown threshold and return to 1/2.

This means that there is a $200 range in there (from $600 to $800) where I may be either at 1/2 or at 2/4 depending on whether my last move was up or down.

That’s clearly suboptimal, so here’s another idea.

In an attempt to approximate Kelly style movement, I could break my roll into a reasonable number of bets, and use that number of bets to determine the stakes that I’m playing at. As I sit down and get up from various tables, I’d have to redistribute the roll and recalculate the stakes that I’m playing at. In effect this means that I size each bet that I make at the poker tables to roughly approximate the same percentage of my roll regardless of the stakes I play, which I believe is the spirit of the Kelly criterion.

After creating some tables, setting my bankroll to equal 250 bets seems to most closely approximate the 200 and 600 bb thresholds that I currently employ, at least at the lower levels. At the higher ones, it obviously will move quicker but that’s a reflection of the system, not the initial setting. I only play 2 tables at a time, so it doesn’t look like I’ll run into the potential issue of buying in at different limits on different tables too often. (this would be caused when buying in at one table would cause the remaining roll to move past a movedown threshold before buying into the next table)

In this system my thresholds would be unified, and therefore I would spend any time rebuilding after a movedown at different stakes than I played while moving up. At 250 bets, the thresholds for moving up or down would be as follows [these numbers are in $50 increments from a chart I made, so excuse the approximations]

$150 .5/1 $300 1/2 $1050 2/4 $1550 3/6 $2550 5/10 etc.

again, these seem to reasonably mimic the current thresholds that I have set.

Is this dumb? What are the consequences on the outer reaches?

thx!!

PairTheBoard · #2 01-11-2007, 12:07 PM

Sounds like an improvement on your current method.

PairTheBoard

Guruman · #3 01-12-2007, 08:22 PM

is that because there's no overlap or because it's percentage based (logarithmic) growth?

any other insight from anyone?

thx!

PairTheBoard · #4 01-13-2007, 04:43 AM

[ QUOTE ]
is that because there's no overlap or because it's percentage based (logarithmic) growth?

any other insight from anyone?

thx!

[/ QUOTE ]

As I understand it you're doing an aproximate Kelly method now via Steps. Your new method just uses smaller Steps thus getting closer to continuous adjustments which is what an ideal Kelly Method would use. So it's an improvement.

PairTheBoard

Guruman · #5 01-13-2007, 01:54 PM

cool. thanks.