While poker theory is a relatively new field, modern economic theory
has been around for decades. The question "How do I maximize my
long-term profits in risky ventures?" has been answered with finality.
The Kelly Criterion, according to Chapter 24 of Chen and Ankenman's Mathematics of Poker,
will do better than any essentially different strategy in the long run.
Why choose a Kelly strategy? For starters, it completely negates the
concept of risk-of-ruin. The kelly involves fluidly moving up and down
between limits, as dictated by your bankroll. If you go on a tear, you
will move up in limits. If you run bad, you are able to drop down.
Risk-of-ruin calculations use the premise, "Assuming I will play $20
games until I am broke or robusto, what is the likelyhood that I will
one day be broke?" I would contend that this assumption is complete
horse shit on all counts, and kelly simply outperforms it on every
level.
Kelly Formulas
How do we apply a Kelly strategy to heads-up bankrolls? First, we have
to determine how aggressive we want to be with our bankroll. If we are
not playing professionally, or our bankroll is replenishable (say,
<$200), we can apply a maximally aggressive strategy.
The formula for this, where K is the percentage of our bankroll to
wager, is: K = ROI * Bankroll. For example, with a bankroll of $150,
and an ROI of 8%, our K= .08 * $150 = $12. This $12 represents the
highest buyin level that you should play.
As we increase in stakes, we should become more conservative.
Professional gamblers are recommended to use a "quarter-kelly"
bankrolling strategy; they should multiply their K number by 25%.
The formula for this is: K = (ROI * Bankroll) * .25. With our $150
bankroll and 8% ROI, using a quarter-kelly strategy, our max buyin is
$3. If this seems low, then you may want to be more aggressive with
your kelly strategy.
Based on your risk aversion, you should choose the kelly number that is
right for you. Remember, the higher your kelly number, the greater your
swings, and the higher your long-term EV.
Applying a Kelly Formula
Personally, I use a half-kelly strategy. My kelly number is: K = (.05 * 5000) *.5; or $125.
This means, with a 5% ROI and a $5000 bankroll, I can comfortably play
games with a buyin up to $125. If I was to play a game with a buyin of
$150, I would be making a long term -EV decision. It's vital to never exceed your kelly number when using a kelly strategy.
What Kelly Number am I?
For starters, your kelly number should never be higher than 1, and
never lower than .25. Next, you should estimate your ROI on the
conservative side, as over-estimating your winrate will yield a much
too aggressive bankrolling strategy. Finally, if you are prone to tilt
because of large swings, you should be very careful with choosing a
volitile kelly bankroll. If your ROI changes, you may begin playing in
a -EV bankroll situation.
Limitation of Kelly - Inconsistency in Past or Future Play
Even if you've played thousands of games in the past, this is not a definite indicator that your future ROI will be the same as your past ROI. The games may get softer or harder. You may move around in limits. You may switch sites. You may watch a bad video or hear some bad advice and your play will suffer from it. The rake can change. This is why it's vital to estimate your ROI on the conservative side when using the Kelly strategy.
(Caveat: these formulas are simplified, but the simplification causes them to err on the conservative side.)
Urinurine September 24, 2009 5:41 PM
Hey Saje - solid info.
First time on your site, I like it. I notice that the comments field doesn't sync up on your site and husng - I wonder if there is any way to make that happen.