Using The Kelly Criterion In Poker
A New Approach to SNG Bankroll Management
The Kelly Criterion Involves Managing Your Poker SNG Bankroll
To Avoid Going Broke Using A Formula First Published in 1956.
The Kelly Criterion was first published in 1956. It is a mathematical formula which is designed to be used in any gambling situation in which you have a positive expectation. While the formula may look a little complex to those not mathematically minded the concept is actually very simple: How much of your bankroll can you bet on any given positive expectation outcome without risking going broke!
The emphasis on positive expectation is of course deliberate – if you play in a poker game where your outcome is negative (are a losing player once we strip out the variance + rake) then you will lose your bankroll eventually! No formula can help you here…
The idea of the Kelly Criterion is that it assigns the highest bets (SNG Buy-in levels for our example) that can be made without going broke. This means that instead of the traditional SNG Bankroll Management approach of ‘when to move up’ we ask the following question: What is the highest level of SNG that I can play with my current bankroll and after how many losses do I need to move down levels?
The math below looks in more detail at the formula and how to apply this to SNGs, if you are not mathematically minded then skip this part and move to the applications / conclusions section below.
Basic Kelly Criterion Formula: f* = (bp-q)/b
f* is the fraction of the current bankroll to bet
b is the odds received on the bet
p is the probability of winning
q is the probability of losing, which is 1 - p
p is our ITM
So the first question becomes what data can we assign to ‘b’ (odds received on our bet). This of course is dependant on the ROI of the individual SNG player. If we calculate ROI using the ‘standard’ definition of (wins – losses) / investment and use the buy-in level as the bet we end up with a definition for f* (the correct fraction of our bankroll to bet).
This is:
f* = ROI * ITM / (ROI + 1 - ITM)
Now we can plug in some realistic numbers for SNG players and make sure the equation works.
For a 10% ROI player with 45% ROI the f* score becomes 6.9% = 15 Buy-ins
For a 16% ROI player with 45% ROI the f* score becomes 10.1% = 10 Buy-ins
Experienced SNG Players will note that these numbers are far lower than the ‘standard’ 50 to 100 buy-ins commonly suggested for bankroll management. The key factor is that applying the Kelly Criterion to Poker involves moving down levels after losses… The next question then becomes when to move down?
Here are some examples working with 15 buy-ins:
$33 SNGs Start With $407 Move Down At $305
$22 SNGs Start With $272 Move Down At $158
$11 SNGs Start With $136
The great thing about applying the Kelly Criterion to Poker is that your chances of going broke are small so long as you maintain the discipline to move down levels after losing a couple of SNGs.
For many though the bankroll used for each buy-in level is uncomfortable, there is a perception of risking too much of you roll at any one point. If this describes you then there is always the option of using the ‘Half-Kelly’ or ‘Quarter-Kelly’ options instead. These basically double and quadruple the bankroll requirement and carry proportionally less risk at each stage… here are the same figures as above using the Half and Quarter options:
Half Kelly Bankroll 10% ROI + 45% ITM
$33 SNGs Start With $815 Move Down At $576
$22 SNGs Start With $543 Move Down At $294
$11 SNGs Start With $272
Quarter Kelly Bankroll 10% ROI + 45% ITM
$33 SNGs Start With $1630 Move Down At $1120
$22 SNGs Start With $1087 Move Down At $565
$11 SNGs Start With $543
Every winning player knows that good bankroll management is the key to success with online poker. Make sure you have an even greater edge by checking out our Rooms and Bonuses section today for the latest freerolls and $ bonuses.
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