Good morning gunfighters!
Last week I was reading an account of the performance of Kelly staking in meaningful timeframes. The article suggested that while Kelly staking is optimal for maximum growth of bankroll – that is, it has the shortest expected duration of bets to reach a target – its volatility means that it can take a large number of bets/time before you can be totally sure that you are ahead of any other staking system. If you’re unfamiliar with it, Wikipedia has the background on Kelly staking. So let’s move on to some experimental work.
I constructed this-spreadsheet to compare Kelly with level stakes betting, then added in two more methods: percentage betting; and one used by many of the Champion Bets analysts: staking to win 5% of the bank off the rated price.
Rather than dwell forever in academic fairyland, I made the following assumptions:
- Cap the betting run at 500 bets. I figure in real life, if you have made it to 500 then in all but extreme odds cases you will be reflecting on the performance of your betting, and trying to gauge whether you do in fact have an edge
- Maximum bet is to collect $2,000
- Make the scenario easily adjustable, so that volatility of results can be observed
- Include a scaling factor so that Kelly can be detuned to your choice
- Select any rated price and the market on offer – a random engine adjusts automatically
It’s a bit synthetic, in that most punters face a range of odds and supposed advantages, but let’s use the “odds held constant” scenario just to compare staking performance.
Set some numbers into the yellow boxes then sit back hitting the F9 key to watch scenario after scenario materialise.
Volatility can be scary… yes, very scary.
It’s easy to outperform Kelly for many runs using a high enough percentage bet, but watch the minimum bank figure. How close to zero could you handle before you ultimately decide to pilot something a little more stable?
Playing around with this, I think you will find that while Kelly staking is proven to be optimal, it is not sensationally superior to other strategies in a meaningful number of betting sequences.
Kelly staking got a good write-up in Fortunes Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, by William Poundstone.
It is one of gambling’s must reads – beyond Kelly staking it covers some intriguing characters.
For some of the nefarious background to the story, listen to the first half of this interview.
(And if you happen to be finance orientated, the paper I was reading is here).