Bellman Bets Meets Shannon's Demon
As 'Royal Ascot' week is upon us with a splendid array of graded stakes races, it would be nice to enjoy some convex betting opportunities without risking too much capital and ending the week with either a small loss or a small gain.
To that end and with a certain amount of tongue-in-cheek attitude, we present our 'Bellman Bets meets Shannon's Demon' (or Session Handicapping meets Market Rebalancing) strategy. The ideal conditions for using this approach include:
- Markets should be volatile (i.e. range of short-, medium-, and long-priced winners),
- Markets should be negatively correlated (i.e. Local Track and Royal Ascot) or uncorrelated (e.g. cash), and
- Rebalancing costs should be very low or zero.
Let us assume that we have the following parameters for both markets:
- Number of Races = 7
- Current Bankroll = 117
- Target Bankroll = 525
- Win Probability (Avg) = 0.15
- Decimal Odds (Avg) = 7.00
- Current Race = 1
In order to put the protocol through its paces, we simulate the first four Bellman bets (assuming three losses and one win):
[Local Track; 13:45]
java.exe GamblersRuin 7 117 525 0.15 7.00 1
Success = 0.23789
Stake = 13.0
[Local Track; 14:20]
java.exe GamblersRuin 7 112 525 0.15 7.00 2
Success = 0.22352
Stake = 29.0
[Royal Ascot; 14:30]
java.exe GamblersRuin 7 103 525 0.15 7.00 1
Success = 0.21001
Stake = 36.0
[Local Track; 14:55]
java.exe GamblersRuin 7 131 525 0.15 7.00 3
Success = 0.24309
Stake = 19.0
leaving us with the a small profit. Note that the winning bet at Royal Ascot assumes it was on one of multiple selections in that particular market.
Ideally, we should consider quitting for the day if we either win or lose 50% of the initial bankroll. If the former outcome occurs, then we should also revisit our estimates for average price and average win percentage. Either way, our 'portfolio' is automatically rebalanced for the next day.
Mathematically, Bellman maximizes our probability of reaching a specific target using a limited number of events and Shannon reduces the impact of volatility drag on our portfolio by rebalancing after every event.
Tread carefully, do your own research, and enjoy!