by AimHigher » Wed Jul 21, 2010 8:09 am
These are my 2 cents, based on my knowledge of sports betting, statistics, money management theory and my experience as a user of Odds Wizard/Stake Wizard. How much you should be willing to risk on a bet, or a series of bets, is a function of the expected value AND the probability of winning. As an example, let’s say we have two bets:
Bet A: Fair odds 1.5 Line odds 1.8
Bet B: Fair odds 4 Line odds 4.8
Both bets have the same expected value of 20% (1.8/1.5 - 1 = 4.8/4 - 1). However, the probability of winning is very different. Bet A has a probability of winning of 1/1.5 = 66.67% while Bet B only has a probability of winning of 1/4 = 25%. Hence, the variability of your bank roll if you play a series of Bet B will be a significantly greater than for Bet A. Also, because of this variability, if you bet the same amount on both bets the "risk of ruin" (chance that your bank roll goes to 0 before realizing the long run return) is a lot greater for Bet B than for Bet A. So if you want to achieve a good balance between "risk of ruin" and long term return, you would bet less on Bet B than on Bet A. Presumably, the algorithm Stake Wizard uses will accomplish this goal better than the standard Kelly formula (or variants thereof) and I don't doubt that it does. So with this in mind, how much SW will recommend that you bet is a function of the absolute level of the fair odds (theoretical probability of winning that bet) and the expected value for the bet. For Bet A (using your 2000 and 20000 numbers) SW will recommend to bet 292.76 while for Bet B it will recommend betting 58.90. If the fair odds calculated by Odds Wizard are absolutely correct I have no reason to don't doubt that these levels are the optimal ones. However, my personal preference is to be less aggressive since the fair odds are only a theoretical number and other factors (injuries, motivation, weather etc) play in as well. So if my actual bankroll is 2000, I might use a bankroll of 500 with a target of 5000 when calculating the bet sizes. If, after several hundred "live" bets, Odds Wizard's fair odds have proven to be very accurate (on the leagues that I am betting on) then I might consider using a “fund” amount closer to my actual bank roll when calculating my bet sizes.
I also know that some successful sport bettors will be risking a certain % of their bankroll on a given bet as you mention. If you only place bets where the probability of winning and expected value is similar e.g. your estimated fair odds is always around 2 and expected value is always around 10% , then this method can make sense. However, if you place bets with varying probability of winning OR with varying expected values, it does not make sense to me for the reasons mentioned above.
For your last question regarding combining bets, it works differently for different bookmakers. Some of the bookies I use will automatically give me the option to place a bet on a “double” if I select two separate bets before entering a bet amount (or “triple” if I select three bets etc). “Double” would mean that both bets would have to win for the bet to be graded as a winner and the odds of the bet would be the individual odds multiplied with each other. Other bookies, such as Pinnacle Sports, will have a separate section (for Pinnacle it is called Parlays/Accumulators) where they have certain bets where they offer the opportunity to combine bets. You would then simply select the bets you would want to combine and then enter the combined bet amount (18 in your example) in the next step. Keep in mind that some bets can’t be combined (in the case of Pinnacle you can only combine bets in the same league as far as I know) and you can only combine bets (in a simple way anyway) by placing them with the same bookmaker. If you have two bets, where the first bet ends before the second one starts, you could "combine" the bets using different bookmakers by placing the suggested bet amount on the first bet and then if it is a winner, place the total initial bet plus the winnings on the second bet. Since I personally find placing combined (parlay) bets to be a hassle (more effort that it is worth), I set the number of accumulators to 1 in Stake Wizard so that Stake Wizard only calculates bet sizes for individual bets. I don’t know how much this will impact the long term expectancy versus allowing for combined bets but since I can’t place many of the combined bets anyway with my bookmakers, it is a moot point (for me).
Hope it helps,
Aim