I'm eager to get college football and basketball underway, and I've been feeling a little restless, so I decided to take a little deeper look at the way we bet on games. I've heard countless times that the reason that 90%+ of sports bettors lose is because of improper bankroll management. I've also heard varying theories of how much of your roll a "unit" should be. So I decided to do the math for myself and share it with all of you. Hope this helps!
I started with the simple scenario of assuming that every game I bet has the same probability of winning, no single play is stronger than another. Also, at this point we will assume there is no juice. Each game is Bet $X to win $X. If I bet X percent of my roll on each game, and continue to adjust my wager (this is a fluid model, allowing for the changing size of the bankroll with each play), after 100 bets I have multiplied my bankroll by: Y = ((1+X)^A)*((1-X)^B)
where X is the percentage of my bankroll bet on each play,
A is my number of wins, B is my number of losses, and A+B=100.
Now assume that I know I will hit 56 of these 100 bets. What percentage of my bankroll should I bet on each game? Some people might argue that I should bet a large portion of the roll, perhaps 50%, so each bet is +EV. Others might say that minimizing risk of ruin is important, so only bet about 1% (remember, however, that this is a fluid model, which essentially eliminates ROR). But both of these notions are actually costing the bettor value. When we model the equation using differential calculus (or a handy graphing calculator
we see that the function maximizes at X = .12 . Therefore, the optimal percentage of my roll to bet, under these circumstances, is 12% on each game. If you don't believe it, try it! Using the above equation (with A=56 and B=44) try to find a value for X that gives a better return than .12 does (which would multiply my bankroll by roughly 2.06).
Now it's time to look at a more practical application, which includes juice and a varying number of games selected. For the math in this part, I always assumed juice was 10% (since I bet with a local this all I can get). Our new growth formula becomes:
Y = ((1+X)^u)*((1-(1.1X))^w)
where X is, again, the % of your roll being bet each game. u is the percentage of games you win, w is the percentage of games you lose, Y is the amount your initial stake will be multiplied by, and u+w = 100.
Using the same fundamentals as earlier, I calculated the following optimal bet chart based on the percentage of wagers you anticipate hitting:
% of wagers hit % of bankroll wagered per play Y value after 100 bets
53 1.182 1.0077
54 3.09 1.0540
55 5.00 1.1477
56 6.909 1.3013
57 8.82 1.5366
58 10.73 1.8899
59 12.64 2.4220
60 14.55 3.2347
Notice that with each % of wagers hit, the % of your bankroll wagered goes up linearly but the impact it has on your initial stake rises exponentially!
Here is a final chart, which I found eye-opening. This is the results of using an optimal betting system for 1,000 bets.
% of wagers hit % of bankroll wagered per play Y value after 1000 bets
56 6.909 13.9272
58 10.73 581.4
60 14.55 125,438.37
To explain, this means that if you were to hit 560 of your next 1000 wagers, and for each wager you bet 6.909% of your bankroll, you would multiply your stake by nearly 14! And if you were able to have no problems with credit limits, and somehow hit 600 of your next 1000 wagers, by betting 14.55% of your role per play you could turn $100 into over $12 million!!
Things I noticed by doing this analysis:
1) Juice cuts a 56% bettor's profits by nearly 70%.
2) It is VERY important to keep track of your bets and know exactly what percentage you hit. This can affect the exponential growth of your starting stake.
3) If you like certain plays more than others, adjust your bet for those particular plays according to the chance that they will hit.
4) It is very important to keep a fluid model of growth!
5) There are no fancy betting systems that can overcome being a substandard bettor. If you can't hit 52.4% of your games, you can not win in the long run.
Hope this helps! Good luck this year everyone!
I started with the simple scenario of assuming that every game I bet has the same probability of winning, no single play is stronger than another. Also, at this point we will assume there is no juice. Each game is Bet $X to win $X. If I bet X percent of my roll on each game, and continue to adjust my wager (this is a fluid model, allowing for the changing size of the bankroll with each play), after 100 bets I have multiplied my bankroll by: Y = ((1+X)^A)*((1-X)^B)
where X is the percentage of my bankroll bet on each play,
A is my number of wins, B is my number of losses, and A+B=100.
Now assume that I know I will hit 56 of these 100 bets. What percentage of my bankroll should I bet on each game? Some people might argue that I should bet a large portion of the roll, perhaps 50%, so each bet is +EV. Others might say that minimizing risk of ruin is important, so only bet about 1% (remember, however, that this is a fluid model, which essentially eliminates ROR). But both of these notions are actually costing the bettor value. When we model the equation using differential calculus (or a handy graphing calculator
we see that the function maximizes at X = .12 . Therefore, the optimal percentage of my roll to bet, under these circumstances, is 12% on each game. If you don't believe it, try it! Using the above equation (with A=56 and B=44) try to find a value for X that gives a better return than .12 does (which would multiply my bankroll by roughly 2.06). Now it's time to look at a more practical application, which includes juice and a varying number of games selected. For the math in this part, I always assumed juice was 10% (since I bet with a local this all I can get). Our new growth formula becomes:
Y = ((1+X)^u)*((1-(1.1X))^w)
where X is, again, the % of your roll being bet each game. u is the percentage of games you win, w is the percentage of games you lose, Y is the amount your initial stake will be multiplied by, and u+w = 100.
Using the same fundamentals as earlier, I calculated the following optimal bet chart based on the percentage of wagers you anticipate hitting:
% of wagers hit % of bankroll wagered per play Y value after 100 bets
53 1.182 1.0077
54 3.09 1.0540
55 5.00 1.1477
56 6.909 1.3013
57 8.82 1.5366
58 10.73 1.8899
59 12.64 2.4220
60 14.55 3.2347
Notice that with each % of wagers hit, the % of your bankroll wagered goes up linearly but the impact it has on your initial stake rises exponentially!
Here is a final chart, which I found eye-opening. This is the results of using an optimal betting system for 1,000 bets.
% of wagers hit % of bankroll wagered per play Y value after 1000 bets
56 6.909 13.9272
58 10.73 581.4
60 14.55 125,438.37
To explain, this means that if you were to hit 560 of your next 1000 wagers, and for each wager you bet 6.909% of your bankroll, you would multiply your stake by nearly 14! And if you were able to have no problems with credit limits, and somehow hit 600 of your next 1000 wagers, by betting 14.55% of your role per play you could turn $100 into over $12 million!!
Things I noticed by doing this analysis:
1) Juice cuts a 56% bettor's profits by nearly 70%.
2) It is VERY important to keep track of your bets and know exactly what percentage you hit. This can affect the exponential growth of your starting stake.
3) If you like certain plays more than others, adjust your bet for those particular plays according to the chance that they will hit.
4) It is very important to keep a fluid model of growth!
5) There are no fancy betting systems that can overcome being a substandard bettor. If you can't hit 52.4% of your games, you can not win in the long run.
Hope this helps! Good luck this year everyone!
