Ask The Wizard #409
Suppose a sports bet pays 10 to 1 and the fair odds are 7 to 1. What is my advantage and how much of my bankroll should I bet?
Let:
- f = fair odds (on a "to one" basis)
- a = actual odds (on a "to one" basis)
The formulas are:
- Advantage = (a-f)/(f+1)
- Share of bankroll to bet = advantage/a.
In this case, f=7, a = 10.
- Advantage = (10-7)/(7+1) = 3/8 = 37.5%.
- Share of bankroll to bet = 37.5%/10 = 3.75%.
Alice is half as old as Bob now.
10 years ago, Alice was 2/5 of Bob's age will be 10 years from now.
How old is Alice now?
Let:
- a = Alice's age now
- b = Bob's age now
We're given:
- 2a=b
- a-10 = (2/5)*(b+10)
Looking at the second formula:
a-10 = (2/5)*(b+10)
5a-50 = 2b+20
5a-50 = 4a+20
a=70
Alice and Bob have a 100-meter race. When Alice finishes, Bob still has 10 meters to go.
To give Bob a handicap, in a second race Alice has to run 110 meters and Bob 100.
If both run at the same speed at the first race, who will win?
nbsp;
In the second race, after the same time it took Alice to cover 100 meters in the first race, both will be 10 yards from the finish line. Since Alice runs at a faster, she will cover that 10 meters faster and thus win the whole race.