Reference
The formula card
Every rule the problems use, with one worked example each. Odds are decimal; amounts are in naira and rounded to the kobo.
Combined odds
multiply the decimal odds of every leg
Example 1.50 × 2.00 × 1.80 = 5.40
Return
stake × combined odds
Example ₦1,000 × 5.40 = ₦5,400
Profit
return − stake
Example ₦5,400 − ₦1,000 = ₦4,400
Fractional to decimal
1 + top ÷ bottom
Example 5/4 → 1 + 1.25 = 2.25
Implied probability
1 ÷ decimal odds
Example 1 ÷ 1.25 = 0.80 = 80%
Combined implied probability
multiply the legs' implied probabilities
Example 0.80 × 0.80 = 0.64
Margin in one market
sum of implied probabilities − 1
Example 0.5236 + 0.5236 − 1 = 4.7%
Void leg
counts as odds of 1.00 where the rules say so
Example 1.50 × 1.00 × 1.80 = 2.70
Number of k-leg bets from n selections
n! ÷ (k! × (n − k)!)
Example 4 selections, doubles: 6
Full cover, every size from doubles up
2n − n − 1 bets (add n for singles)
Example 4 selections: 11, or 15 with singles
Total stake of a system
number of bets × stake per bet
Example 6 × ₦200 = ₦1,200
Percentage added to profit
profit × (1 + p)
Example ₦4,400 × 1.10 = ₦4,840
Effective odds
total return ÷ stake
Example ₦5,840 ÷ ₦1,000 = 5.84
Notation used in the book
- Decimal odds
- What one unit of stake returns, stake included: 2.00 returns ₦2 for every ₦1.
- Fractional odds
- Profit to stake: 5/4 means ₦5 profit for every ₦4 staked, the same as decimal 2.25.
- System k/n
- Every k-leg accumulator that can be made from n selections, each a separate bet.
- Void leg
- A leg the slip's rules cancel; in these problems it counts at odds of 1.00.