Acca Arithmeticworked problems for accumulator maths
Chapters

Chapter 1

Combining odds

An accumulator multiplies the decimal odds of its legs. These problems build the habit: combined odds, return, profit, and what happens when one leg loses.

Problems 1–6 · 3 warm-up · 2 steady · 1 stretch

1.501.50×2.003.00×1.805.405.40
The red figure under each leg is the running total: the combined odds so far.

Problem 1: A three-leg accumulator

Warm-up

An accumulator has three legs at decimal odds 1.50, 2.00, 1.80. The stake is ₦1,000. What are the combined odds, the return if every leg wins, and the profit?

Legs
1.50 × 2.00 × 1.80
Stake
₦1,000
Show working for problem 1
  1. Combined odds: 1.50 × 2.00 × 1.80 = 5.40.
  2. Return: ₦1,000 × 5.40 = ₦5,400.
  3. Profit: ₦5,400 − ₦1,000 = ₦4,400.

Answer Combined odds 5.40; return ₦5,400; profit ₦4,400.

Problem 2: One leg loses

Warm-up

The same accumulator (1.50 × 2.00 × 1.80, stake ₦1,000). The first two legs win and the third loses. What comes back?

Legs won
2 of 3
Stake
₦1,000
Show working for problem 2
  1. An accumulator pays only if every leg wins (or is void under the rules).
  2. A lost leg multiplies the whole bet by zero.

Answer Nothing comes back: the whole ₦1,000 stake is lost.

Problem 3: Fractional odds first

Steady

A slip shows fractional odds 1/2, 5/4, 4/5. Convert them to decimal, combine them, and find the return on ₦500.

Fractional odds
1/2, 5/4, 4/5
Stake
₦500
Show working for problem 3
  1. 1/2 → 1 + 1 ÷ 2 = 1.50.
  2. 5/4 → 1 + 5 ÷ 4 = 2.25.
  3. 4/5 → 1 + 4 ÷ 5 = 1.80.
  4. Combined odds: 1.50 × 2.25 × 1.80 = 6.075.
  5. Return: ₦500 × 6.075 = ₦3,037.50.

Answer Decimal odds 1.50, 2.25, 1.80; combined 6.075; return ₦3,037.50.

Problem 4: Does the order matter?

Warm-up

The legs of problem 1 are entered in a different order: 1.80 × 1.50 × 2.00. Does the combined odds figure change?

Legs
1.80 × 1.50 × 2.00
Show working for problem 4
  1. 1.80 × 1.50 × 2.00 = 5.40.
  2. Multiplication gives the same result in any order.

Answer No. The combined odds are 5.40 either way.

Problem 5: How many legs to reach 10?

Stretch

Every leg is priced at 1.40. What is the smallest number of legs whose combined odds reach at least 10?

Each leg
1.40
Target
10.00 or more
Show working for problem 5
  1. Combined odds for n legs: 1.40n.
  2. 1.406 = 7.53, still below 10.
  3. 1.407 = 10.54, the first value at or above 10.

Answer 7 legs (combined odds 10.54).

Problem 6: Rounded or unrounded?

Steady

Legs at 1.85 × 1.72 × 2.10, stake ₦2,000. The combined odds are shown to two decimal places. How much does the return differ depending on whether the unrounded or the shown figure is used?

Legs
1.85 × 1.72 × 2.10
Stake
₦2,000
Show working for problem 6
  1. Unrounded: 1.85 × 1.72 × 2.10 = 6.6822; return ₦2,000 × 6.6822 = ₦13,364.40.
  2. Shown figure 6.68: return ₦2,000 × 6.68 = ₦13,360.
  3. Which one applies is set by the slip's rules; the gap is small but real.

Answer ₦13,364.40 unrounded against ₦13,360 from the shown odds: a difference of ₦4.40.