Chapter 9 · Worked solutions
Chapter 9 workings: The Exchange Revolution (and the In-Play Casino)
Chapter nine worked: lay liability, commission on a winning back bet, the effective price after commission, and when an exchange beats a bookmaker.
One idea runs through all five: commission comes off winnings, so the price you are paid is 1 + (decimal odds − 1) × (1 − commission). Everything else follows from that.
The exercises
Laying £25 at 5/2
Find the liability on a £25 lay at 5/2 and what you collect if the selection loses.
Liability
The backer's profit if it wins: £25 × 5/2 = £62.50. That is the sum the exchange holds from you.
If it loses
You keep the backer's £25, less commission on that net win.
The answer
Liability £62.50; you collect £25 before commission if it loses.
Backing £20 at 15/8 with 6 per cent commission
A £20 back at 15/8 wins with 6 per cent commission. Gross profit, commission, net profit and effective decimal odds.
Gross
£20 × 1.875 = £37.50.
Commission
6 per cent of £37.50 = £2.25.
Net
£37.50 − £2.25 = £35.25.
Effective odds
1 + 1.875 × 0.94 = 2.7625.
The answer
Gross £37.50, commission £2.25, net £35.25, effectively 2.7625.
What 2.2 is really worth
At 6 per cent commission, find the effective price of a 2.2 back and its break-even, against the break-even at the displayed price.
Effective
1 + 1.2 × 0.94 = 2.128.
Break-even
1 ÷ 2.128 = 47.0 per cent, against 1 ÷ 2.2 = 45.5 per cent on the screen.
The answer
Effective 2.128; break-even 47.0 per cent rather than 45.5 per cent, a point and a half dearer.
Exchange 6/4 or bookmaker 11/8 at 45 per cent?
You rate a result at 45 per cent. Compare 6/4 on an exchange charging 6 per cent with 11/8 at a bookmaker, by EV per £1.
Exchange
Effective 1 + 1.5 × 0.94 = 2.41. EV = 0.45 × 2.41 − 1 = +8.45p.
Bookmaker
11/8 is 2.375. EV = 0.45 × 2.375 − 1 = +6.875p.
Choose
The exchange, by about a penny and a half per pound, provided your 45 per cent is right in the first place.
The answer
Exchange +8.45p per £1, bookmaker +6.875p: take the exchange.
The break-even commission
At what commission rate do the two prices in exercise 4 pay the same?
Set them equal
1 + 1.5 × (1 − c) = 2.375, so 1 − c = 1.375 ÷ 1.5.
Solve
c = 8.33 per cent. Above that the bookmaker's shorter price wins.
The answer
8.33 per cent.
These are the workings. The argument for them, and the exercises themselves, are in chapter 9 of the book, The Exchange Revolution (and the In-Play Casino).
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