Chapter 15 · Worked solutions
Chapter 15 workings: The Ten-Point Price Check
Chapter fifteen worked: one away price at 12/5 taken through the claim, a de-vigged sharp market, an edge threshold and a quarter-Kelly stake.
One exercise in four parts, on a specimen market: 12/5 for the away side at a soft firm, and 2.34, 3.58, 3.12 at the sharpest firm.
The exercises
What 12/5 claims
Turn 12/5 into the probability it implies.
Convert
5 ÷ (12 + 5) = 5/17 = 29.4 per cent.
The answer
29.4 per cent.
The fair away probability
Remove the margin from 2.34, 3.58, 3.12.
Implied
42.74%, 27.93%, 32.05%; booksum 102.72 per cent.
Scale
Divide each by the booksum: away 31.2 per cent, fair decimal 3.20.
The answer
31.2 per cent, a fair price of 3.20.
Does it clear 4 per cent?
Test the edge at 12/5 (3.40) on the market's number and on your own 30 per cent.
Market
0.312 × 3.40 − 1 = +6.1 per cent.
Yours
0.30 × 3.40 − 1 = +2.0 per cent.
Which counts
The sharp market rates the chance above my own figure, so leaning on its number is the cautious choice here, not the bold one.
The answer
Yes on the market's fair probability (+6.1 per cent); no on your own (+2.0 per cent).
A quarter-Kelly stake
At the fair probability and 12/5, what share of the bank is quarter Kelly?
Full Kelly
(2.4 × 0.312 − 0.688) ÷ 2.4 = 2.5 per cent.
Quarter
0.63 per cent of the bank.
The answer
About 0.6 per cent of the bank.
Related on this site
These are the workings. The argument for them, and the exercises themselves, are in chapter 15 of the book, The Ten-Point Price Check.
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