Chapter 1 · Worked solutions
Chapter 1 workings: Confessions of a Stat Man
The working behind the four exercises that close chapter one: the memory audit, a fair coin at three prices, the Leicester question, and the one number you should decide while calm.
Chapter one prints short answers. These are the long ones, with every step shown, so you can see where each figure comes from and check your own. Only the coin exercise needs a calculator; the other three need honesty, which is harder to borrow.
The exercises
Memory against the record
Recall your last three months of bets without looking anything up, then set that list beside your account history.
Write the remembered version first, and finish it
One sitting, app closed. Every bet you can recall, with its stake and result. If you peek halfway through, the exercise is spoilt, because the whole point is to capture what your memory believes before the evidence turns up.
Pull the recorded version
UK-licensed firms show a full bet history in the account area, and most will let you download it. Take the same three months from every firm you use, not just the one you like.
Compare three totals
Number of bets, total staked and net result, in two columns headed Remembered and Recorded. Three rows is enough. Nobody needs a pivot table to be humbled.
Measure the gap
Recorded net minus remembered net. As an illustration: remember being £40 down, find the record says £190 down, and the gap is £150. That is a discount your memory gave you and the bookmaker did not.
The answer
The size of the gap is the answer. From now on, only the recorded column counts.
One coin, three prices
A fair coin is priced at 4/5, then evens, then 11/10 for heads. Work out the average profit or loss per £1 at each price.
Set out the two outcomes
Heads comes up half the time. A winning £1 bet collects the fractional profit and the stake back; a losing one costs the £1. So the average result is 0.5 × profit − 0.5 × £1.
At 4/5
0.5 × 0.80 − 0.5 = −0.10. You lose 10p for every pound, on average, for ever. The price 4/5 is claiming 55.56 per cent (five chances in nine) about an event that happens 50 per cent of the time.
At evens
0.5 × 1.00 − 0.5 = 0. Evens claims exactly 50 per cent and the coin agrees, so nobody holds an edge, the firm included.
At 11/10
0.5 × 1.10 − 0.5 = +0.05. Now the price claims 10/21, which is 47.62 per cent, and the coin still lands heads half the time. The 2.38-point gap is worth 5p a pound.
| Price | Claims | True chance | Average per £1 |
|---|---|---|---|
| 4/5 | 55.56 per cent | 50.00 per cent | −10p |
| Evens | 50.00 per cent | 50.00 per cent | 0p |
| 11/10 | 47.62 per cent | 50.00 per cent | +5p |
The answer
4/5: −10p. Evens: 0p. 11/10: +5p per £1. The coin never changed.
The Leicester question
A friend argues that Leicester winning the league at 5000/1 proves that big outsiders are where the value is. Find the single question that takes the argument apart.
Translate the price
5000/1 claims 1 ÷ 5001, which is 0.020 per cent: one title for every 5,001 seasons.
Ask it
What was their true chance? Value is the comparison between that number and 0.02 per cent. The trophy tells you which way one coin landed. It says nothing about how the coin was weighted.
Try two versions of August 2015
If the honest chance was one in 10,000, a £1 bet was worth 0.0001 × 5001 − 1 = −£0.50, and it still won. If it was one in 2,000, the bet was worth about +£1.50. Same result, opposite verdicts, and the result cannot tell you which world you were in.
Count the losers nobody filmed
The argument quietly needs every 5000/1 shot that lost as well, and those do not get documentaries. Chapter 5 does the full count.
The answer
“What was their true chance?” One result cannot answer it.
The number decided in calm
Name the sum you could lose in full without it touching the rent, the bills, any debts or the people who rely on you.
Start from the month, not the balance
Take what comes in each month and subtract rent, bills, debt repayments, food and anything owed to anybody. A betting bankroll can only ever come out of what is left, and some months nothing is left, which is also an answer.
Assume it is already gone
Write the figure as if it has been lost. If losing it would mean a conversation you would rather not have, it is too big. Halve it and ask again.
Put it on paper today
Chosen on a quiet Tuesday, the number is a limit. Chosen after a bad Saturday, it is a negotiation, and you are negotiating with the worst version of yourself.
Let the tools hold the line
UK-licensed firms have to offer deposit limits, so set one to match. If naming the number at all felt uncomfortable, the National Gambling Helpline on 0808 8020 133 is free, confidential and open around the clock.
The answer
One figure, written before the next bet. If you had to check your balance to name it, that tells you something worth knowing.
Related on this site
These are the workings. The argument for them, and the exercises themselves, are in chapter 1 of the book, Confessions of a Stat Man.
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