In the last sentence:
"A winning punter will win $4 for each $5 bet. Assuming that the punters will win 50% of the time, the bookmaker only has to pay out on average $80 for each $100 gambled, yielding a profit margin of 20%."
Punters winning 50% of the time implies that out of the $100 dollars gambled $50 will be winning bets. The bookie gets $100 upfront, but has to pay out $50 (winning bets) + $40 (winning gains), leaving him $10, which is a 10% gain on $100.
I'm not sure how the $80 payout is calculated, would you please clarify?
There has been a problem with the nabble forum so I only just saw this posting.
To answer your question:
Suppose 40 punters each bet $5 on the outcome of the coin toss.
20 bet on Heads and 20 bet on Tails.
Then exactly 20 will win their bet and 20 will lost.
The book takes $100 profit from the 20 losers and pays out $80 ($4 each) to the winners.
Another reader wrote to me about this and I now see that there is indeed an error.
in the last 2 lines of box 4.1 on Page 71, we need to replace:
“..the bookmaker will only have to pay out on average $80 for each $100 gambled, yielding a profit margin of 20%."
“..the bookmaker will only have to pay out on average $90 for each $100 gambled, yielding a profit margin of 10% (profit margin is defined as: profit as percentage of selling price or revenue, i.e. 10/100) "
this is because for each $100 gambled we assume $50 is on H and $50 on T. The winners get back their stake ($50) plus $40 profit making $90 out. I have added this to the errata page.