Box 4.1, p71

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PD
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Box 4.1, p71

PD
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?

Thanks in advance, (and for a great book!)
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Re: Box 4.1, p71

norman@eecs.qmul.ac.uk
Administrator
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.

Norman Fenton
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Re: Box 4.1, p71

Jim
In reply to this post by PD
Isn't easier to simply note that 4$ is 80% of $5 thus leaving 20% to the bookie!
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Re: Box 4.1, p71

norman@eecs.qmul.ac.uk
Administrator
In reply to this post by PD
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%."
with
“..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.

Norman Fenton