The Disembodied head of Ray Winstone

It’s nigh-on impossible to watch sport on TV these days without Ray Winstone popping up to tell you the latest in-play odds. I like to assume that he calculates these odds personally, and I think it’s great that he’s always available to do the live updates.

It’s often noted (though, ironically, not now) that England are among the favourites to win whatever football tournament they happen to be in (and similarly, other home nations are usually given lower odds than you might expect in other events). Given that they usually don’t live up to this billing, this would suggest that the bookies are persistently getting it wrong. Usually, they aren’t, but that’s mostly because the media often uses bookmakers’ odds as a proxy for the actual probability of winning.

Below is a rather crude worked example, but hopefully you can get a rough idea as to how the industry goes about its business. But don’t forget, gambling is bad, kids, the bookie always wins in the long run (unless they pursue bad strategies as I show below).

Suppose that I a start a (somewhat boring) sweepstake with 6 friends. They all enter £1, and they all get a different number between 1 and 6. I roll a die, and the person whose number comes up gets the lot. The friends each put in £1 and if their number comes up, they get their £1 back, plus an extra £5. The odds of winning (regardless of choice of number) are 5/1.

But what’s in it for me? Other than not really understanding the meaning of the word “fun”, I don’t get anything for providing this service: it’s worth noting that it isn’t really the bookmaker’s money you’re hoping to win, but the other punters’ (though not always). Suppose, then, that I keep £1 from the pot as my wage and give £4 + the £1 stake to the winner. The odds therefore drop to 4/1 (for every number).

Number Bet Odds Potential Winnings (including stake)
1 1 4/1 5
2 1 4/1 5
3 1 4/1 5
4 1 4/1 5
5 1 4/1 5
6 1 4/1 5
Total 6 Max profit 1
Min profit 1

What happens when my friend who has a hunch that the die is biassed towards his number (let’s say 6) and wants to put £2 in, such is his confidence? If I agree (rendering the competition no longer a sweepstake), the pot has £7 in total. I suppose that I keep the £1 as before, leaving £6 for the winner. The friends with numbers 1-5 who bet £1 can get a total of £6, so their odds are 5/1, and the friend 6 bet £2 and can get £6 total, so his odds are 2/1 (£2 stake plus £4 winnings). So, the amount that people bet affects the odds. This assumes that my friends accept that they will get only what’s in the pot after the event and that I have not made any promises to them.

However, suppose I do not believe that my friend will bet £2, and I tell everyone that the odds are 4/1 for all 6 numbers. My friend then, all of a sudden, bets £2 on 6. There is £7 in the pot: but if I roll a 6, I will have to pay him £10, as I promised him that these were the odds. If I do not roll a 6, I make a profit of £2, but if I do, I am £3 out of pocket.

Number Bet Odds Potential Winnings (including stake)
1 1 4/1 5
2 1 4/1 5
3 1 4/1 5
4 1 4/1 5
5 1 4/1 5
6 2 4/1 10
Total 7 Max profit 2
Min profit -3

Before I roll the die, another 6 friends show up. They want to play too, and they have no idea of the odds I quoted my other friends. However, I have a sneaking suspicion that word might have got round to them that the dice might be biassed. I don’t know if it is or not: all I know is that I need to offset any loss that rolling a 6 might get me. I should probably assume the betting pattern will be the same as before (as I have nothing else to go on). I could guarantee myself £1 from the second set of friends whatever the outcome by setting odds of 5/1 for 1-5 and 2/1 for 6, but I’d still be £2 down if I rolled a 6 (this counting my first 6 friends). This would be a reasonable strategy, as I can expect to make a profit of just over £2.17 (prior to the second friends turning up, it was £1.17).

I could also offer odds of 6/1 on 1-5 and Evens (1-1) on 6: this would mean that overall I would break even if 6 were rolled, and I’d still get my £2 for any other number. But of course, I’d land myself in even more difficulties, as odds of 6/1 for rolling a dice would be quite attractive, and my friend with number 1 might decide to bet £2, meaning that if I rolled a 1, I’d have to pay him £13, leaving me £3 out of pocket (including the first 6 friends) if 6 pays £2 and the others pay £1. If a third set of friends comes along, I’ll have to go through the whole thing again. If I was to come up with a new set of odds, I’d have to compensate for this possibility.

Old Friends New Friends
Number Bet Odds Potential Winnings (including stake) Number Bet Odds Potential Winnings (including stake)
1 1 4/1 5 1 1 5/1 6
2 1 4/1 5 2 1 5/1 6
3 1 4/1 5 3 1 5/1 6
4 1 4/1 5 4 1 5/1 6
5 1 4/1 5 5 1 5/1 6
6 2 4/1 10 6 2 2/1 6
Total 7 Max profit 2 Total 7 Max profit 1
Min profit -3 Min profit 1

So you’re hopefully beginning to see that this whole process, while initially simple, becomes very complicated very quickly. I started with rolling a die, which is easy to model probability-wise and start with my initial figures, but something that’s harder to model, such as who’s going to win the World Cup requires more than a few cue cards to work out.

It’s not just the money bet that goes towards the odds, but also form, competition (you could be tempted to spread bets around different bookies, using the one with the longest odds for each entry, and guarantee yourself a profit, but that’s not usually possible as they make sure that this isn’t possible), and bookies’ judgement. For example, if I had the money, I could bet £5 000 000 on Northern Ireland winning the 2018 World Cup, currently at odds of 1000/1. The bookie might happily take my money, but it’s unlikely this would cause the odds on this to change much.

Essentially, however, the point is that the whole thing is largely money-driven: the reason England in the past have tended to be among the favourites for tournaments is due in part to them being a fairly good team in those days, but also due to the fact that large amounts of money were bet on them, mostly by patriots, and also perhaps by a few scots who might not like the idea and want something by way of compensation. Going to a French, Spanish, Italian, or German betting website (which I can’t seem to do as it always redirects you to the UK one), a different market, would make England’s odds higher, because the bookies have less money to lose if they do. Similarly, patriotic betting would mean the odds were lower for their own respective countries.

But then, of course, the bookie always wins.

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