Welcome. 
In a 3 horse race where there is a massive favourite, say at 10-1 on :eek: , what sort if odds do the other two horses get?
Suppose a) both weaker horses are roughly equal and b) one weaker horse is clearly better than the other.
Next in a 2 horse race, if the favourite is 10-1 on, what odds would apply to the other.
Thank you!
10-1 means the horse has a 10 per cent chance of winning - assuming 10-1 means you get $10 for every dollar staked if you win, not $10 plus your initial dollar, totalling $11. There are various formats in use internationally, and I’m not sufficiently familiar with them to know what 10-1 exactly means. In continental Europe, it would be expressed as a decimal, but IIRC the British format adds the repayment of the initial stake.
This leaves winning chances of 45 per cent for each of the other two horses. The fair odds are the reciprocal of the winning probability, so in decimal odds, the fair odds would be 2.22 for each of the other horses (meaning for every dollar you bet, you get a total of $2.22 if the horse wins). If you express the odds in the way which I assumed to be the British one, it would be 1.22-1.
At least in the US, the wagering is parimutuel, meaning that the total pot is divided amongst the winners, net of the track’s cut.
If we assume a two horse race, and a zero track cut, or “vig” in US slang, 10 to 1 on one horse means the other horse must be 1.11 to 1
IOW, 9 people bet on A and one person bet on B. Either Mr. B wins all 10 dollars & gets 10 dollars back for his 1 dollar bet, or else the 9 people who bet on A get to split the $10 9 ways, getting $1.11 each.
IIRC, the vig at typical US tracks is ~17%. Call it 20% for round numbers, and we get:
9 people bet on A, 1 bets on B, total pool = $10. Track takes $2. if B wins, the one winner gets the $8 for payoff odds of 8-1. If A wins, 9 people split the $8 for payoff odds of 0.88 to 1, more commonly expressed as (rounded off) 3.5 to 4 or 7 to 8.
Not that “odds” is really a misnomer. None of this has anything to do with the likelihood of eaither horse actually winning. It only has to do with the payoff rate which is simply total payoff pool divided by amount of winning bets. If everybody decided to bet on a sympathy case, he’d be the “favorite” & pay low odds even though an objective assessment of his chances of winniong would be nil.
In a three runner event, a track bookmaker will normally bet to circa 5% overround. If he has a perfect book this means that for every £105 he takes in total bets on the race he pays out £100 and keep the £5 as profit. In case 1(a) where the favourite is 1-10 and the other two runners can’t be split in the betting, the advertised prices would look something like this:
Glee Club…1-10
Chez Moi…12-1
Cecil’s Folly…12-1
A perfect book would comprise bets totalling £90 for Glee Club and £7.75 each for Chez Moi and Cecil’s Folly, giving a total take of £105.50. If the favourite obliges our bookmaker pays out £99 (£90 @ 1-10 including stake) winning £6.50 on the race. If either of the other two wins the race he pays out £100.75 (£7.75 @ 12-1 including stake) winning £4.25 on the contest. Please note the round figures.
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In case 1(b), using similar logic, the prices would look something like this:
Glee Club…1-10
Chez Moi… 8-1
Cecil’s Folly…25-1
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In a two runner event the bookmaker’s board would show as follows:
Glee Club…1-10
Chez Moi…7-1
The book for this race is only 2½% overround but such a margin is not uncommon for a two horse race.
If the odds are “fair”, then in a 2-horse race, if one horse is 10-1 on, the other would be 10-1 against. You can assume that this roughly reflects each horse’s chance of winning the race.
Bookies’ odds, of course, are not “fair” - if they were, they wouldn’t make any money. You can see this in the above example: by betting £10 on the horse at 10-1 on, and £1 on the horse at 10-1 against, you break even whichever horse wins (apologies if this is too simplistic).
This means that if, in a two-horse race, one horse is 10-1 on, the other horse would probably be (say) 7-1 against. This gives the bookie a profit margin, which they can increase (by making the outsider 5-1 against) or decrease (9-1 against).
Similarly, in a 3 horse race where the favourite is 10-1 on, and they other two horses are equal, they could both be priced at 4-1 against. If one is significantly better than the other, the 2nd best could be 2-1 against and the outsider 6-1 against.
Of course, if you are actually a bookie, other factors may come into play, such as wanting to attract more punters on the outsider. I think I have heard of cases where bookies actually offer far longer odds than what they assess the actual chance of winning to be, to attract some money away from the favourite and to lay off other bets. I may be wrong about this, however.
The maths involved in working out the above is made a lot easier if the decimal odds system is used (i.e. evens is 2, 5-2 against would be 3.5, etc.), but I’ll leave the explanation of that to someone else as my understanding of it is sketchy to say the least.
Too late to edit: Chez beat me to it with a better explanation, which also includes some more realistic odds for the 3-horse race.
Sorry, I should have explained better (I’m not a gambler). Here in England ‘10-1 on’ means you bet 10 to win 1 (plus your orginal stake) making 11.
Thanks, that’s exactly what I wanted! 
Here is your (pitiful) reward:
I’m running a roleplaying game in the Game Room here and want to have some gambling on an election with three candidates initially - and perhaps one will drop out…
Whilst I appreciate your post, I have to say that you shouldn’t become a bookmaker!