Back in Sky Masterson & Nathan Detroit’s day, how did the track keep track (heh) of the bets/odds/payouts without the aid of computers? Surely there must have been some way of calculating all those payouts, while providing periodic updates of the odds to the bettors before Post Time, but I don’t see what that way could have been - sort of a whole team of mathematicians working behind the scenes.
Wouldn’t it be a simple matter of collecting all the bets and dividing by how much had been placed on each horse?
Totes are relatively easy as chacoguy points out. By a sort of double entry book-keeping, each new bet gets added to two totals - one to the overall total for the race and one to the total for each horse being bet on in that race. You thus have multiple running totals that you can poll at any given moment to do a relatively simple division (factoring in taxes and profit to the tote) of what the payout will be for any given horse. It gets a little more complicated with place bets, but they set up quick algorithms to do all these things on the fly by hand.
Apart from totes, old school bookies were REALLY good at mental arithmetic. One of the smartest guys I ever met was an illegal bookie. They got very adept at mentally adjusting the odds in each race so that their total hold was ideally always greater than their expected payout, constantly adjusting the odds on the board to attract or repel punters on various horses, and constantly keeping an eye on the competitor bookies and what they were doing, at the same time factoring in whatever expert (or insider) knowledge they had of the horses and jockeys.
Helluva way to make a living, because the ideal of the total hold always outweighing the expected payout does not always work out in the real world, where punters flood the bookies with bets on the favourite and those bets are not balanced by bets on the long shots, so being a bookie could be a nail-biting life. They also had to compete with betters who were as mathematically adept as they were. There used to even be betters who undertook a sort of arbitrage, betting for and against horses in the same race at different odds with different bookies so that whether the horse won or lost, they made money.
Find a copy of John Scarne’s book on gambling. It has a long, long section on the history of race betting, ending with the first computerized tracks in the early 1970s.
Racetrack computers have been around longer than you think:
They built vast mechanical calculatorsthat could keep track of all the betting in parallel and display the odds in real time.
Way back in the 60s I used to go to dog racing at Wembley Stadium. You could bet on the tote or with bookmakers and I usually used the tote. At the desk, the clerk worked a brass arm (like a speed control on an old fashioned tramcar) which could make one of six contacts (six dogs in each race). You placed your bet and could see the spark as the lever made the contact.
Behind all that was an electro mechanical calculator which displayed the payouts for each dog and the combinations on a huge screen, constantly updated as the bets went on.
Bookmakers were so called because they ‘made a book’ of bets. At most race meetings the Bookie would be taking the bets, while someone beside him recorded them, literally, in a book. The odds would be calculated from a combination of bets placed, the bookies expectation of the form of the horse or dog and signals from the Tic-tac man about what the other bookies were doing. Tic-Tac: The Bookies Secret Hand Signals Explained | BettingSites.co
The Eckert–Mauchly Computer Corporation (EMCC) was founded by J. Presper Eckert and John Mauchly, and built the first commercial computers under the Univac brand name in 1947-1950. Their major financial backer (40% stockholder) was Harry L. Straus of the American Totalisator Company. He was looking for an all-electronic way to make a parimutual calculating machine, to avoid the constant maintenance problems of the mechanical ones.
After his death in a plane crash late in 1949, the remaining directors of his company withdrew their financial support, so Eckert & Machly were forced to sell their company to Remington Rand (later Sperry Rand, today Unisys).
So some vital support for the computer industry at a critical time came from the pari mutual betting industry.