The Kelly Criterion Explained: A Staking Formula Built on Odds

What odds are: the payout multiplier on a winning ticket

Odds are an approximate multiplier showing what a winning ticket pays⁴. That is the whole idea. If you hold a ticket at odds of 4.5 and it wins, your return is your stake multiplied by 4.5. A JPY 100 keirin ticket at odds of 4.5 pays JPY 450¹.

The same arithmetic runs through every bet type:

Two things follow from that, and both matter for any staking formula.

First, odds are a multiplier, not a probability. They tell you what you get if you win, not how often you win. A price of 26.6 on a horse in a race at Kasamatsu is a payout figure, not a 1-in-26.6 chance, though the two are related once you account for the margin built into the pool⁴.

Second, the size of the multiplier varies enormously from one selection to the next. In one published race at Hokkaido, the runners were priced like this⁸:

• 18.9
• 22.4
• 26.6
• 39.3
• 59.0
• 61.8
• 84.1
• 129.7
• 231.6
• 566.8

The shortest price in that field pays roughly thirty times less than the longest. Any formula that takes odds as an input will produce wildly different outputs across that range, which is exactly what it is supposed to do.

Why odds fall when a horse is popular

Odds are not handed down. They are produced by money. The payout on a horse changes depending on how many people buy it and how much they put on, so odds shift from moment to moment and are recalculated by computer and displayed on the big screens and odds boards at the track⁴.

The direction is simple. The lower the odds, the more popular the selection; the higher the odds, the less popular it is¹. A short price means a lot of money has already gone onto that horse, so each winning ticket takes a smaller share of the pool. A long price means few people have backed it, so a winning ticket takes a larger share.

You can see this in the same field of ten runners. The 18.9 shot is the one the money has found. The 566.8 shot is the one almost nobody wants. Both are the same kind of bet on the same race; the difference is entirely how the crowd has spread its money.

This is why "value" and "favorite" are not the same word. A favorite at 1.5 can be poor value if its true chance is 60 percent. A 566.8 outsider can be good value if its true chance is better than the price implies. The odds tell you what the market thinks. They do not tell you what is true.

Odds change from moment to moment while betting is open

On pari-mutuel bets, the dividend is not fixed until the pool closes. The operator may decide from time to time which bet types to offer for a race, and the pool keeps building until sales stop¹⁰. The odds you see at 2:00 PM are a snapshot of a pool that is still filling.

On fixed odds bets, the operator states the fixed odds at which the stake will be multiplied if the selection wins, and may change the fixed odds for a bet type at any time¹¹. Once your bet is recorded, neither the operator nor you may change the recorded fixed odds of a valid bet, regardless of later odds changes¹¹. So the price on your ticket stands, but the price on the board may not.

The same pattern shows up in sports betting. Handicap lines and odds will change during betting². The operator may change the fixed odds for a particular football bet type at any time before bet placement¹². On a single-match football lottery, odds fluctuate according to betting volume until sales close⁵.

Where to check current odds: monitors inside the racecourse

At a JRA racecourse, you can buy betting tickets at the 10 racecourses and the off-track betting facilities around the country³. Odds are displayed on the large screens and odds boards around the venue, and the numbers refresh as money arrives.

At a BOAT RACE stadium, odds are displayed on monitors inside the stadium, on the jumbo screen and on the website⁹. As an example of what a price looks like, predicting the order 1-3 pays 8.4 times the amount of your bet⁹.

At a keirin velodrome, the odds screens show the race number, rider name, prefecture, class or rank and riding style in the race table¹³. You can search odds by specifying a combination of race numbers, and switch the display order between standard, which is ascending race number, and popularity order, which is ascending popularity rank¹³. When you are viewing today's race program, a "my selections" button shows your bet selections, the odds and the estimated payout amounts¹⁴. The selections screen lists the bet information for standard bet types, race by race¹⁴.

If you are betting from a phone or computer rather than at the venue, the same odds are published on the operator's site, and the numbers move in the same way.

The cutoff: betting closes 2 minutes before post time

At JRA racecourses, the cut-off time for placing bets is two minutes before the post time¹⁵. You can purchase tickets up until two minutes prior to post time, when the bell rings signaling the end of sales for that race³.

Keirin works differently. Voting is accepted from 8:00 AM on race day until three minutes before each race's scheduled start, with previous-day sales running from 6:30 PM the day before until 8:00 AM the next morning¹⁶. Night races and midnight keirin can also be purchased¹⁶.

Sports betting has its own cutoffs, and they vary by product and payment method:

The practical point for any staking plan: the price you calculate from is only live until the cutoff. After that, the pool closes and the dividend is settled.

How odds feed a staking formula like the Kelly criterion

The Kelly criterion takes two numbers and returns a third.

The first input is the odds, expressed as a decimal multiplier. If a ticket pays 4.5 times your stake, the decimal odds are 4.5. If a horse is priced at 26.6, the decimal odds are 26.6⁸. This is the number the market is offering you.

The second input is your estimate of the probability that the selection wins. This is not on the board. It is not in the pool. It is your own judgment, and it is the number the whole calculation rests on.

The formula combines them into a suggested fraction of your bankroll. The logic is that a larger share of the bankroll corresponds to a price that is generous relative to the true chance, and a smaller share, or zero, to a price that is not. Where the estimated probability sits below the break-even point implied by the odds, the formula returns zero.

That is the entire mechanism. It is arithmetic on two numbers.

The difficulty is the second number. Odds are published, precise and observable. Probabilities are not. Nobody hands you the true chance of a horse winning a race, and the market price is itself an estimate produced by everyone else's money. If you feed the formula a probability that is too high, it will tell you to stake too much, and it will do so with the same confident arithmetic as if the estimate were correct.

Fractional Kelly is the common response to this. Instead of staking the full amount the formula suggests, you stake a fixed fraction of it, which reduces the swing in your bankroll when your estimates are off. It does not fix a bad estimate. It only makes the consequences smaller.

Two more practical wrinkles are worth knowing.

First, the odds you feed the formula may not be the odds you get paid at. On pari-mutuel bets, the dividend is settled from the net pool divided by the number of unit bets on the winning combination, and the operator may declare winnings in multiples of S$1, rounded down to the nearest dollar, or in fractions of a dollar²⁰. On JRA bets, the odds shown are provisional, calculated assuming the winning ticket is one unit per race, and may differ from the final odds depending on refunds and other results¹⁹. So the multiplier in your calculation is an estimate too.

Second, dead heats and refunds change the payout in ways the formula does not model. In a dead heat, the stake on each winning selection is divided into equal parts equal to the number of dead heat winners, the payout is one part multiplied by the fixed odds, and the remaining stake is treated as a losing bet²¹. On a fixed odds football bet, a partially void game counts as correctly predicted and its refund odds are set at 1.0¹⁸. Neither outcome is a simple stake times odds.

None of this makes the formula wrong. It makes the inputs uncertain, which is a different thing. The Kelly criterion is a way of turning a price and a belief into a number. It cannot tell you whether the belief is any good, and it cannot tell you what the final dividend will be. It only does the arithmetic in between.