Hedging Bets: The Math on a Rays World Series Ticket and When to Hedge
The World Series is set. The Brewers and Rays open in Milwaukee, and somebody bought the Rays in August when the price was cheap. The ticket holder now faces the oldest question in betting: hold the ticket, or bet the other side and lock a profit.
Most hedging advice stops at "lock the profit" or "never hedge." Both are wrong as rules. A hedge is a second bet at the book's price, so the hedge always costs expected value. Whether the cost is worth paying depends on one number most guides skip: the size of the ticket against the size of your bankroll. This guide prices the hedge on real October 20 and 21 numbers, then gives the bankroll line where the answer flips.
The Ticket and the Market
Action Network reported Kalshi's Rays championship contract near 6% in August. Use the August price as the ticket: $60 buys 1,000 Rays contracts at 6 cents, each paying $1 if the Rays win the World Series. The ticket returns $1,000 on a Rays title and nothing otherwise.
Now the series price. On October 20, SI's opening odds for the matchup listed DraftKings at Brewers -160 and Rays +140. On October 21, Action Network had Polymarket at 62.2% Brewers and 37.6% Rays, with Kalshi at 62.1% and 38%.
Strip the vig from DraftKings' series price
Rays +140: 100 / 240 = 41.67%
Brewers -160: 160 / 260 = 61.54%
Sum: 103.21%. The book keeps 3.21 points.
Rays fair: 41.67 / 103.21 = 40.37%
Brewers fair: 61.54 / 103.21 = 59.63%
The sportsbook's fair price and the prediction markets sit within about 3 points of each other. The math below uses the DraftKings no-vig number, 40.37% Rays. The no-vig calculator runs the same conversion on any two-way price.
Three Exits, Priced
The ticket holder has three choices: hold, sell the contracts back on the exchange, or hedge with a Brewers bet at DraftKings.
Exit one: hold
Rays win: +$940. Brewers win: -$60.
Expected value: 0.4037 × $1,000 - $60 = +$343.73
Exit two: sell at about 38 cents
1,000 × $0.38 - $60 = +$320.00 locked, before exchange fees
Exit three: full hedge, Brewers -160 (decimal 1.625)
Hedge stake = ticket return / hedge decimal = $1,000 / 1.625 = $615.38
Rays win: $1,000 - $60 - $615.38 = +$324.62
Brewers win: $615.38 × 0.625 - $60 = +$324.62
Locked: +$324.62 either way
The hedge beats the sale here by about $5, and both trail the hold by about $19 to $24 in expected value. The $19.11 gap between holding and hedging is the vig on the hedge bet: $615.38 × 3.11% expected loss at a fair 59.63% Brewers price. The $19.11 is the full cost of turning a +$940 or -$60 coin into a sure +$324.62.
Shop the hedge before you place the bet. Fanatics' series preview listed the Brewers as short as -175 at BetRivers and Fanatics. At -175, the full hedge needs $636.36 and locks $303.64. The same lock costs $21 more at the worse book.
The Partial Hedge
You do not need to choose between all and nothing. A smaller hedge buys a floor and keeps upside. Every hedge dollar costs 3.11 cents of expected value at this price, so the cost scales with the stake.
| Brewers hedge | If Rays win | If Brewers win | Expected value |
|---|---|---|---|
| $0 (hold) | +$940.00 | -$60.00 | +$343.73 |
| $300 | +$640.00 | +$127.50 | +$334.41 |
| $615.38 (full) | +$324.62 | +$324.62 | +$324.62 |
A $300 hedge guarantees a profit on either result for $9.32 of expected value. The full hedge costs $19.11. Neither number tells you which row to pick. Your bankroll does.
The Bankroll Rule: Kelly Picks the Hedge Size
John Kelly's 1956 paper in the Bell System Technical Journal set the rule behind bankroll-growth betting: choose the bet sizes maximizing the expected logarithm of wealth. Apply the rule to the hedge decision instead of a new bet. Let W be your cash bankroll, not counting the ticket. Let p be the true chance your ticket wins, P the ticket's return, and D the hedge's decimal odds. The log-optimal hedge stake is:
Kelly-optimal hedge
h = (1 - p) × (W + P) - p × W / (D - 1)
Rays ticket: h = 0.5963 × (W + 1,000) - 0.4037 × W / 0.625
Simplified: h = 596.3 - 0.0496 × W
No hedge once W reaches $12,000
| Cash bankroll | Kelly hedge on the Brewers | Share of the full $615 hedge |
|---|---|---|
| $1,000 | $547 | 89% |
| $2,500 | $472 | 77% |
| $5,000 | $348 | 57% |
| $10,000 | $99 | 16% |
| $12,000 or more | $0 | 0% |
Read the table as the answer to "should I hedge." With $1,000 in the account, a $1,000 ticket is a bankroll-sized swing, and Kelly hedges almost all of the position. With $12,000 or more, the ticket is a normal-sized bet, and the right move is to let the bet ride. The $19 vig on the hedge buys real protection for the small bankroll and nothing worth the price for the large one.
Your own read on the game moves the line. If you think the Rays win 45% of the time, not the market's 40.37%, the formula becomes h = 550 - 0.17 × W. The no-hedge point drops from $12,000 to about $3,235. A bettor with an edge on the ticket side hedges less. A bettor who thinks the market is right hedges more. Full Kelly assumes your probability is correct. Most bettors run fractions of Kelly for single bets, and the quarter-Kelly guide explains why. The same caution applies here: when unsure of your edge, lean toward the market's number.
Why the Urge to Hedge Runs Ahead of the Math
Kahneman and Tversky's prospect theory, published in Econometrica in 1979, found people weigh outcomes as gains and losses against a reference point, with losses weighed more heavily than equal gains. A bettor holding a live title ticket starts treating the $940 as owned. Losing the ticket now feels like losing $940, not $60.
Grant, Johnstone, and Kwon applied cumulative prospect theory to sportsbook cash-out offers in the Journal of Mathematical Psychology in 2021. The model predicts bettors cash out bets likely to win, not bets likely to lose, and finds partial cash-outs optimal in some cases. Bennett and coauthors ran two experiments with 240 adults for Psychological Science in 2024. Offering a cash-out option raised bet sizes by up to 35%.
Books know this. A cash-out button is a hedge priced by the book, with the margin set by the book. Price any cash-out offer against the hedge you would place yourself at the best available number. If the button pays less than your own hedge locks, the button is the worse exit.
When a Hedge Is a Good Bet on Its Own
Every hedge in this article costs expected value because the hedge price carries vig. Two cases break the rule.
- The hedge price beats the fair line. If one book hangs the other side above the market's no-vig price, the hedge is a positive-EV bet by itself. Shopping across books is where this happens. Check with the odds converter.
- The line moved enough to create a middle. If you hold a team at +7 and the line moves to +3, a bet on the other side at -3 wins both bets on a 4 to 6 point margin. The middle window has to beat the vig on both sides. The key numbers guide shows how often NFL games land on 3 and 7.
Calculator: Price Your Hedge
Enter your ticket's return on a win, what you paid, the current price on your side, the price on the hedge side, and your cash bankroll. Leave "your win %" blank to use the market's no-vig number.
Hedge or hold
The Hedge Checklist
- Price the hold. Use the market's no-vig number or your own, and write down the expected value.
- Price every exit: the cash-out button, a sale on the exchange, and a hedge at the best book.
- Compute the EV cost of the hedge. The cost equals the hedge stake times the hedge's expected loss rate.
- Run the Kelly hedge on your actual cash bankroll. Hedge the amount the formula gives, not the amount fear gives.
- Size futures with the payout in mind next time. A ticket sized as a small slice of bankroll at its full payout rarely needs a hedge.
Want to see how our analysts read a series price? The free Discord room shows how the calls get made. No card needed.
The verdict: a hedge is insurance, and the premium is the vig on the hedge bet. On a $60 Rays ticket returning $1,000, the full Brewers hedge at -160 locks $324.62 and costs $19.11 of expected value. Kelly says hedge about $547 with a $1,000 bankroll and hedge nothing at $12,000 or more. Hedge by bankroll math, shop the hedge price, and never take a cash-out button without pricing the hedge yourself.
Sources and Method
SI supplies DraftKings' October 20 series price. Action Network supplies the August Kalshi price and the October 21 Polymarket and Kalshi prices. Fanatics' preview supplies the -175 quotes. Kelly's 1956 paper supplies the log-wealth rule. Kahneman and Tversky supply prospect theory. Grant, Johnstone, and Kwon supply the cash-out model. Bennett and coauthors supply the 35% bet-size result. Every no-vig figure, hedge stake, expected value, and Kelly stake above comes from the formulas shown, and you recompute each one in a spreadsheet. The Kelly hedge formula comes from setting the derivative of p × ln(W + P - h) + (1 - p) × ln(W + (D - 1) × h) to zero.
Limits: the ticket is a worked example built on the reported August price, and series prices moved after Game 1. Exchange fees and the bid-ask spread lower the sale value. The Kelly hedge assumes your probability is right and ignores the rest of your open bets.