How Much Should You Bet? Kelly, Half-Kelly, and the 60/40 Coin Game That Bankrupted the Pros

Everyone asks "what should I buy?" Almost nobody asks "how much?" Yet that second question is the one that decides whether you survive. A rigged coin, a Bell Labs physicist and a Nobel-laureate hedge fund blow-up all point to the same lesson: having an edge is not enough if the bet is too large.

Sizing is the bridge between a favorable idea and a survivable path. Kelly provides a mathematical ceiling for a repeatable edge; half-Kelly and smaller fixed fractions acknowledge that estimates are wrong, losses cluster and real people only get to live one outcome.

A game you can't lose, and 28% lost everything

In 2013, Victor Haghani and Rich Dewey ran an experiment that should be required reading for anyone who has ever placed a trade. They gave 61 finance-trained participants, including economics and finance students plus analysts from two leading asset managers, $25 each and a simple video game: flip a virtual coin for 30 minutes and bet on the outcome. Everyone was told up front that the coin was programmed to land heads 60% of the time. They could bet any amount at even payout and cash out up to a $250 cap.

This is about as close to free money as markets ever get. A boring, sensible strategy, betting a fixed 10-20% of the bankroll on heads every flip, wins big almost every time. By the authors' simulations, about 95% of players following it should have hit the $250 maximum.

What actually happened, as Haghani and White report in The Missing Billionaires:

• Only 21% of participants reached the $250 cap.
• The average payout was $91, versus roughly $240 for a good fixed-fraction strategy.
• One third finished with less than their $25 starting stake.
• 28% went completely bust in a game rigged in their favor.

Across all 7,253 flips in the study, the coin came up heads 59.6% of the time. The edge was exactly as advertised. Luck owed these players nothing. They did not lose because the game was unfair; they lost because of how much they bet: full-bankroll punts, doubling down after losses and even betting on tails. Sixty-seven percent did that at least once despite knowing it was the 40% side.

These were people with formal financial training. If they could not size bets in the cleanest positive-expectancy game imaginable, there is little reason to trust instinct alone in a real market.

The question nobody teaches

Haghani and White's larger point in The Missing Billionaires is that finance media and education pour essentially all their attention into what to buy and almost none into how much. The asymmetry is brutal: pick a bad investment at a sensible size and you lose money but live to trade again. Pick a great investment at the wrong size and, in their words, "you can easily go broke from normal ups and downs while waiting for things to pan out."

Haghani knew this from the inside. He was a founding partner of Long-Term Capital Management, the hedge fund staffed with Nobel laureates that collapsed in 1998. As William Poundstone documents in Fortune's Formula, LTCM's arbitrage spreads were tiny and its conviction was huge, so the fund levered up roughly 30-to-1. A portfolio of individually reasonable trades became a fatal one. Many positions eventually converged, exactly as the models predicted. The fund still lost about 90% of its peak value because "eventually" arrived later than solvency did. Being right about what is no defense against being wrong about how much.

The formula that answers how much

There is a formula. In 1956, Bell Labs physicist John Kelly Jr. asked what fraction of a bankroll should be bet on a favorable, repeatable gamble, not to maximize this bet's expected value, which pushes toward all-in, but to maximize the long-run growth rate of the money. His answer, in gambler's shorthand:

optimal fraction = edge / odds

Here, edge is the expected profit per dollar staked and odds is the payout ratio, what is won relative to what is risked. For an even-money bet like the 60/40 coin, it simplifies to p - q: 60% minus 40% means betting 20% of the bankroll.

Two things about this formula matter more than the arithmetic:

1. "Don't bet" is part of the formula. When the edge is zero, the Kelly stake is zero. Poundstone puts it flatly: "When edge is zero, the Kelly wager, edge/odds, is zero. Don't bet." A position size of zero is a valid, often optimal, position size.
2. Overbetting is not more aggressive. It is mathematically self-destructive. The relationship between bet size and compound growth is a hill, not a straight line. Growth rises toward the Kelly fraction, peaks there, then falls as the bet gets larger while volatility keeps climbing. At double Kelly, long-run compound return is approximately zero. Beyond it, growth turns negative.

In Fortune's Formula, the line beyond Kelly separates ordinary aggression from sizes that "are insane... because they decrease compound return while producing even more volatility."

The market version of that hill appears in The Missing Billionaires as a thought experiment: suppose you could go back to 1927 knowing the S&P 500 would return 9.8% a year for the next 96 years. How much leverage would you use? Their table, with daily rebalancing and borrowing at T-bills plus 1%, says 2x leverage produced the highest ending wealth at the cost of a 98.5% drawdown. At 3x, ending wealth shrinks. At 4x, the investor survives a 99.999% drawdown to finish with about $5. At 5x, a single day, October 19, 1987, wipes the account out. Even with a crystal ball, position size sets the ceiling.

Why professionals cut Kelly in half

If Kelly marks the top of the hill, why do serious practitioners such as Ed Thorp, professional card players and horse-race syndicates habitually bet less? Three reasons pull in the same direction.

The top of the hill is flat

Because growth peaks at Kelly, stepping left costs less than it appears. The gambling world's standard is half-Kelly, half the formula's fraction. Per Poundstone, the trade is remarkably cheap: giving up only a quarter of the growth rate, so 10% compounding becomes 7.5%, while risk falls sharply. A full-Kelly bettor has a 1 in 3 chance of halving the bankroll before doubling it; at half-Kelly it is 1 in 9.

Your edge estimate is probably optimistic

Bill Benter, who built one of history's most successful horse-betting operations, observed that even the best models tend to overestimate their edge. If the true edge is half the estimate, then what looks like full Kelly is actually double Kelly, the zero-growth point. Betting a fraction of Kelly is insurance against overconfidence.

Kelly maximizes the median outcome, not your outcome

This was Paul Samuelson's famous objection. Even in a wildly favorable game, Poundstone shows a four-bet Kelly sequence with a 1-in-16 chance of losing 87% of the bankroll. "The Kelly guarantee of avoiding ruin," he writes, "is somewhat hollow." The math is patient; people are not. Mortgages, retirement dates and risk tolerances are why the practical descendants of Kelly all involve betting less than the theoretical maximum, never more.

For completeness, Haghani and White frame the same idea through the Merton share, the investor's version of Kelly with a personal risk-aversion dial. For a typical investor, it lands in roughly the same place: about half of what a pure log-wealth maximizer would hold.

From coin flips to your trading account

You are not flipping rigged coins. Here is how the framework translates into trading and how each piece maps to a calculator on this site.

1. Measure your edge before sizing anything. Trading expectancy is (win rate x average win) - (loss rate x average loss). Feed real results into the Expectancy Calculator. If the number is not positive, remember that when edge is zero, optimal size is zero.
2. Know your odds. Kelly's odds are the payoff ratio, average win relative to average loss. The Risk/Reward Calculator makes that relationship explicit. A 2:1 payoff with a 40% win rate and a 1:1 payoff with a 55% win rate are different sizing problems.
3. Convert risk into position size mechanically. Decide what fraction of the account a stop-out may cost, then let arithmetic set the share count. The Position Size Calculator takes account size, risk percentage and stop distance and returns position size. If a Kelly-style estimate says 8%, half-Kelly discipline and estimation error both argue for starting much lower; a common professional convention is 1-2% or less per trade.
4. Respect the path, not just the average. A 60% win rate will produce losing streaks. The questions are how long and whether sizing survives them. The Losing Streak Calculator estimates the probabilities, while the Monte Carlo Simulator shows the distribution of equity paths at a chosen risk fraction, including the ugly percentiles Samuelson warned about.

The bottom line

• A positive-expectancy system does not protect an account from ruin. Sizing does. The coin never cheated; the bettors overbet.
• Optimal size is edge divided by odds. When no edge can be demonstrated, the formula says zero.
• More size stops meaning more return at the Kelly point. Past it, extra pain comes with lower expected growth. Double Kelly compounds to roughly nothing.
• Professionals use half Kelly or less because the hilltop is flat, edges are overestimated and each person only lives one path.
• Decide risk per trade first as a fixed, small fraction of the account, then let a calculator turn it into share count.

Sources: Victor Haghani and James White, The Missing Billionaires: A Guide to Better Financial Decisions (Wiley, 2023), including the biased-coin experiment with Rich Dewey, the 1927-2022 leverage tables and the Merton share framework; William Poundstone, Fortune's Formula (2005), including the Kelly criterion's history, overbetting analysis, half-Kelly practice, LTCM and the Samuelson critique. This article is educational content, not investment advice; all calculators on this site are analytical tools, not recommendations.