# One timeline *The average you never get* --- Someone offers you a game. Flip a fair coin: heads, your stake grows by half; tails, it shrinks by 40%. You do the maths. Half the time you gain 50%, half the time you lose 40%, so on average each flip pays 5%. A good game - you should play as often as they'll let you. You start with £100. Heads: £150. Tails: £90. Heads again: £135. Tails again: £81. Two heads and two tails, a perfectly average run, and you're down 19%. Play on and every balanced pair of flips multiplies your stake by 1.5 × 0.6 = 0.9. The 5% average is real, and your money is disappearing at about 5% a flip. --- Both numbers are true at once. Send a thousand players in with £100 each and after twenty flips the group's total pot has grown handsomely, with almost all of it sitting with the handful who hit improbable streaks of heads. Most of the thousand are nursing heavy losses. The expected value averages across the thousand parallel players. You don't get to be a thousand players. You get one sequence of flips, one after another, and on a single timeline the order and the compounding are what matter. (There's a formal name for the gap - whether time averages match ensemble averages is the "ergodicity" question - but you don't need the word to feel the trap.) --- Versions of this game land on your desk looking nothing like games. A deal that bets a third of the balance sheet. A capex programme sized against the upside case. A hiring plan that only works if the new market ramps on schedule. Each one positive on expected value, because expected value averages across the worlds where it works and the worlds where it doesn't. But losses don't average, they sequence. Drop 40% and you need 67% just to get back to where you started, and [[Year one]] walks the same asymmetry through an ordinary growth plan: the low start that quietly puts the base case out of reach. --- So the useful question is rarely whether the expected value is positive. It's what the losing branch does to your ability to keep playing. Sized so that a loss stings, most positive-value bets are worth taking, and taking often. Sized so that a loss ends the game, no expected value justifies it, because the game ending is the one outcome later wins can't repair. There's a formula for the optimal bet size (the "Kelly criterion"), and you'll never run it in a boardroom. The working version: take every good bet you can afford to lose, and none you can't. ---