Locking in profit on a three-horse race

A race has three horses. A $1 stake on horse 1 returns $2 if it wins, a $1 stake on horse 2 returns $4 if it wins, and a $1 stake on horse 3 returns $6 if it wins; losing stakes return nothing, and the stake is not refunded on top of these amounts. You have exactly $1 and may split it across horses in any fractions.

What is the largest profit you can guarantee whatever the outcome?

$\tfrac{1}{11}$ dollar. The implied probabilities $\tfrac12+\tfrac14+\tfrac16 = \tfrac{11}{12}$ sum to less than one. Stake in proportion to them, i.e. $\tfrac{6}{11}, \tfrac{3}{11}, \tfrac{2}{11}$, so every outcome returns $\tfrac{12}{11}$; equalising the returns maximises the worst case, giving a sure profit of $\tfrac{1}{11}$.