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You have a bankroll of 4000 dollars at a fairground stall.
The stallholder rolls a single fair six-sided die.
You may bet on the event that the die shows a 6. The stallholder offers you American odds of +800 on this bet. American odds quote the payout against a 100 reference: a line of means a stake of 100 wins a profit of , and a line of means you must stake to win a profit of 100. When you win you keep your stake plus the profit; when you lose you lose the stake.
Using the Kelly criterion (bet a fixed fraction of the bankroll, chosen to maximise the long-run growth rate of the bankroll), how many dollars of your 4000-dollar bankroll should you stake? Give the answer as an integer number of dollars.