[MentalNomad]

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My impression was that a smaller bet size will decrease variance, so you have a better chance at staying close to the number you're at (so if you're up you have a better shot at staying up). You've swung up, now you reduce the chance that you will swing down. Wrong?


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Correct, but irrelevant. If you have to make $500 more in bets to clear the bonus, then you have to make $500 more in bets. Your -EV on those $500 in bets is the same whether you bet $1 or $10 at a time.

It's time that matters. A smaller bet takes more time to clear bonus, and your hourly rate is bonus divided by hours. As long as there is little risk of bankrupting, you should not reduce your profit rate!

Your variance down is reduced with smaller bets, and so is your variance up -- but the combination of them does not affect your profit, so long as you are not at risk of losing the bankroll. The profit is the bonus. The variance will balance out; the bonus does not.

Think of this: let's say you go in betting $10 against a bankroll of $200. You're wildly ahead, say $400; bankroll is now $600. Should you reduce the bet size to $5 to protect your win? If you're so concerned about protectin $400 extra dollars, why were you not concerned about protecting the first $200? After all, the risk of that first $200 getting crushed by the $10 bet was FAR greater.

But let's say you clear the bonus, and have $700 now. You deposit at the next site, and have another $100 of bonus to clear, but your total bankroll is now $700. Are you still going to bet $5? By your logic, you can not move up to $10. After all, you still have all those winnings to "protect."

In fact, by the "protect the win" logic, you can never, ever increase your bets. The logic is correct within context of the game itself, which is a loser -- you SHOULD reduce your bets to $0.00. The profit is in the bonus. You must apply your logic to the bonus.

If you are very averse to the risk, you can figure out the minimum hourly rate you will accept to play for the bonus. Pick a dollar bet size that will clear your bonus fast enough to make that rate, and no more than that. If you come up with a small enough bet size, you can make more money per hour with less risk by working at McDonald's, and you'll get free fries, to boot.