[yellowjack]

[ QUOTE ]
The third question was as follows: "You can gamble any amount of credits on the spin of a roulette wheel Red or Black. You can keep gambling until you either win, or go bust. Of course if you go bust, then you won't be progressing any further. If you win, then you will go through the next door.

Dave frowned. "This one is impossible," he explained. "There is no play that gives us a long term edge."

TC thought he had a solution. "I want to have a go at this," he told Dave.

Dave shrugged. "There is no correct answer, so you might as well do what you like."

TC placed a bet of one credit on Red. It lost. He then bet two credits on Red. It lost again.

"You cannot win with this doubling-up system," shouted Dave. "It's called the Martingale system. It is doomed to failure. Trust me on this — you will regret this. These people know all about negative expectation."

TC did some quick counting on his fingers and looked back at Dave. "I have enough credits to bet eight times. I'd be pretty unlucky if they all lost," he explained.

TC proceeded to lose the next five bets of four, eight, sixteen, thirty-two and sixty-four credits.

Dave was looking at his own card and wondering how best to solve this problem. At least they still had a second chance.

TC typed in the last bet, hit red, and waited.

To his surprise, the game didn't play, and a message came up on the screen.

"You win. This was the right strategy to make a profit nearly every time. Despite the plays being negative in the long run, they were the best available to solve the problem."

Dave didn't know whether to laugh or cry.

[/ QUOTE ]

I don't think the Martingale strategy is the best option. I'd go with betting 0, but if that were not an option, then betting the minimum of 1 is optimal.

While both the Martingale strategy and betting 1 credit are both -EV, betting 1 credit has a higher expectation. I worked out the math on betting on something that wins less than 50% of the time using the Martingale, and found that your EV is more and more negative for each additional bet you are willing to make to recoup your losses.

Apologies if this was already discussed.