Lorinda\'s Story on TC (Roulette bit)
 

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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.

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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.

Re: Lorinda\'s Story on TC (Roulette bit)
 

Hi yellowjack,

I believe you are making the same mistake as Dave, forgive me if I have misunderstood and I'll be more than happy to look at it again.

[ QUOTE ]
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.

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The point here is that the rules are that you be winning at some point, not have the best long term expectation.

I'll use the example where we have 3 chips and a 40% chance of winning.

The first spin of 1 chip is the same either way.(we can never finish up ahead if we bet zero in this instance) 40% of the time we end up winning and stop play.

If we lose the first spin however, we can now either bet 1 or 2 on the next spin.

If we bet 1, there is a 40% chance we get back to level immediately and a 60% chance that we lose, and are now 2 units behind.
If we lose, there is a 60% of 60% chance (36%) that we go bust, and a 40% of 60% (24%) that we get back to one unit behind.
If we win, there is a 40% of 40% chance (16%) that we win again, and a 60% of 40% (24%) chance that we go back to one unit behind.
After three spins therefore we are in the following position: (Assuming we lost the first spin)

Bust: 36%
One unit behind:48%
Ahead: 16%

To get ahead 40% of the time from here, you would need to convert half of the 48% that is still in play. At 40-60, it can be seen that this is unlikely.

With the Martingale system, we simply bet two units on the second spin with a 40% chance of success.

TC has 255 credits with which to try to win. His best chance of getting in front and leaving the table involves the most risk.
On this occasion however, because of the situation he is in, that is the correct option.

I will be happy to answer any more questions or correct any errors I may have made in the article or this post.

Lori

Re: Lorinda\'s Story on TC (Roulette bit)
 

His strategy is fine if he starts with (2^N)-1 chips. Otherwise there is probably a more efficient strategy that utilizes bets on columns, rows, and so on if he has at least Y chips, and sometimes with less than Y chips.

Of course, he starts with (2^N)-1 chips, and only red/black bets are allowed.

Re: Lorinda\'s Story on TC (Roulette bit)
 

Ahh I see, I didn't read the passage with enough detail. Thanks for the reply.