[lorinda]

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.

[/ QUOTE ]

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