Question

The question:

Before I go to the actual question I am going to make an comparison with roullete

For example:

For the sake of the example we will forget the chance of the ball hitting ‘zero’

	Bet	Winnings
Red	1	1
Black	1	1

This means that your total loss will always equal your total win and you could never lose or win

Another example:

Payout	Bet	Winnings	loss
2x	15	30
3x	10	30
6x	5	30
Total bet	30
Total winning	30

But what if the odds where defined as in the tabel, how much dollar on each section would you need to place to always play the optimum.

With the optimum being the closest to 0 or above

Payout	Bet	Winnings	loss
2x
3x
6x
11x
21x
41x

Answer 1

To always play optimum, our winnings should be same in ALL CASES.

Therefore, Winnings will be the LCM of 2,3,6,11,21,41 i.e. 18942

Payout	Bet (18942/Payout)	Winnings	loss
2x	9471	18942
3x	6314	18942
6x	3157	18942
11x	1722	18942
21x	902	18942
41x	462	18942