[Nomad84]

[ QUOTE ]
What should you do, and why?

a) Double up twice. ($5->$10->$20) (25% chance)

or

b) Quadruple up once. ($5->$20) (25% chance)

[/ QUOTE ]

*grunch*

At first I thought it was obvious that it was the same, but then it hit me. If the deck is not reshuffled on the second option, then you should obviously try option b and choose 2 red once and black once. This option actually has about a 2% player edge, if I'm understanding the problem correctly. The first choice is still 26/52, but the second is 26/51 if the first is correct.