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RE: Steem Riddle of the Week #4: Black Cards (Prize for first correct answer)
The chance of getting a black is 50%. So technically you will just break even at the end of the game. To optimize winning, let the dealer flip first and observe how many raw cards have been flipped. If more red cards have been flipped, your chances of winning get higher. If let's say 30 cards have been flipped and from the 30, 20 are red so the remaining deck has 22 cards with 6 red and 16 black. So, the chance of winning is now 16/22 and the average winning amount can be 16 x 2 = 32 (with 16 black remaining) and 6 x 1 = 6 (with 6 red remaining) so 32 - 6 = 26,000. Hence, 26000/22 remaining cards is the average amount you will win.
Good general idea, but how often does that happen and more importantly how often does it not happen?
Generally, your chance of winning in the 1st to 51st card is 50% and you have 100% chance of winning in the last card. The best time to bet which will give you a higher chance of winning is on the 2nd card when the 1st card flipped is red (it will give you 50.9% chance of winning $2000) or on the 28th card provided 14 red and 13 black have been flipped (it will give you 52% chance of winning $2000). Hence, your chances of winning are higher on betting at the moment when cards flipped have more than red than black...
that's true but to be sure the strategy would profit you need to figure out how often you end up in a state where more red cards have been flipped than black cards. It is possible for the dealer to go through the entire deck without every being in a situation where more red cards flipped than black cards.