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RE: Steem Riddle of the Week #4: Black Cards (Prize for first correct answer)
I would suggest using the Martingale Strategy which states that should a loss occur, the wager is doubled the next time. Should a win occur, the wager is reset to the original $1000 base amount. The strategy could result in a small net profit assuming the player has an unlimited amount of resources to continue doubling the bet every time a loss occurs.
Good, idea, but unfortunately a martingale strategy still has expected value 0. Furthermore, in this game the question is what is the optimal strategy within a single round where there is only a single bet and how much does it win.
https://math.stackexchange.com/questions/83904/on-martingale-betting-system
Wow, great resource. Thanks.
I gave your riddle more thought and the following strategy is offered as a solution..... I will record every single outcome from the game from the first card flip and continue counting how many red cards versus black cards appear each time. There are only 26 red and 26 black so after having counted the cards that are revealed, as soon as 26 red cards are revealed then the next card is guaranteed to be a black (or vice-versa)....I would place a bet after either 26 red or 26 black cards have been counted.....if 26 red have been revealed then I would bet on black, if 26 black cards were previously revealed then I would bet red...... By counting the cards revealed, you would be guaranteed to win by the final card flip.....all 51 cards were revealed so you should know exactly what colour card remains on the final 52nd card flip.
Good idea, but you are only allowed to bet that the next card is black. Otherwise that would work :)
Ok, well if one can only bet on black then I would wait for 26 red cards to appear. As soon as the 26 red cards appear then there will be a guaranteed black card next. Alternatively, one will have to keep track of the number of black cards revealed too.... if there is a trend of red cards being revealed then the odds would be weighted towards a black card appearing. For example, let's assume 20 red cards have been revealed and only 15 black cards, then the odds would be weighted towards black.....
Waiting until more cards are revealed provides a greater level of predictability. Ideally, you would want 26 red cards to appear before the last card is revealed.... any time before the 52nd-card is shown, if 26 red appears, the bet on black would be a guaranteed win.