Consider a standard 52 card deck shuffled randomly. Cards are dealt face-up one
ID: 3356112 • Letter: C
Question
Consider a standard 52 card deck shuffled randomly. Cards are dealt face-up one by one and you may say 'stop' at any point during this process. After you say 'stop', you win if the next card dealt is red and lose if it is black. (If you don't ever say 'stop', the very last card decides the outcome of the game, by default.) Of course, by waiting for the very last card (or saying 'stop' before the first card is revelaed), you can win with probability 1/2. How much better can you do with a better strategy?Explanation / Answer
The better strategy is to count the cards when they are placed
At any point, among the cards revealed, if the number of cards that are black are more, it means that the probability of dealing a red card increases.
For example, when twelve cards are remaining and 40 are shown, then if the number of blacks reveled is 25, it means that only 1 of the remaining 12 i9s black and hence you have a greater chanc of getting a red on next draw. But at the same time, it can also happen so that the red cards are dealt more in number initially and most that remains can be black, which will result in lower probability of winning.
The best strategy that can be adopted here is to wait till 8-10 cards are dealt, the see if the number of red remaining are more or not. If more reads are already dealt, then say stop before the probability goes down furthur. If more blacks are dealt, then you can continue till some more cards are dealt and then you can say stop.
But it is to be noted that, on long run, the probability of winning or loing remaing the same as 0.5