Guess the High Card: Win 20 Dollars?

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SUMMARY

The discussion centers on a card game involving a 104-card deck created by combining two decks of playing cards, where players aim to identify the highest card. Players pay $5 to participate and can win $20 if they correctly identify the highest card after turning over cards one by one. The optimal strategy suggested is to turn over thirty-eight cards before selecting the next highest card, which statistically increases the chances of winning to between 33% and 40%. This indicates that the game can be slightly profitable when played with the correct strategy.

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This discussion is beneficial for game theorists, statisticians, and anyone interested in gambling strategies or probability analysis in card games.

dilletante
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Two decks of playing cards are combined to make a 104 card deck. On the face of each card is written a number. The numbers are all different and can be of any magnitude. You do not know the range of the numbers. The deck is shuffled and placed on the table face down.

Your task is to turn over the cards one by one until you think you have turned the card with the highest number, at which point you stop. If the number on your last card turned is the highest in the entire deck you win, otherwise you lose. Note that it has to be higher than any card previously turned as well as those left unseen.

You pay 5 dollars to play the game and if you win, you receive 20 dollars. Is this a profitable game to play?
 
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Looks like if you play with the correct strategy, you should be able to win somewhere between 1/3 and 2/5 of the time-- I'm not sure exactly what the "sweet spot" is for the strategy. But yes, that means that it is slightly profitable.

DaveE
 
Turn over thirty-eight cards and then pick the next highest one :wink:
 

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