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Betting on red
Posted 30 January 2014 - 02:46 PM
Here's a variation on a previous puzzle that let you make multiple bets while choosing the color of the next card.
I shuffle an ordinary deck of playing cards and then turn over the top card sequentially so that you can see it. At any time you may ask me to stop and place a $1 bet that the next card to be exposed will be red. If you never ask me to stop, you will automatically bet on the last card. To summarize:
- You can bet on only one card.
- You don't get to choose the color.
- You must bet the card will be red.
What is your best strategy?
How much better than even can you do?
Vidi vici veni.
Posted 02 February 2014 - 12:17 AM Best Answer
Posted 02 February 2014 - 12:31 AM
based on computer simSpoiler for
Very interesting strategy.
I was working on something like bet after so many [3 or 4] black in a row. The addition of a red component seems very counter intuitive - although in my small number of simulations, the red strategy paid off much better than the black strategy.
Overall in 60 iterations [Excel sheet that is very labor intensive] I had the following results:
- The red component successfully bet 22 times
- The black component successfully bet 2 times
- Note: no instance went to the last card
- Total number of successful bets - 24 out of 60
- The actual random return [no bet] for the cases I ran were 28
I reanalyzed the data using just the black component of the strategy
- The black component successfully bet 26 times
- 4 instances wne to the end of the sequence
- 3 of these ended in Red
- 1 ended in Black
- Thus using just the Black component of this strategy, resulted in 29 wins out of 60 [vs 28 based on no bets at all.
Since your sim is probably much more automated, it might be interesting to see what happens if you use only the black component of your strategy.
Posted 04 February 2014 - 01:37 PM
A priori, the p of any card being red is the same, so it does not matter on which card you bet. (Therefore the best strategy is to bet on the first card because you are not losing time.)
Roulette gamblers will not agree with this, they will argue that if there remain 3 red cards and 1 black card, p=3/4.
Is there an easy way to calculate the p that R red cards and B black cards remain?
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