Please help with this gambling/math word problem.?

Question

I have this word problem that I can mostly figure out but I am confused by this one part of the problem. 

The con man says, "I'll bet you even money that the other side of the card is also red." Does that mean the con man, or Ray wins if the other side is also red?

Here is the context if that helps:

"I have this little silk bag. In it are three cards. One of them is green on both sides. Another one is red on both sides. And the third is red on one side and green on the other.

"I'm going to allow you to inspect the bag and put the cards inside. Without looking, I will let you pull one of the cards and place it on this little table in front of me without revealing what's on the bottom of the card."

You reach into the bag, deftly pull out one card, and put it on the table. You see a red face.

The con man says, "I'll bet you even money that the other side of the card is also red."

Should you take the bet?

LegFuJohnson · Accepted Answer

The con man would win the bet if the other side is red.

? · Answer

I agree that it's similar to the Monty Hall problem but this particular problem is much easier to figure out. Instead of thinking in terms cards with two faces, think in terms of individual faces. You just placed a red face on the table. There are three faces in the bag that are red. On the opposite side of two of those faces are red faces. On the opposite side of one of the red faces is a green face. This makes your odds 2:1 against it being green. Another way of stating that, as PDQ did, is that you have a 1 in 3 chance of it being green. This is definitely a losing bet.

To figure out your average loss against the con man the formula is <win chance> * <win amount> + <lose chance> * <loss amount>. That'd be (2/3 * 1) + (1/3 * -1) = 0.33% Over time, on average, you'll lose 33 cents per dollar bet.

pdq · Answer

If you listened carefully to Click and Clack, (the Car Talk guys where you heard this puzzler), they gave you a big hint.  They said it was just like the "Let's Make a Deal", or the "Monte Hall Puzzler".  (One in the same.)

Read through the Monte Hall Puzzler and you will understand why the answer is "No, you should NOT take the bet."  In fact, he has a 2/3 chance of being right.

Below is a link to the Monte Hall Puzzler, then the Answer, then the Mathematical Proof for the Answer:

crazyfool · Answer

even money bet is 50/50
since the card shows red then it can only be one of two cards, again 50/50
makes no sense to take the bet with no long term profit margin, it is a waste of time
any bet under even money is profitable

Please help with this gambling/math word problem.?

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