Simple gambling problem

Originally posted by brobluto
So, would you agree that it would be a fair bet if I said that I hold the Ace of Hearts in my hand and I bet you even money that the other card is also an Ace? (assuming that I don't know what the other card is or course)

Yes, I would.

Originally posted by kbaumen
You get this one right. How come you don't get the original problem? It's the same logic, just there you have to look at sides instead of cards, because each side is defined regardless of the other side, hence choosing silver side is an event, instead of choosing SG card. 3 possible events. 3 is odd, so it can't be 50/50.

Because S1 and S2 are still the same card. When it comes down to it, for a one time event, it's either the SS or the SG card. I have a 50/50 chance each time, but over time, assuming the question changes with the side being shown, I'll lose 2/3 of the time. If the question doesn't change every time we do it, "even money that the other side is silver" even though the side showing is gold, would render me winning 50% of the time. would it not?

i.e. playing 30 times with the person still asking me "even money that the other side is silver." even when the side showing is gold, would allow me to win 15 times, right?

likewise, if he kept changing the question to match the color of the side showing, I would lose 20 of those 30 times.

In the one time event though, it's either SS or SG. 50/50

Originally posted by PBE6
Yes, I would.

Then, I hold the SS card OR the SG card in my hand. even money that the other side of the bar I hold is silver.

Is that a fair bet?

Originally posted by brobluto
Then, I hold the SS card OR the SG card in my hand. even money that the other side of the bar I hold is silver.

Is that a fair bet?

No, it's not.

Originally posted by brobluto
Because S1 and S2 are still the same card. When it comes down to it, for a one time event, it's either the SS or the SG card. I have a 50/50 chance each time, but over time, assuming the question changes with the side being shown, I'll lose 2/3 of the time. If the question doesn't change every time we do it, "even money that the other side is silver" even t ...[text shortened]... lose 20 of those 30 times.

In the one time event though, it's either SS or SG. 50/50

They are the same card but no the same side. And you see a side, not a card.
2 cards - G/S, S1/S2
3 cases:
1)you see S, other side G
2)you see S1, other side S2
3)you see S2, other side S1

As we can see, in two of these cases, the other side is silver and in only one the other side is gold. If you can't understand this, than you can't solve this exercise. It's a problem 119 years old.

http://en.wikipedia.org/wiki/Three_cards_problem

Originally posted by brobluto
Then, I hold the SS card OR the SG card in my hand. even money that the other side of the bar I hold is silver.

Is that a fair bet?

He, you write those cards with two letters.

Now consider a bag with 4 letters: 3 S's and 1 G. You draw out one letter from the bag. It's S. What's the probability that the next letter you get is also S?

Originally posted by brobluto
Because S1 and S2 are still the same card. When it comes down to it, for a one time event, it's either the SS or the SG card. I have a 50/50 chance each time, but over time, assuming the question changes with the side being shown, I'll lose 2/3 of the time. If the question doesn't change every time we do it, "even money that the other side is silver" even t ...[text shortened]... lose 20 of those 30 times.

In the one time event though, it's either SS or SG. 50/50

So are you saying that for a one-time bet, the probability of the other side being silver P(other side is silver) = 1/2, or are you denying the existence of P(other side is silver) altogether?

Originally posted by PBE6
No, it's not.

It's the SAME question.

Forget about the original question. This is a new one.

(a) There is a gold card and silver card. I have one of them that I haven't looked at and we can't see the other. even money that the card I hold is gold. Fair Bet?

(b) There is a card that is silver on both sides and another that is silver on one side and gold on the other. we don't know which one, but I have one in my hand. even money that it's the all silver card. Fair bet?

These questions are no different that the scenario posed originally for a ONE TIME event. The only information that the silver side showing provides us, is the fact that the GG bar is not included in the solution.

Originally posted by brobluto
(b) There is a card that is silver on both sides and another that is silver on one side and gold on the other. we don't know which one, but I have one in my hand. even money that it's the all silver card. Fair bet?

These questions are no different that the scenario posed originally for a ONE TIME event. The only information that the silver side showing provides us, is the fact that the GG bar is not included in the solution.

b is different from the original question. In your question we consider cards. In the original question one must consider sides. 3 silver sides -> 3 possible events.

Originally posted by kbaumen
They are the same card but no the same side. And you see a side, not a card.
2 cards - G/S, S1/S2
3 cases:
1)you see S, other side G
2)you see S1, other side S2
3)you see S2, other side S1

As we can see, in two of these cases, the other side is silver and in only one the other side is gold. If you can't understand this, than you can't solve this exercise. It's a problem 119 years old.

http://en.wikipedia.org/wiki/Three_cards_problem

Yes. I agree. But NOT for the ONE TIME event. The one time event, the decision has been made that the GG is excluded, now it's a choice between SS and SG.

just because it's old, doesn't make it right. look at politicians.

Edit: I'm merely saying that there is an exception for the one time only event.

Originally posted by brobluto
Because S1 and S2 are still the same card. When it comes down to it, for a one time event, it's either the SS or the SG card. I have a 50/50 chance each time, but over time, assuming the question changes with the side being shown, I'll lose 2/3 of the time. If the question doesn't change every time we do it, "even money that the other side is silver" even t ...[text shortened]... lose 20 of those 30 times.

In the one time event though, it's either SS or SG. 50/50

You didn't respond to my post:

You say it's a one time event, well, imagine standing at the back of a line of people all participating in the card game. Each person has one bash at the game. As the queue grows shorter you start to notice that 2/3 of the people are handing over money while only 1/3 are collecting. Aren't these all one time events? I don't know about you but I would step out of the line at that point.

Do you disagree with it? What is the likelihood of your becoming one of the 2/3 of the people who paid out money if you play the game? Is it not 2/3? Will this inform your decision to remain in the queue?

Originally posted by brobluto
It's the SAME question.

Forget about the original question. This is a new one.

(a) There is a gold card and silver card. I have one of them that I haven't looked at and we can't see the other. even money that the card I hold is gold. Fair Bet?

(b) There is a card that is silver on both sides and another that is silver on one side and gold on the o ...[text shortened]... lver side showing provides us, is the fact that the GG bar is not included in the solution.

So are you saying that for a one-time bet, the probability of the other side being silver P(other side is silver) = 1/2, or are you denying the existence of P(other side is silver) altogether?

Originally posted by brobluto
Yes. I agree. But NOT for the ONE TIME event. The one time event, the decision has been made that the GG is excluded, now it's a choice between SS and SG.

just because it's old, doesn't make it right. look at politicians.

Edit: I'm merely saying that there is an exception for the one time only event.

So are you saying that for a one-time bet, the probability of the other side being silver P(other side is silver) = 1/2, or are you denying the existence of P(other side is silver) altogether?

Originally posted by brobluto
Yes. I agree. But NOT for the ONE TIME event. The one time event, the decision has been made that the GG is excluded, now it's a choice between SS and SG.

just because it's old, doesn't make it right. look at politicians.

I agree about the politicians. Most of them can't spell mathematics correctly.

I've mentioned several times that the choice is between two cards, hence two outcomes. However, the probability of them is different. To calculate it, we must consider sides, not cards.

Originally posted by kbaumen
b is different from the original question. In your question we consider cards. In the original question one must consider sides. 3 silver sides -> 3 possible events.

Yes, and for MULTIPLE tries you are right, we need to consider sides and I agree. But for the one time event, it's 50/50 SS vs SG.