A Much Simpler Version Of The "Blackjack Paradox"

[DrSavage]

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I can't believe any intelligent person would think this is a question worth posing.

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[PokrLikeItsProse]

They're both playing independently against the house, despite being at the table and seeing the same cards. They both have the same edge against the house. Player A's action has no effect on player B's action, yet some people wrongly think that A has an effect on B.

So, to answer the actual questions posed....yes, it makes sense, since they break even the times they bet opposite colors and have an edge when they bet the same way, and they bet the same way a non-zero number of times, and yes, a non-expert in statistics can show that, as has been demonstrated in this thread.

[TomCollins]

4 Cases:

They both see red- 1/2*25/51 = 24.5%
They both see black 1/2*25/51 = 24.5%
Bottom is black, other is red 1/2*26/51 = 25.5%
Bottom is red, other is black 1/2*26/51 = 25.5%

Using cummulative knowlege, knowing what both of those cards are, we can assess the probability that they will win-

51% of the time, there is no advantage. 49% of the time, there is an advantage, but it is even MORE than the player figured.

So 49% of the time, the player bets more with a chance of winning 52% of the time. The other 51% of the time, it wins 50% of the time. Overall, the player wins 51% of the time, which is identical to 26/51.

[David Sklansky]

"To "make the numbers work out":

- chances player B sees the same colour as player A are 25/51. So 25/51 they bet the same way. Then they both win 26/50 of the time.

- chances player B sees the opposite colour are 26/51. Then they bet opposite ways and each wins 50% of the time.

So the probability of winning for either player is (25/51 * 26/51) + (1/2 * 26/51) = 26/51.

Still don't see what the problem is."

Guy.

Cool. Most people can't answers problems they see. You answered one you couldn't see.

[El Diablo]

DS,

Perhaps you will find this similarly complex paradox equally fascinating!

Three men go to a hotel. The desk clerk charges them $30 for the room. Each man gives the clerk $10. Shortly afterwards the desk clerk realizes that he has overcharged the three men by $5. He calls the Bell Boy over, gives him the $5 and explains to him that he has overcharged the three men and asks him to go up and give them the $5. On his way up, the Bell Boy thinks they will be happy to get a refund so why don't I give them each $1. They will be happy and I will have picked up $2. But when he does that and gives each man $1, that means they only paid $9 each for the room, which is a total of $27; plus the $2 the Bell Boy pocketed is a total of $29. But they gave the desk clerk $30! Where did the extra $1.00 go??!!?!

[starbird]

El D,

Rake.

[mornelth]

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DS,

Perhaps you will find this similarly complex paradox equally fascinating!

Three men go to a hotel. The desk clerk charges them $30 for the room. Each man gives the clerk $10. Shortly afterwards the desk clerk realizes that he has overcharged the three men by $5. He calls the Bell Boy over, gives him the $5 and explains to him that he has overcharged the three men and asks him to go up and give them the $5. On his way up, the Bell Boy thinks they will be happy to get a refund so why don't I give them each $1. They will be happy and I will have picked up $2. But when he does that and gives each man $1, that means they only paid $9 each for the room, which is a total of $27; plus the $2 the Bell Boy pocketed is a total of $29. But they gave the desk clerk $30! Where did the extra $1.00 go??!!?!

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Oldie, but goodie...

[Turkish Mickey]

[ QUOTE ]
Three men go to a hotel. The desk clerk charges them $30 for the room. Each man gives the clerk $10. Shortly afterwards the desk clerk realizes that he has overcharged the three men by $5. He calls the Bell Boy over, gives him the $5 and explains to him that he has overcharged the three men and asks him to go up and give them the $5. On his way up, the Bell Boy thinks they will be happy to get a refund so why don't I give them each $1. They will be happy and I will have picked up $2. But when he does that and gives each man $1, that means they only paid $9 each for the room, which is a total of $27; plus the $2 the Bell Boy pocketed is a total of $29. But they gave the desk clerk $30! Where did the extra $1.00 go??!!?!

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there is no extra dollar.

they paid $27 for a $25 room, with the bell boy taking the extra $2.

[chopchoi]

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The other player is also catching aqglimpse of one card but not the bottom one.

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If the card he catches a glimpse of is sometimes the card that is being dealt, but he doesn't know that, and bets the opposite way, this could be a disadvantage.

[Smarty]

Would it have anything to do with the fact that one gets to see the bottom card, meaning his information is useful for the first 51 decisions, whereas the second person has seen card X, where X < 52, and thus this information is only valuable up to card X, and not afterwards? This might be idiotic...