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The Magic Cafe Forum Index » » Puzzle me this... » » A really fair bet. (0 Likes) Printer Friendly Version

magicjohn2278
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OK, here is a six sided die. If you roll a ONE, you win and get back twice the amount of your bet. If not, I keep your bet.

"Ahh, “, you say, “But...my chances of winning are only one out of six."

"True," I agree, "So I'll give you three tries to get a one."

So consider this. Three tries, with each try having a 1/6 chance of winning. Your chances of winning are 3 x 1/6 = 3/6 or 50-50. So it's a fair bet.

Is it not?


:die:
TomasB
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And if you want to make it even fairer you can offer him money odds 1:2 if his number shows twice and odds 1:3 if they show three times. That's called Chuck a Luck and can be seen described at

http://www.themagiccafe.com/forums/searc......=4365108

/Tomas
magicjohn2278
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Thanks for the link Tomas - I still can't see how it works (or doesn't!)

It certainly looks like a 50/50 bet - but obviously isn't.

I think I confused myself in trying to calculate the actual odds of winning once out of the three rolls.... Three rolls, 18 possible outcomes, chance of a one showing is 3 out of the 18 - which is equivalent to 1 out of 6. - The same as just rolling one die - I'm going wrong somewhere!
TomasB
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John, rolling two dice gives 36 combinations and rolling three dice gives 6 times as many possible outcomes.

/Tomas
magicjohn2278
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Quote:
On 2006-03-22 13:28, TomasB wrote:
John, rolling two dice gives 36 combinations and rolling three dice gives 6 times as many possible outcomes.

/Tomas


Yes - but I'm only using one dice, and rolling it 3 times?

1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6

..only 18 combinations?
TomasB
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That doesn't matter. Imagine that you have three identical dice, roll one, place it aside, roll the next place it aside then roll the last one and place it aside. Using a single die three times is the same as using three dice once.

If the first roll is 1 and the second 1 you still have a total of six combinations with the last throw: 111 112 113 114 115 116
If the first throw is one and the second 2 you have six more as 121 122 123 124 125 126 so that's 12 combinations already and we haven't even gotten started in recording them all. There are a total of 6*6*6 outcomes with three throws.

/Tomas
LobowolfXXX
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Quote:
On 2006-03-22 12:32, magicjohn2278 wrote:
OK, here is a six sided die. If you roll a ONE, you win and get back twice the amount of your bet. If not, I keep your bet.

"Ahh, “, you say, “But...my chances of winning are only one out of six."

"True," I agree, "So I'll give you three tries to get a one."

So consider this. Three tries, with each try having a 1/6 chance of winning. Your chances of winning are 3 x 1/6 = 3/6 or 50-50. So it's a fair bet.

Is it not?


:die:




Well, it is not. Smile To look at it another way, if you rolled the die SIX times, would the chances be 100%? Clearly not. The actual odds are 1-[(5/6)(5/6)(5/6)]
"Torture doesn't work" lol
Guess they forgot to tell Bill Buckley.

"...as we reason and love, we are able to hope. And hope enables us to resist those things that would enslave us."
The Magic Cafe Forum Index » » Puzzle me this... » » A really fair bet. (0 Likes)
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