Classic Type Game Theory Problem

[alThor]

[ QUOTE ]
"This game doesnt exist. Because its impossible to deal real numbers out of all real numbers. The set of cards must be finite."

For those who don't get it, he only means the above in an irrelvant technical way due to the way infinity is handled. If the question stipulated that the cards ranged from zero to one. in jumps of one billionth, and I asked for the answer to four decimal places, the answer would be just what was calculated.

Meanwhile one wonders why the point is brought up at all. Could it perhaps be a gut reaction to an inability to do the problem even if it was rephrased in a way to meet the objection?

[/ QUOTE ]

Don't even validate (by response) this insanity that is occurring on the Theory and Science boards, with people claiming there is "no such thing as a uniform distribution on [0,1]." It is pure nonsense. The people saying this are either trolling, or beyond reason.

Your initial phrasing of the question (and all previous times you've implicitly invoked this uniform distribution) need no explanation, and are correct.

Here is one of many reputible sites that discusses this elementary distribution:
http://mathworld.wolfram.com/UniformDistribution.html

And for those that think continuous distributions don't exist in the real world, perhaps they can use their wisdom to describe a discrete distribution that tells us the timing of the decay of radioactive particles. Good luck with that.

alThor

P.S. As has been said countless times on the probability board, there is no uniform distribution on [0,infinity]. I often wonder if people are confusing this with the current case.

[punter11235]

Its important, because you need number N (number of cards) which is important part of the solution. You can rephrase this problem to : "there is N cards dealt uniformly at random etc..." and then this problem make sense.
Uniform distribution does exist but it doesnt change the fact that picking real numbers uniformly at random is impossible.

Best wishes

[punter11235]

[ QUOTE ]
P.S. As has been said countless times on the probability board, there is no uniform distribution on [0,infinity]. I often wonder if people are confusing this with the current case.

[/ QUOTE ]

alThore, uniform distribution over [0;1] does exist but it is not possible to use it to pick up numbers from [0;1] at random. You can construct statement as : "probability of choosing number from 0.25 to 0.75 is such and such" but you cant calculate probability of choosing any particular number. This is why I said that you need finite set. It is important because if you try any calculations you need the number of all cards in the game. Hopefully the solution the solution may be written as simple function of N and then you can extend N as high as you wish.

Best wishes

[Vincent Lepore]

Hi Gabe,

I don't know the correct strategy but I'll bet you should not Draw if b is =<.65 Like I said I don't know the right answer but I wanted to say hello.

Vince