Math Is Fun Forum

Hi bobbym

How did you interpret this question? I interpreted each line as having a x-intercept and y-intercept that sum to 9.

Hi guys,

If you multiply the fraction by 6 instead of 0.6, you get the answer in the picture. It seems that .6 meant times six, not shorthand for 0.6.

Ok,  I will explain

I put $2 in a jar, and flip a coin: if it comes up tails I will give you the $2, and if it comes up heads I will double the money to $4, and repeat. So if you were especially lucky and I flipped four heads and then a tail, you would get 2^5 = $32.

The paradox part comes when you work out the expectation of the game. First, there is a 50% chance you will get tails first and get $2 - this possibility is worth $1 (outcome times probability). Then there is a one in four chance that you get tails on the second flip and earn $4 - again, this possibility is worth $1. Then there is a one in eight chance that tails comes up third and you get $8 - expectation $1 again.

This process continues indefinitely, and so when you add the value of the possibilities you get $1 + $1 + $1 + ... infinitely many times, which tends to infinity.

In a nutshell, this game has an infinite expected value. Decision theory suggests that you should be willing to give up your house, millions, billions, anything at all to play this game: but half the time you walk away with $2 and 87.5% of the time you walk away with $8 or less. That's the paradox.

So, yes, the ordinary problem is: How much should you pay to play this game? (Anything)

The real problem is: Now come on, what should you REALLY pay to play this game?

Hello!

Hello

It works well. However, I have noticed some idiosyncrasies with many digits and repeating digits. It seems indecisive about whether to count a pattern as recurring or not when it repeats over 30 times, sometimes doing so, usually not. Also, every now and again (with over 30 digits) the greatest common factor is negative.

I think it is convenient that there is a way for it to interpret patterns as recurring, though

Hi;

I do not know what this thread is about, but the bottom equation can be simplified if you define x=a=b:

Which is 28/135 when x=a=b is 2/5

That is definitely the most logical name. Haha

Hello

Haha, yes that would have been neat, but the numbers do not increase rapidly enough to continue in that manner.

The method is to define a polynomial with a degree one less than the amount of numbers you have (in this case, degree 2). So you get ax^2 + bx + c
You then substitute x=1 for the first number, x=2 for the second, and so on.
a+b+c = 1
4a+2b+c=12
9a+3b+c=123

Solving that system of equations gives the polynomial 50x^2 - 139x + 90, which exactly fits the numbers.

But you asked how I made the rule. I put the numbers in a table in a graphing calculator. As I said: lazy

Yes, it is about gambling values. What are your gambling values?

Actually, buying lottery tickets may have a positive expectation if they are cheap and the jackpot is very high - but you will have to buy millions of tickets before you can expect a profit.

I was talking about expectation that includes things other than money, like satisfaction. What did you mean about positive utility?

Hello;

Do you mean: Gambling can benefit some people even though they lose the gambling games? That could make it rational for some people to gamble; rationality has to do with decision-making, not values.

I recall a study that showed that buying lottery tickets is a satisfying experience that could easily be worth the loss of money. The same may be true of many kinds of gambling, if the bankroll is not needed.