andysif
Joined: Aug 8, 2011
• Posts: 433
February 20th, 2012 at 9:51:19 PM permalink
Start with 40. Roll a dice, and subtract that number from the count until you reach 0. But there is a twist, if you roll a 1, you start from 40 again.

Actually, this is the math homework for my grade 3 son to work on his subtraction. But as a father who is stuck with it, you want to get it over with as quick as possible. So what is the expected number of times you have to roll the dice to reach 0?

I know the chance of getting through in one pass t = (5/6)^x.
My guess of x is : 40/mean of (2 to 6) = 40/4 = 10 . This way of thinking is probably correct if not for the "bankrupt" feature, but I am not sure if it is still good with it.
WongBo
Joined: Feb 3, 2012
• Posts: 2126
February 20th, 2012 at 9:54:20 PM permalink
Let me get this straight.
You are asking for help with your eight year old son's math homework?
In a bet, there is a fool and a thief. - Proverb.
PopCan
Joined: Feb 15, 2012
• Posts: 178
February 20th, 2012 at 10:11:28 PM permalink
You know why I love this post? It allows me to say the following:

So I ran a million trial simulation on your son's third grade homework and got the following results:

Rolls: 33,360,950
Average Rolls Until Total <= 0: 33.36
MathExtremist
Joined: Aug 31, 2010
• Posts: 6526
February 20th, 2012 at 10:18:32 PM permalink
I don't think he should be able to turn that in.

Question: does a roll that puts you below zero not count, equivalent to Chutes and Ladders? Or is the ending criteria zero or lower, equivalent to Candy Land?

(It's a safe bet I have kids, huh?)
"In my own case, when it seemed to me after a long illness that death was close at hand, I found no little solace in playing constantly at dice." -- Girolamo Cardano, 1563
YoDiceRoll11
Joined: Jan 9, 2012
• Posts: 532
February 20th, 2012 at 10:18:49 PM permalink
Quote: PopCan

You know why I love this post? It allows me to say the following:

So I ran a million trial simulation on your son's third grade homework and got the following results:

Rolls: 33,360,950
Average Rolls Until Total <= 0: 33.36

But it is homework. Must show math!!! ;)
Triplell
Joined: Aug 13, 2010
• Posts: 342
February 20th, 2012 at 10:21:29 PM permalink
Quote: WongBo

Let me get this straight.
You are asking for help with your eight year old son's math homework?

He's taking his son's homework, which is simply to help with subtraction, and asking a new question of it. What is the expected number of rolls before you would be complete.

The average value of each roll that would have subtraction value would be (2+3+4+5+6)/5, which is 4. This means that 5/6 of the time, you can expect a subtraction of 4. The other 1/6 of the time, you would reset to 40.
WongBo
Joined: Feb 3, 2012
• Posts: 2126
February 20th, 2012 at 10:28:29 PM permalink
Ummm ok. My post was a joke. Sorry you didn't get it.
In a bet, there is a fool and a thief. - Proverb.
Triplell
Joined: Aug 13, 2010
• Posts: 342
February 20th, 2012 at 10:30:13 PM permalink
Quote: WongBo

Ummm ok. My post was a joke. Sorry you didn't get it.

Don't be sorry. Sarcasm is often lost over the internet. I was simply pointing out that the problem he asked is not typical of 8 year old math curriculum.
PopCan
Joined: Feb 15, 2012
• Posts: 178
February 20th, 2012 at 10:32:52 PM permalink
Quote: Triplell

Don't be sorry. Sarcasm is often lost over the internet. I was simply pointing out that the problem he asked is not typical of 8 year old math curriculum.

If that was typical 3rd grade math homework casinos would be out of business.
WongBo
Joined: Feb 3, 2012