Wizard
Joined: Oct 14, 2009
• Posts: 25448
August 26th, 2020 at 10:18:02 AM permalink
Quote: Ace2

If you start rolling a standard die and record the results, how many rolls will it take, on average, for all six numbers to have an equal number of hits?

Infinity.

Even with just a coin, the expected number of flips for the number heads and tails to be equal is infinity.

That paradoxical thing is that the probability they will ever be the same is 1. If it will eventually happen, how can it take an infinite number of flips?
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
ThatDonGuy
Joined: Jun 22, 2011
• Posts: 5748
August 26th, 2020 at 12:02:21 PM permalink
Quote: DJTeddyBear

It takes 25,855 spins before it exceeds Excel's capabilities and incorrectly returns a value of zero.

There is a way around it.
Note that log ((36/37)^N) = N (log 36 - log 37), where log is the base 10 logarithm
If the value = a + b, where a is an integer and 0 <= b < 1, then (36/37)^N = 10^a 10^b
You can calculate a and b using the floor() function

 26,000 4.170 558 E-310 27,000 5.259 820 E-322 28,000 6.633 574 E-334 29,000 8.366 124 E-346 30,000 1.055 118 E-357 40,000 1.074 158 E-476 50,000 1.093 541 E-595 60,000 1.113 274 E-714 70,000 1.133 363 E-833 80,000 1.153 815 E-952 90,000 1.174 635 E-1071 100,000 1.195 832 E-1190 200,000 1.430 013 E-2380 300,000 1.710 055 E-3570 400,000 2.044 938 E-4760 500,000 2.445 401 E-5950 600,000 2.924 288 E-7140 700,000 3.496 956 E-8330 800,000 4.181 771 E-9520 900,000 5.000 694 E-10,710 1,000,000 5.979 988 E-11,900 2,000,000 3.576 025 E-23,799 3,000,000 2.138 459 E-35,698 4,000,000 1.278 796 E-47,597 5,000,000 7.647 183 E-59,497 6,000,000 4.573 006 E-71,396 7,000,000 2.734 652 E-83,295 8,000,000 1.635 318 E-95,194 9,000,000 9.779 184 E-107,094 10,000,000 5.847 940 E-118,993
Ace2
Joined: Oct 2, 2017
• Posts: 2387
August 26th, 2020 at 4:21:33 PM permalink
Quote: Wizard

Infinity.

Even with just a coin, the expected number of flips for the number heads and tails to be equal is infinity.

That paradoxical thing is that the probability they will ever be the same is 1. If it will eventually happen, how can it take an infinite number of flips?

You refreshed my memory.

I’ve seen the case for a random walk where there’s a 50/50 chance of going left or right. It can be proven that there’s a 100% chance of eventually returning to the origin, but potentially infinite waiting time. Same concept as the coin flip..

Thanks for the replies
It’s all about making that GTA
Wizard
Joined: Oct 14, 2009
• Posts: 25448
August 26th, 2020 at 7:03:24 PM permalink
Quote: Ace2

You refreshed my memory.

I’ve seen the case for a random walk where there’s a 50/50 chance of going left or right. It can be proven that there’s a 100% chance of eventually returning to the origin, but potentially infinite waiting time. Same concept as the coin flip..

Thanks for the replies

You're welcome.

Funny how many paradoxes come up when it comes to infinity.

I still say infinity is more of a philosophical concept than a number and claim there is nothing in the physical universe that is infinite in nature.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
Ace2
Joined: Oct 2, 2017
• Posts: 2387
August 26th, 2020 at 11:46:48 PM permalink
Quote: Wizard

I still say infinity is more of a philosophical concept than a number and claim there is nothing in the physical universe that is infinite in nature.

So you believe space and time come to an end somewhere/sometime?

Much of calculus is based on infinity
It’s all about making that GTA
Wizard
Joined: Oct 14, 2009
• Posts: 25448
August 27th, 2020 at 4:46:57 AM permalink
Quote: Ace2

So you believe space and time come to an end somewhere/sometime?

I believe space does. Time is a tougher one.

Quote:

Much of calculus is based on infinity

I, of course, know that. However, calculus is not a physical thing.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
Wizard
Joined: Oct 14, 2009
• Posts: 25448
August 27th, 2020 at 4:46:57 AM permalink
Quote: Ace2

So you believe space and time come to an end somewhere/sometime?

I believe space does. Time is a tougher one.

Quote:

Much of calculus is based on infinity

I, of course, know that. However, calculus is not a physical thing.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
Wizard
Joined: Oct 14, 2009
• Posts: 25448
August 27th, 2020 at 4:47:09 AM permalink
Quote: Ace2

So you believe space and time come to an end somewhere/sometime?

I believe space does. Time is a tougher one.

Quote:

Much of calculus is based on infinity

I, of course, know that. However, calculus is not a physical thing.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
Wizard
Joined: Oct 14, 2009
• Posts: 25448
August 27th, 2020 at 4:47:10 AM permalink
Quote: Ace2

So you believe space and time come to an end somewhere/sometime?

I believe space does. Time is a tougher one.

Quote:

Much of calculus is based on infinity

I, of course, know that. However, calculus is not a physical thing.
“Extraordinary claims require extraordinary evidence.” -- Carl Sagan
DJTeddyBear
Joined: Nov 2, 2009
• Posts: 10903
August 27th, 2020 at 4:57:32 AM permalink
Quote: ThatDonGuy

There is a way around it.
Note that log ((36/37)^N) = N (log 36 - log 37), where log is the base 10 logarithm
If the value = a + b, where a is an integer and 0 <= b < 1, then (36/37)^N = 10^a 10^b
You can calculate a and b using the floor() function

I’m barely an arithmetic guy. Calculus? Fuggedanoudit.

On the other hand...
Quote:

 10,000,000 5.847 940 E-118,993

I’m a little surprised you didn’t continue this till the exponent got too big for Excel - or became got expressed as scientific notation itself.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ ————————————————————————————————————— Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁