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Wizard
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Wizard 
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June 25th, 2010 at 3:04:23 PM permalink
Quote: joshyeltman

On average, how many spins does it take to see a previously rolled number? Not necessarily back to back, but to repeat any number that has previously been rolled. A couple of us have made guesses, but we can't figure out an accurate way of calculating the average.



I get a mean of 8.408797212, but invite somebody else to confirm. This is similar to the "birthday problem," which asks, how many people do you need for there to be a 50% or greater chance of a common birthday?
It's not whether you win or lose; it's whether or not you had a good bet.
Nareed
Nareed
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June 25th, 2010 at 4:36:51 PM permalink
Quote: Wizard

I get a mean of 7.408797212, but invite somebody else to confirm. This is similar to the "birthday problem," which asks, how many people do you need for there to be a 50% or greater chance of a common birthday?



Funny thing, once I was discussing the birthday problem with someone who turned out to have the same birthday as me, albeit in a different year.
Donald Trump is a fucking criminal
DJTeddyBear
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June 25th, 2010 at 5:09:32 PM permalink
Quote: Nareed

Funny thing, once I was discussing the birthday problem with someone who turned out to have the same birthday as me, albeit in a different year.

Different year is the key. Make it the same year and the number skyrockets.

I remember this being discussed one night on Carson's Tonight Show. I believe the number was in the low 20's.

Johnny "tested" it by proposing to ask the people in one section of the audience. The rows only had 6 or 8 people in them. He was on the third or fourth person in the first row when someone in the second row reacted that they had the same day as the person he had just asked.
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
Wizard
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Wizard 
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June 25th, 2010 at 10:39:18 PM permalink
The answer to the birthday problem is 23.

Back at my last real job there were about 30 people in the office, and we had two sets of common birthdays, as I recall. There were also a whole bunch of birthdays in June, about 25% of the entire office. If I were still there I'd be enjoying longer breaks and eating lots of cake about this time. As long as I'm on the topic, my two brothers have the same birthday, but four years apart.
It's not whether you win or lose; it's whether or not you had a good bet.
Chuck
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June 26th, 2010 at 4:18:54 AM permalink
Quote: Wizard

As long as I'm on the topic, my two brothers have the same birthday, but four years apart.



I also have two brothers with the same birthday, two years apart. I counted back and could never figure out what was so special about the conception date.
Wizard
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Wizard 
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June 26th, 2010 at 11:46:16 AM permalink
Quote: Chuck

I also have two brothers with the same birthday, two years apart. I counted back and could never figure out what was so special about the conception date.



I never thought of that before, but both my younger brothers would have been conceived right around my birthday. Hey, I'm the one who is supposed to have fun that day!
It's not whether you win or lose; it's whether or not you had a good bet.
DJTeddyBear
DJTeddyBear
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June 26th, 2010 at 3:10:53 PM permalink
Um... Ew. Ick!

Can we please get this thread back on topic?
I invented a few casino games. Info: http://www.DaveMillerGaming.com/ 覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧覧 Superstitions are silly, childish, irrational rituals, born out of fear of the unknown. But how much does it cost to knock on wood? 😁
joshyeltman
joshyeltman
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June 26th, 2010 at 11:40:47 PM permalink
What I really want to know is what formula you used to come up with that number. I arbitrarily guessed around 8, and I'm glad I was close, but I'd like to know how to calculate this.
Wizard
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Wizard 
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June 27th, 2010 at 7:21:34 AM permalink
Quote: joshyeltman

What I really want to know is what formula you used to come up with that number. I arbitrarily guessed around 8, and I'm glad I was close, but I'd like to know how to calculate this.



First you need to know the formula for the probability of a repeat repeat number with exactly n spins. That probability is 1-(37/38)*(36/38)*...*((38-n+1)/38). Here are some values by n:

2 0.026316
3 0.077562
4 0.150386
5 0.239819
6 0.339843
7 0.444078
8 0.546485
9 0.641962
10 0.726760
11 0.798666
12 0.856947
13 0.902121
14 0.935606
15 0.959330
16 0.975384
17 0.985749
18 0.992124
19 0.995855
20 0.997927
21 0.999018
22 0.999561
23 0.999815
24 0.999927
25 0.999973
26 0.999991
27 0.999997
28 0.999999

Let f(n) be the probability of a repeat within n spins. Let g(n) be the proability that the first repeat is on exactly the nth spin. Then g(n)=f(n)-f(n-1). Here are some values for g(n)

2 0.026316
3 0.051247
4 0.072824
5 0.089433
6 0.100024
7 0.104235
8 0.102407
9 0.095477
10 0.084799
11 0.071905
12 0.058281
13 0.045175
14 0.033485
15 0.023724
16 0.016054
17 0.010365
18 0.006376
19 0.003731
20 0.002073
21 0.001091
22 0.000543
23 0.000254
24 0.000112
25 0.000046
26 0.000018
27 0.000006
28 0.000002
29 0.000001

Then you take the dot product of the above table to get the expected number of spins, which is...

2*0.026316 + 3*0.051247 + 4*0.072824 + ... = 8.408795574

p.s. In writing this up I realize my original answer was off by exactly 1, I think because I wasn't counting the first spin.
It's not whether you win or lose; it's whether or not you had a good bet.
LMyztik
LMyztik
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September 4th, 2014 at 4:26:42 PM permalink
Does anyone here know the name of the "roulette system" where people would bet most red numbers (no black numbers) and some other times most black numbers (no red numbers)?

I've seen only one person doing it and it is amusing since most red numbers are covered and the chances of red/black are higher than the straight bets.

Does this increase the chances or reduces the house edge in any way? Is this just as bad as any other "method"?

i.e.: on a single zero roulette, making $5 bets, straight bets on 5-7-9-12-14-16-18-21-23-25 + Split bets on 27/30 and 0/1. (All red numbers and covering 0).

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