Two Dice Challenge

Quote: ThatDonGuy

Er, when (and where) is the challenge, anyway?
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Right between the Star Trek Convention and the Dungeons & Dragons Annual Meeting

Quote: Ace2

Quote: ThatDonGuy

Er, when (and where) is the challenge, anyway?
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Right between the Star Trek Convention and the Dungeons & Dragons Annual Meeting
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Got it - it's "in Vegas."

And you don't want to know how many people whine year after year that the GenCon gaming convention, which gets its name from the fact that originally it was held in the city where the company that originally made D&D was headquartered, is far too big for Indianapolis (seriously, the annual "housing lottery" to see who lets shut out of a hotel that isn't within 10 miles, much less "walking distance," from the convention center, is a sight to behold) and needs to be moved to somewhere with far more concentrated hotel space - say, the Las Vegas strip. Don't worry; it will almost certainly never happen, for two reasons; it needs to be much closer to the eastern half of the country, and yes, they do realize that quite a few of the attendees are under 21.

I think the math may get different if you borrow dice from the D&D group.

The challenge went well. Forum members attending were DJTeddyBear, LoquaciousMoFW, SphinxOfCups, and me. Besides the proxy, there were four other friends who attended at least part of it.

Recall that LoquaciousMoFW agreed to keep playing until he lost $200, betting $5 at a time. That said, here is a count of every turn.

0 2's: 225
1 2: 104
2 2's: 8
Total: 337

The net win for LoquaciousMoFW was 104*-5 + 8*40 = -200.

The ratio of two 2's to bets resolved was 8/112 = 7.14% or 1 in 14.

The expected number of two 2's in 112 bets resolved is 112/11 = 10.18. So, there was a small shortfall in two 2's, but nothing to be suspicious about. It took quite a while to see the first pair of 2's. As I recall, the proxy was down about $120 by the first time it happened.

The total rolling time I would estimate was a little under an hour.

A video will be forthcoming documenting the event.

I would like to thank LoquaciousMoFW for both the nice suite to perform the challenge and taking the losing side. I also thank the Proxy for her help.

Thanks for the report. Who's proxy was that? Or is it a secret.
Didn't Coachbelly show?

Quote: Wizard

Recall that LoquaciousMoFW agreed to keep playing until he lost $200, betting $5 at a time. That said, here is a count of every turn.

0 2's: 225
1 2: 104
2 2's: 8
Total: 337

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112 resolutions does seem a little low, but it turns out that 3/8 of the time, the bettor loses the entire $200 in 112 or fewer resolutions. The median length is around 148.

Quote: Wizard

here is a count of every turn.

0 2's: 225
1 2: 104
2 2's: 8
Total: 337

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So, there were 112 trials in which at least one of the two dice was a 2. And only 8 out of 112 times were both dice a 2. If the frequency of two 2s in this challenge was 1 in 6 then we would have expected an average of about 18.7 pairs of 2's out of 112 trials in which at least one of the dice was a two.

I imagine that no one has changed their mind because of this trial, and that the earth continues to spin around the sun.

The NULL hypothesis here was "1/6-th of the time that one of the dice shows a two they will both show a two."

In other words, if you take the total number of times there was a two and divide that by 6, you should get the number of times both were two. Since there was a 2 on 112 tosses, the NULL hypothesis predicts that 112*(1/6) = 18.7 of those should have been 2-2 and the other 84.3 should show only one two.

Chi-square analysis of this experiment gives a p-Value of 0.004. This is widely recognized as sufficient to negate the NULL hypothesis. Often, p < 0.05 is used as evidence to negate the NULL hypothesis, so this is pretty strong.

Quote: teliot

The NULL hypothesis here was "1/6-th of the time that one of the dice shows a two they will both show a two."
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Meanwhile, here is the same table with expected totals based on correct probabilities.

Twos	Ways	Actual	Expected
0	25	225	234.028
1	10	104	93.611
2	1	8	9.361
Total	36	337	337.000

p value = 0.427605218

Quote: gordonm888

I imagine that no one has changed their mind because of this trial, and that the earth continues to spin around the sun.
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Well, I maintain that the world is not round.

(It’s an oblate spheroid.)