Preview Ask the Wizard #278

As usual, I hope y'all can preview my latest column and correct any typos, ask for a clarification for anything that isn't clear, or otherwise try to make the column better. All these topics have been discussed here already, so if you want to address the topic in general, follow the link provided. For the question about the safeties, follow average field goals thread.

Ask the Wizard #278.

Thanks.

Concerning the question about the stacked dice. The state of Pennsylvania pretty much copied New Jersey's regulations word for word. In Pa, stacked dice would be a no roll. Section 537.9(a) in the following link:


http://gamingcontrolboard.pa.gov/files/regulations/Temporary_Table_Games_Regulations.pdf

Quote: Fleaswatter

The state of Pennsylvania pretty much copied New Jersey's regulations word for word.

Thanks. They didn't "pretty much" copy it, they did so exactly, word for word, at least pertaining to the question at hand.

On the question about the expected number of rolls of two dice, in the last sentence of paragraph 4 you say, "Thus, the expected number of rolls to get a two, three, and four is 43.8 + (7/90)×7.2 = 44.816. "

I think you meant, "... a two, three, four, and five is ...."

About that point, my eyes and brain started to glaze over, so I can't vouch for the rest one way or the other.

You should check the spelling in the stacked dice question. Several times it appears as "role" instead of "roll"

Mike,

This is nit picky, but it sounds kind of weird to me. There is no mention of 'number', which is really what people want to know...what was the number that was rolled on the lower(or bottom) die?

What would happen if the two dice landed stacked in craps. Would it be a valid roll? If so, how would the dealers determine what the lower die landed on?

How about reword to something like this:

What would happen if the two dice landed stacked in craps. Would it be a valid roll? If so, how would the dealers reveal(or you can leave the word determine) the number that was rolled on the lower die?

You also use the same language in your answer.....this needs the same fix applied.

"...he said if it did<add comma here> the dealers would simply move the top die to see what the lower die landed on."

I question the ability of determining the top by only looking at the four sides.

They could be left-handed dice, and/or have non-traditional pip arrangements on the 2 and 3 sides.

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Quote: Fleaswatter

The state of Pennsylvania pretty much copied New Jersey's regulations...

There was a third state mentioned in the original thread as also having copied NJ's regs.


I didn't look into the third state's regs, but over a year ago, while doing research for my Poker For Roulette bet, I was comparing some of the Roulette rules for NJ & PA. Both states have a rule, with identical wording, that allows a double-zero wheel to be used on a single-zero layout, with a 00 result being a push.

It would not surprise me to learn that, except for the statue numbers and rules that are actually different, the remainder of the NJ & PA rules are identical.

In the safeties question:

"This should be considered as just a rough guess. There are factors to the game that I'm not taking into account, in the interests of simplicity."

Drop the "s".


Concerning the "stacked dice" response:
Would it be wise to insert a disclaimer in case some casino is using "left handed" dice, as DJ mentioned. I haven't been confirming the consistency of the layout of the faces. Perhaps a quick survey is in order.

A follow up to the "All" dice question:

If the odds of rolling a 2 are 1/36, wouldn't the "average" number of rolls in 36 trials to produce one be 18, not 36? In 36 rolls, you would expect to roll at least one on average, but wouldn't you expect the first to occur anywhere from the first to the 36th roll with equal frequency, and an average of 18? If so, doesn't this shorten the number of expected rolls to hit all 11 outcomes?

Thanks for the additional comments.

Quote: DJTeddyBear

They could be left-handed dice, and/or have non-traditional pip arrangements on the 2 and 3 sides.

I have never heard of left-handed dice. Do you have anything to support their existence? I'm pretty sure there is a very strict, yet unofficial, policy about the way the sides of the dice are arranged, and any craps dice you see in Vegas will follow that policy.

Quote: Ayecarumba

If the odds of rolling a 2 are 1/36, wouldn't the "average" number of rolls in 36 trials to produce one be 18, not 36? In 36 rolls, you would expect to roll at least one on average, but wouldn't you expect the first to occur anywhere from the first to the 36th roll with equal frequency, and an average of 18? If so, doesn't this shorten the number of expected rolls to hit all 11 outcomes?

The mean number of rolls to get a total of 2 is 36. In fact, the calculation is pretty easy. Let x be the expected number of rolls to bet the first two. Starting with the first roll there is a 1/36 chance it will take one roll only, and a 35/36 chance it will take 1+x, because the first roll was not successful. So, let's solve for x:

x=(1/36)*1 + (35/36)*(x+1)
36x = 1 + 35*(x+1)
x=36

The question you seem to be asking is the median number of rolls required. However, the answer to that is not 18 either. It is 25. In other words, there is a 50.55% chance that if you roll two dice 25 times that you will get at least one 2.

When dealing with independent events, as a rule of thumb, you multiply probabilities, not add.

Quote: Wizard

The question you seem to be asking is the median number of rolls required. However, the answer to that is not 18 either. It is 25. In other words, there is a 50.55% chance that if you roll two dice 25 times that you will get at least one 2.

Thanks Wizard! I went back to the original thread and note that mustangsally's post addresses my confusion, and her 1M trial simulation produces a median of 35 - 37 rolls to produce all 11 possible outcomes. I think what's throwing me is the use of the term "average" with "first" (e.g., "...it would take 36 rolls on average to get the first 2." Actually, the "first" two will show up more than half the time within the first 25 rolls.) Perhaps "first" should be dropped in favor of "a" (e.g., "... it would take 36 rolls on average to get a 2"?)

I suggest changing the title of the first column in the "Expected Number of Rolls Problem" table from, "Highest Number Needed" to, "Highest Value Remaining" to clarify between the "target values" and the "number of rolls".

You need to copy and paste this, you didn't change enough:

What would happen if the two dice landed stacked in craps. Would it be a valid roll? If so, how would the dealers reveal the number that was rolled on the lower die?

same with the answer portion.

Quote: Wizard

I have never heard of left-handed dice. Do you have anything to support their existence?

There was a thread here last spring that discussed the configuration of dice. There I commented that all of the dice I am familiar with are what I would consider left handed, meaning that if you look at the 1-2-3 point or the 4-5-6 point those numbers are arranged counter-clockwise.

Several of the posts in that thread comment on web sites that have illustrations of dice that are not proper. One that I still can find shows an ad with a die that has the 2 face adjacent to the 5 face. There are also comments about a "bizarre" illustration on the "dice specifications" page at Midwest Game Supply Company. The illustration I found there today looks OK.

However, I did notice some security options that Midwest Game Supply Company offers, including a "reverse 2-3" configuration. (Someone had posted here -- somewhere -- that this was an indication of loaded dice, but apparently that is not so.) Of the two dice shown below, the one on the right is the standard configuration, with the pips of the 2 and 3 "touching" close to the 6, while the die on the left has them touching near the 1. Both dice are in the counter-clockwise "left-handed" configuration I am familiar with, but I am not aware of ever having seen a die like the one on the left.



This may or may not have any affect on your stacked-dice answer.

Thanks Doc.

I was about to link to (sigh) a Wikipedia page to support my post.

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On second thought, a quick search of some gaming supply comany websites, including one for Midwest Game Supply, produced nothing but left-handed dice.

I.E. I'm now on a mission to find RIGHT handed casino quality dice!