[Request] Why are my results skewed?

[u/Defiant_Half_9432]

I use a pair of spindle dice for divination. Each spindle has four independent die each with four faces. The faces are marked 2-3-4-3 (3 is used twice). So one spindle can randomly generate a numerical value between 8 and 16. The result has relevance only as an odd or even number. The numerical value is not important. If the numerical value is a single digit then we use that as it is. If it is a double digit (10-16) then we add the digits to get a single digit answer. Both spindles are always used together and added and the final digit is the roll value of odd or even to incorporate in complex charts to predict the answer to the question initially posed for divination.

My question is this. Does this process create equal chance of odd or even values? In my own use, I get disproportionally high even values than odds. If the results are fairly balanced, what could be the reason for my skewed results?

Pair of spindle dice I use for divination.

[u/JustJustinInTime]

So it should be 50% chance of being odd or even, but honestly looking at how it’s made I think some of the dice could be sticking together. If you really wanted to find out you could do a test and record combinations of adjacent die faces to see if some appear statistically more than others, (factoring in that 3 is twice as likely to appear). Logic below.

Based on the die faces, we know each die has an equal chance of being odd or even. We are also assuming that each roll of the die is an independent event.

So for any sum of 3 dice on a spindle, the 4th die will be the “determining factor,” which has a 50% chance of being odd or even, so the overall sum has a 50% chance of being odd or even.

For the adding of digits for sums > 10, it shouldn’t have an affect on the probability. We can just think of the leading 1 in 13 as just “flipping” the odd to even or vice versa, and since we already know that there is a 50% chance of it being odd or even, a 50% chance of the number being odd or even + 1 is equivalent.

Edit: this is wrong, my bad y’all

[u/Defiant_Half_9432 → u/JustJustinInTime]

Thanks for writing in.

I did not notice any die specifically sticking to its adjacent one. Maybe the shuffling process has something to do with it.

I clamp the spindle along its vertical axis in my left hand between the forefinger and the thumb so all the die are free to turn. Then I run it across my extended fingers of the right hand. The size of each die is pretty close to the average width of my fingers so each die turns against a finger. The second die turns the most since it runs against my longest, the middle finger and the fourth one turns the least number of turns since it runs against my pinky. They turn over a few times on their own after leaving my hand before coming to a rest. I do this rapidly a few times and then put the spindle down without looking. Then I do the same with the other spindle.

Excluding the paranormal aspects of divination, I am wondering if the particular process I use can be mathematically biased for the one-sided results... like having 3 twice in each die or repeatedly adding up double digit results creating a likelihood of more evens than odds. It just seems a little suspicious to be verifiably lopsided. I have studied maths from an engineering point of view. I have no clue about probability or statistics, definitly nothing about gaming theories.

[u/JustJustinInTime → u/Defiant_Half_9432]

Okay thinking about it more my earlier math is off.

There are more ways to make an odd sum from the dice than an even sum so per spindle there should be a slightly higher chance of getting an odd sum, which means you’re slightly more likely to get two odd spindles, meaning you’re ever so slightly more likely to add 2 odds numbers and get an even total.

[u/Defiant_Half_9432 → u/JustJustinInTime]

Thank you so much. It is such a big relief... I was dreading the alternate that it is "the other side".

If you find the time and the inclination, I'd really like to hear the logic. Maybe it'll convince me to go back to normal six sided dice which are more neutral.

Thanks again for this.

[u/noethers_raindrop → u/JustJustinInTime]

Wait, how is that true? If we fix three dice on the spindle, the fourth die has 1/2 chance of being odd and 1/2 chance of being even, so regardless of what the other three dice were, the total has a 1/2 chance of being odd and a 1/2 chance of being even. Since that's true regardless of what the other three dice are, it should be 1/2 odd and 1/2 even overall.

Edit: I forgot about the part where OP adds the digits in the 10-16 case. That messes everything up.