View Full Version : Do You Believe in Diminishing Probability?

Soft Serve

09-27-2014, 02:10 PM

Some people have that special dice that most recently rolled a NAT 1, meaning its less likely to roll a 1 again in the future because the odds that it rolls 1 twice are 1/400 right? How true is that, or is it just superstition?

This is basically the same as the old "flip a coin three times" question.

There's a %50 chance you'll flip a coin heads or tails no matter how many times you've flipped it prior. The previous tests have no contribution to the current test. But at the same time, there's 8 possible outcomes of flipping a coin three times. So a %12/5 chance of getting any of those results.

As the results come in the probability increases. The first flip is Heads for example, 4/8 possible ends are eliminated leaving you a %25 chance of getting either H-H-H, or H-T-H, or H-H-T, or H-T-T.

It's all very complicated for the guy who failed math class (me) but I'm interested to see what other people think about it.

8 Possible Results:

H-H-H

H-H-T

H-T-H

T-H-H

H-T-T

T-H-T

T-T-H

T-T-T

nijineko

09-27-2014, 04:17 PM

it largely depends on how you hold the RGU, and subsequently release the RGU.

if one could control their spatial positioning such that they hold the RGU the exact same way each and every time, release the RGU at the exact same spatial positioning with the exact same amount of force each and every time, they would get the exact same result every time. this assumes a physical RGU as opposed to a digital RGU.

(RGU = result generation unit) ^^

Soft Serve

09-27-2014, 07:25 PM

it largely depends on how you hold the RGU, and subsequently release the RGU.

if one could control their spatial positioning such that they hold the RGU the exact same way each and every time, release the RGU at the exact same spatial positioning with the exact same amount of force each and every time, they would get the exact same result every time. this assumes a physical RGU as opposed to a digital RGU.

(RGU = result generation unit) ^^

Does that actually exist?

Well... apparently so. (https://www.google.com/search?q=dice+control&oq=dice+control&aqs=chrome..69i57j0l5.1405j0j4&sourceid=chrome&es_sm=122&ie=UTF-8)

Interesting way to adjust the probability of a roll. But after a few bored moments of staring at d20's I think they're built against that type of thing. The 2 and 8 sides are next to the 20. It might be possible to use Dice Control on a Roll-down style dice since the high and low numbers are all right next to eachother (and for this reason I do not allow roll-down dice at the table, or spinning your dice like a top since you can put the 20 up and hope it just slow-spins down.)

It would take an insane amount of precision to do that, I doubt anything other than a robotic arm could accomplish it.

jpatterson

09-28-2014, 05:19 AM

I am also not a math whiz and never had a physics or probability or any classes that would be helpful in this example, but I think comparing a coin flip to a die roll is perhaps a flawed analogy because one is binomial and the other has a larger set of results.

As you provided, probability is based on your criteria (getting a heads result) and the total possible outcomes (which include adding all the possibly combinations of outcomes together).

1 coin or flip = H or T = 2 outcomes; 1H = 50%

2 coins or flips = HT, HH, TH or TT = 4 outcomes; 50%

3 coins or flips = HHH, HHT, HTH, HTT, TTT, TTH, THT, THH = 8 outcomes;

In 1 flip, Heads is at 1/2 (50%) to come up on flip 1 (the only flip).

In 2 flips, Heads is at 1/2 to come up on flip 1 and 1/2 on flip 2.

Multiply the 1/2 probability of flip 1 and 2. 1/2 x 1/2 = 1/4.

Divide 100 by the denominator to get the percent probability. 100/4 = 25%.

Any of these 4 results has a 25% chance of happening in 2 flips.

Add the 1/4 probability of flip 1 to flip 2. 25% + 25% = 50%.

This is the chance of getting a Heads out of 2 flips.

For calculating each additional Heads chance, lower the 50% by the 25%, so 25% for 2 Heads on 2 flips.

In 3 flips, Heads is at 1/2 to come up on flip 1, 1/2 on flip 2 and 1/2 on flip 3.

Multiply the 1/2 probability of flip 1 and 2 and 3. 1/2 x 1/2 x 1/2 = 3/8.

Divide 100 by the denominator to get the percent probability. 100/8 = 12.5%.

Any of these 8 results has a 12.5% chance of happening in 2 flips.

Add the 3/8 probability of flip 1 to flip 2 and 3. 12.5% + 12.5% + 12.5% = 37.5%.

This is the chance of getting 2 Heads out of 3 flips.

For calculating each additional Heads chance, lower the 37.5% by the 12.5%, so 12.5% for 3 Heads) on 3 flips.

This means that effectively, the mathematics of probability is an infinitely long coin flip exercise, because the chance of you flipping a Heads is really more reliant on how many flips you've made in this trial, which started with your first flip, however many years ago that was. This is because probability gets more and more accurate with a larger trial or pool of flips, so if you do 1000 flips, you're much more likely to get a very even split down the middle between heads and tails, in that data set.

Dice then, is an even more convoluted topic that has all the above intricacy, plus 4 extra faces per random object, and then factor that appropriately for rolling more than one die, and criteria like "19 or more", etc. To me, this interesting but also boring examination leads me to believe that coins and dice and all that are indeed eminently "fair" and follow the 50% rule inherently. The only confusion is when you try to determine or legislate when a trial for a die begins. The fact is, if you kept track of ALL your rolls you EVER make with one die, on your next roll, if you've made a LOT before this, you could probably easily call the result with some confidence - and much more so a coin flip (though the coin itself may have its own probability independent of its flippers...)

Soft Serve

09-28-2014, 11:50 AM

Dice then, is an even more convoluted topic that has all the above intricacy, plus 4 extra faces per random object, and then factor that appropriately for rolling more than one die, and criteria like "19 or more", etc. To me, this interesting but also boring examination leads me to believe that coins and dice and all that are indeed eminently "fair" and follow the 50% rule inherently. The only confusion is when you try to determine or legislate when a trial for a die begins. The fact is, if you kept track of ALL your rolls you EVER make with one die, on your next roll, if you've made a LOT before this, you could probably easily call the result with some confidence - and much more so a coin flip (though the coin itself may have its own probability independent of its flippers...)

This makes me want to roll every dice I have with an excel spreadsheet ready to record and find their averages. Which, I guess, means "yes" we believe in diminishing probability?

If you have a record of the last 50 rolls of a dice, and are familiar with the results before rolling, and you feel like you're confident you'll get a result that you want, then yes you believe in diminishing probability. Basically...

nijineko

09-28-2014, 03:56 PM

Does that actually exist?

Well... apparently so. (https://www.google.com/search?q=dice+control&oq=dice+control&aqs=chrome..69i57j0l5.1405j0j4&sourceid=chrome&es_sm=122&ie=UTF-8)

Hey, it works for Martians. ;D (obscure sci-fi reference)

Also reminds me of the old school grognard munchkins who would gently heat their old dice in a frying pan, because the process used would embed air-bubbles inside of the plastic, and heating them slightly would allow the bubbles to migrate to the top of the die - done correctly, the air-bubbles would not break through the surface, and in effect "weight" the dice by making one side lighter than the rest. ^^

Soft Serve

09-29-2014, 11:10 AM

Hey, it works for Martians. ;D (obscure sci-fi reference)

Also reminds me of the old school grognard munchkins who would gently heat their old dice in a frying pan, because the process used would embed air-bubbles inside of the plastic, and heating them slightly would allow the bubbles to migrate to the top of the die - done correctly, the air-bubbles would not break through the surface, and in effect "weight" the dice by making one side lighter than the rest. ^^

Wow, some people take things way too seriously. I could never torture my dice like that, imagine how poorly they'd roll afterwards?

DMMike

09-29-2014, 06:40 PM

The fact is, if you kept track of ALL your rolls you EVER make with one die, on your next roll, if you've made a LOT before this, you could probably easily call the result with some confidence - and much more so a coin flip (though the coin itself may have its own probability independent of its flippers...)

I hope this means, "if you're an expert die roller, and can call your roll 9 times out of 10, then you can easily call the result with some confidence."

If it means, "if you've recorded every roll you've ever made, then you'll be able to predict your next roll," it will need more justification. Because there are a few factors that complicate a die roll so extensively, that it should be treated as completely random (meaning each outcome has an equal chance of happening):

-position of the die in your hand

-force used to roll the die

-angle of the die exiting your hand

-texture of rolling surface

-weight of die used

-plasticity of die used

-air motion during roll

-air temperature during roll

-breath applied to die

-height above rolling surface...

jpatterson

09-30-2014, 02:27 PM

Well that's a given, all those variables you mention would assume to be relatively even or consistent. And obviously most trials are done in any experiment using in the hundreds or sometimes thousands because probability does seem to "pool" in certain threshholds, and smaller trials (of say 300 rolls) behave as a sort of microcosm of the larger macrocosm. You will have a trial of 300 dice that comes out to an even distribution, but within a larger trial of say 10,000 rolls that may be heavy toward a few numbers. But yes, if you have rolled very few 2's say, especially over a larger trial set like 100, then yes you can predict with *some* certainty, one and likely more than one 2 will roll. Again that's with *some* certainty - not that you can predict it infallibly - that's why it's probability.

nijineko

10-05-2014, 01:56 PM

it's called probability simply because we don't yet have the ability to measure and subsequently calculate all the variables simultaneously in real time and get a meaningful and timely answer.

tesral

10-15-2014, 02:53 AM

Some people have that special dice that most recently rolled a NAT 1, meaning its less likely to roll a 1 again in the future because the odds that it rolls 1 twice are 1/400 right? How true is that, or is it just superstition?

Probability has no memory. Your chance of rolling a 1 on a d20 (providing the die is fair) is 1/20, as is the probability pf any number on the die. A roll of 1 does not change the probability of the next roll in the least still 1/20 of any given result, including 1.

Those that tell you otherwise are math challanged, and likely depending on the lottery as their retirement plan.

There is a lengthy test to determine if the die is fair, it involves a lot of rolling and recording each result. I take my digital verniers to any die I suspect is off. Much quicker,

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