Alrighty, I have a rather difficult probability question. I've scoured the interwebz, and my resident mathematician isn't available. Let's say I have 2d10 (to generate a 1-100 value); one die represents the units, and one represents the tens. How would you rank/stack/order these dice options from a statistical perspective?

Option 1: Flip the dice to generate a different result

Option 2: Re-roll the dice to generate a different result

Option 3: Roll an additional d10 to generate two different units values. You take the higher of the two units values.

Any help would be greatly appreciated!

May need more context as to what you're trying to do with the mechanic, exactly.

For d100 the units place contributes very little to the basic chance of success - a d100 roll is ([Ten's Die]*10) + Units' Die so contributes 1/11th of the total result on average (about 9%). So for a basic roll there's not much difference between reversing the numbers and rolling a different d100 entirely- your Option 1 and 2.
Option 1 is perhaps slightly faster and is possibly a reason why you might have wanted to use d100 in the first place.

I guess my answer could change if you're doing something specific like a hit location table, where exact numbers could be important  rather than just overall probability? - or if you have any weird rules like HarnMaster's "any roll ending in 5 or 0 is a critical" as well. Just be careful you're not setting it up so every head shot is a critical or something, I guess.

Option 3 is different again since its [highest of two d10s] rather than just a d10 roll.

Quote from: Bloody Stupid Johnson;563540May need more context as to what you're trying to do with the mechanic, exactly.

For d100 the units place contributes very little to the basic chance of success - a d100 roll is ([Ten's Die]*10) + Units' Die so contributes 1/11th of the total result on average (about 9%). So for a basic roll there's not much difference between reversing the numbers and rolling a different d100 entirely- your Option 1 and 2.
Option 1 is perhaps slightly faster and is possibly a reason why you might have wanted to use d100 in the first place.

I guess my answer could change if you're doing something specific like a hit location table, where exact numbers could be important  rather than just overall probability? - or if you have any weird rules like HarnMaster's "any roll ending in 5 or 0 is a critical" as well. Just be careful you're not setting it up so every head shot is a critical or something, I guess.

Option 3 is different again since its [highest of two d10s] rather than just a d10 roll.

Sorry about that, I should have clarified.

Assume that 50% or below succeeds, and 51% or above fails. There aren't any other fiddly rules.

Quote from: ZWEIHÄNDER;563519Alrighty, I have a rather difficult probability question. I've scoured the interwebz, and my resident mathematician isn't available. Let's say I have 2d10 (to generate a 1-100 value); one die represents the units, and one represents the tens. How would you rank/stack/order these dice options from a statistical perspective?

Option 1: Flip the dice to generate a different result

Option 2: Re-roll the dice to generate a different result

Option 3: Roll an additional d10 to generate two different units values. You take the higher of the two units values.

Any help would be greatly appreciated!

Well, if 50 or below is success and 51 or above is fail:

1) You now have a 26% of failing and 74% chance of success:

01-50  is already success. As is 51-54, 60-64, 70-74, 80-84, and 90-94.

2) You now have a 25% chance of failure, as the only chance of failing is by rolling 51 or higher twice in a row (1/2)*(1/2) = 0.50

3) You now have 50.9% chance of sucess. The only this way of doing things will help you is if you roll 00 exactly, and then roll a 1 through 9 on the reroll.

After the roll, you'll generally want to take the second option if success is your goal.

Quote from: ZWEIHÄNDER;563623Sorry about that, I should have clarified.

Assume that 50% or below succeeds, and 51% or above fails. There aren't any other fiddly rules.

If that's the case on the initial roll then the units roll is the same as rolling a separate d10 - all the numbers are equally likely.

Reversing the numbers you will get on the new roll, [random 10s place], and [units place from 0-5].
01-09 - units place 0 (9 chances out of 50)
10-19 -units place 1 (10 chances)
20-29 -units place 2 (10 chances)
30-39 - units place 3 (10 chances)
40-49 - units place 4 (10 chances)
50 - units place of 5 (1 chance).

Hope that helps a bit. If you have a roll of 01-50, then reverse the numbers and again have 01-50 succeed you'd succeed both on rolls if you initially rolled 01-05, 10-14, 20-24, 30-34, and 40-44, or 25% of the time, with the units place being a bit weird as shown above.

edit

Got it, figured it out! Thanks for the help!

Quote from: ZWEIHÄNDER;563623Assume that 50% or below succeeds, and 51% or above fails. There aren't any other fiddly rules.

You could use a coin flip, like in the Prince Valliant RPG. That would simplify things a lot.