Well, 5 - 4 - 3 - 2 or any other combination of four numbers is figured like this.
Your first number has to come from my set of 4 numbers, so the chance of you getting your first die to match one of mine is 4 / 6
Your second number has to come from the remaining three numbers from my set so that chance is 3 / 6
Your third number has to come from my remaining two numbers so that chance is 2 / 6
And your fourth number has to match my remaining number so that chance is 1 / 6
So, as long as they are all four unique numbers, I think the probability is (4 x 3 x 2 x 1) / (6 x 6 x 6 x 6) = 24 / 1296 or 1 / 54 ~ 2%.
But this only holds true for unique numbers. If I had rolled 3 - 3 - 4 - 5, then it gets harder.
The first number has to be from my original set of three unique numbers, so this is 3 / 6.
But the second die you roll may have to come from only two unique numbers, or it may still come from three unique numbers. Assuming you meet condition #1, then the second die could be 2 / 6 or it could be 3 / 6 again. And each of these paths has to be multiplied by 1 / 2 because you have a 50/50 chance of going down each path.
The third die gets even harder because there are two paths that have to be considered again.
Now if we were to see that I rolled a green 19, what are the chances that you also roll a green 19, and not a purple 19 or a blue 19? Well that gets complicated too.
So in your specific case, with four unique numbers, I believe the probability is 1 / 54.
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Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
12
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
4d6 = 16
Well, 5 - 4 - 3 - 2 or any other combination of four numbers is figured like this.
Your first number has to come from my set of 4 numbers, so the chance of you getting your first die to match one of mine is 4 / 6
Your second number has to come from the remaining three numbers from my set so that chance is 3 / 6
Your third number has to come from my remaining two numbers so that chance is 2 / 6
And your fourth number has to match my remaining number so that chance is 1 / 6
So, as long as they are all four unique numbers, I think the probability is (4 x 3 x 2 x 1) / (6 x 6 x 6 x 6) = 24 / 1296 or 1 / 54 ~ 2%.
But this only holds true for unique numbers. If I had rolled 3 - 3 - 4 - 5, then it gets harder.
The first number has to be from my original set of three unique numbers, so this is 3 / 6.
But the second die you roll may have to come from only two unique numbers, or it may still come from three unique numbers. Assuming you meet condition #1, then the second die could be 2 / 6 or it could be 3 / 6 again. And each of these paths has to be multiplied by 1 / 2 because you have a 50/50 chance of going down each path.
The third die gets even harder because there are two paths that have to be considered again.
Now if we were to see that I rolled a green 19, what are the chances that you also roll a green 19, and not a purple 19 or a blue 19? Well that gets complicated too.
So in your specific case, with four unique numbers, I believe the probability is 1 / 54.
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
14
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
17
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
4d6 = 11
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
8
I am an average mathematics enjoyer.
>Extended Signature<
8
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
4d6 = 10
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
10
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
17
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
4d6 = 12
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
16
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
19
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
18
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
19
17
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
4d6 = 14
18
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
18
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
4d6 = 10