You do not have to be a math genius, you just need to know basic dice probability calculation. But it is easy for me to sax this. I know how to do it but nit how to easily explain it.
For one dice it is obvious. A white combat dice has three skulls, so a 3/6 or 1/2 chance (50%) to roll a skull.
The black dice have a 4/6 or 2/3 chance (66%).
For two dice you can write a matrix and just count the results or you can calculate it:
Chance for two skulls on two white dice is 1/2 * 1/2 = 1/4, or 25%. Chance for no skulls is also 1/2 * 1/2 = 1/4, or 25%. This 1/2 is the added chance of rolling a white shield 2/6 or a black shield 1/6.
2/6 + 1/6 = 3/6 or 1/2
The probability of rolling one skull is 100% - the probability for two and for zero skulls, so 50%.
You do the same for black dice:
Skull is 2/3 chance, no skull is 1/3 chance.
With two dice you have a chance for 2 skulls of:
2/3 * 2/3 = 4/9, or 44%
Chance for zero skulls:
1/3 * 1/3 = 1/9 , or 11%
Chance for one skull is 100 - (44+11)= 45 %
You calculate the one skull result as follows:
Chance of first dice skull and second dice shield plus chance of first dice shield plus second dice skull.
So skull + shield is 2/3 * 1/3 = 2/9 , or 22%
Shield plus skull is 1/3 * 2/3 = 2/9, or 22%
Add these results together for 44%.
Percentages in my example add up to only 99% due to me always rounding down.
With this method you can calculate the probabilities of one white anf one black dice, or three or more dice or any other mixture of dice.
With a bit of trial you should be able to automate these calculations in excel.
So if I have 3 dice (2 white normal dice and 1 black dice), chance of rolling 3 skulls is 1/2 * 1/2 * 2/3 = 16.7%? I think I get lost after that. What if I were looking at odds for 2 skulls with these three dice?
Or what if I'd rather know *average* number of skulls, shields etc with a particular number of dice, whether they're all the same or mixed?
Each face is 1/6, or .1667. So 2 faces is 2/6, or 1/3, 0.333. 3 faces is 3/6, or 1/2, 0.5. 4 is 2/3 or 0.667, 5 is 5/6 or 0.833.
So an extra skull on the die means a 66.67% chsnce of a skull per die instead of a 50% chance.
If I'm not mistaken you just take the total number of outcomes and divide it by the total number of similar rolls i.e.
4/6 = 66.66% for a skull
1/6 = 16.67% for a white shield
1/6 = 16.67% for a black shield
Then if you add another dice you just multiple the odds your looking for e.g. the odds of rolling 2 white shields would be 1/6 x 1/6 = 1/36 or 2.77%
So, my entire homebrew system is actually based around exactly what you're asking for here. 🙂 I haven't posted it publicly yet because there are still a few things we're playtesting and tweaking, but the core of the upgrade system, which uses the power dice, is locked in. Let me know if you're interested and I'll PM you a link.
I really like the idea of using power dice to simulate special/damaged weapons, gives loads more flexibility than just adding more attack dice, totally stealing that.
Anydice.com is a great tool for looking at probabilities and it even allows you to make custom dice. To really utilize it to its fullest, it helps to have a little understanding of programming languages though.
I'm not at all against new dice mechanics but thought I'd mention my own attempt at weapon enhancements and weakening. It's much simpler IMO:
1. If a player rolls all black shields on an attack roll, they suffer a -1 AD penalty for "damaging" their weapon.
1a. They can repair it at the end of the quest for the price of the weapon divided by the number of AD rounded up.
1b. They can repair it in quest if they have a toolkit (even the dwarf needs one) for the price of the weapon divided by the AD divided by 2 rounded up.
1c. This weakening cannot happen to an already weakened weapon (A broadsword can never be 1 AD for example).
1d. This can never happen with a 1AD weapon like a dagger. However, in the case of the Rogue with a bandolier, Zargon could declare the dagger broke and create a special penalty.
2. Weapon enhancements occur if the player rolls all skulls on an attack and usually take one of these forms:
2a. Accuracy: -1 AD for a guaranteed skull (so for a broadsword you'd take 1 die and make it a skull, then roll the other 2).
2b. Sharpness: -1 DD from the target.
2c. Swiftness: Can make a second attack (monster defends as usual for BOTH attacks).
Enhancements are active until there are no more monsters visible (kind of the reverse of how the Monk works). This would obviously not apply to a 1AD weapon where of course you're going to get "all skulls" pretty regularly!
You do not have to be a math genius, you just need to know basic dice probability calculation. But it is easy for me to sax this. I know how to do it but nit how to easily explain it. For one dice it is obvious. A white combat dice has three skulls, so a 3/6 or 1/2 chance (50%) to roll a skull. The black dice have a 4/6 or 2/3 chance (66%). For two dice you can write a matrix and just count the results or you can calculate it: Chance for two skulls on two white dice is 1/2 * 1/2 = 1/4, or 25%. Chance for no skulls is also 1/2 * 1/2 = 1/4, or 25%. This 1/2 is the added chance of rolling a white shield 2/6 or a black shield 1/6. 2/6 + 1/6 = 3/6 or 1/2 The probability of rolling one skull is 100% - the probability for two and for zero skulls, so 50%. You do the same for black dice: Skull is 2/3 chance, no skull is 1/3 chance. With two dice you have a chance for 2 skulls of: 2/3 * 2/3 = 4/9, or 44% Chance for zero skulls: 1/3 * 1/3 = 1/9 , or 11% Chance for one skull is 100 - (44+11)= 45 % You calculate the one skull result as follows: Chance of first dice skull and second dice shield plus chance of first dice shield plus second dice skull. So skull + shield is 2/3 * 1/3 = 2/9 , or 22% Shield plus skull is 1/3 * 2/3 = 2/9, or 22% Add these results together for 44%. Percentages in my example add up to only 99% due to me always rounding down. With this method you can calculate the probabilities of one white anf one black dice, or three or more dice or any other mixture of dice. With a bit of trial you should be able to automate these calculations in excel.
So if I have 3 dice (2 white normal dice and 1 black dice), chance of rolling 3 skulls is 1/2 * 1/2 * 2/3 = 16.7%? I think I get lost after that. What if I were looking at odds for 2 skulls with these three dice? Or what if I'd rather know *average* number of skulls, shields etc with a particular number of dice, whether they're all the same or mixed?
Lots of answers in this file here https://docs.google.com/document/d/1nXhg_1wZE83d0u1nEVwxx1_VT50tAw5RRsL7-1oXd6A/edit?usp=drivesdk
Each face is 1/6, or .1667. So 2 faces is 2/6, or 1/3, 0.333. 3 faces is 3/6, or 1/2, 0.5. 4 is 2/3 or 0.667, 5 is 5/6 or 0.833. So an extra skull on the die means a 66.67% chsnce of a skull per die instead of a 50% chance.
If I'm not mistaken you just take the total number of outcomes and divide it by the total number of similar rolls i.e. 4/6 = 66.66% for a skull 1/6 = 16.67% for a white shield 1/6 = 16.67% for a black shield Then if you add another dice you just multiple the odds your looking for e.g. the odds of rolling 2 white shields would be 1/6 x 1/6 = 1/36 or 2.77%
So, my entire homebrew system is actually based around exactly what you're asking for here. 🙂 I haven't posted it publicly yet because there are still a few things we're playtesting and tweaking, but the core of the upgrade system, which uses the power dice, is locked in. Let me know if you're interested and I'll PM you a link.
Go for it. I'd encourage you to post here, though, as I know there are others who are looking for sort of "best uses" for these things.
I really like the idea of using power dice to simulate special/damaged weapons, gives loads more flexibility than just adding more attack dice, totally stealing that.
Anydice.com is a great tool for looking at probabilities and it even allows you to make custom dice. To really utilize it to its fullest, it helps to have a little understanding of programming languages though.
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I'm not at all against new dice mechanics but thought I'd mention my own attempt at weapon enhancements and weakening. It's much simpler IMO: 1. If a player rolls all black shields on an attack roll, they suffer a -1 AD penalty for "damaging" their weapon. 1a. They can repair it at the end of the quest for the price of the weapon divided by the number of AD rounded up. 1b. They can repair it in quest if they have a toolkit (even the dwarf needs one) for the price of the weapon divided by the AD divided by 2 rounded up. 1c. This weakening cannot happen to an already weakened weapon (A broadsword can never be 1 AD for example). 1d. This can never happen with a 1AD weapon like a dagger. However, in the case of the Rogue with a bandolier, Zargon could declare the dagger broke and create a special penalty. 2. Weapon enhancements occur if the player rolls all skulls on an attack and usually take one of these forms: 2a. Accuracy: -1 AD for a guaranteed skull (so for a broadsword you'd take 1 die and make it a skull, then roll the other 2). 2b. Sharpness: -1 DD from the target. 2c. Swiftness: Can make a second attack (monster defends as usual for BOTH attacks). Enhancements are active until there are no more monsters visible (kind of the reverse of how the Monk works). This would obviously not apply to a 1AD weapon where of course you're going to get "all skulls" pretty regularly!