For this scenario, imagine four players rolling 4 d6's each. If each needs to contribute a "1" result to a common pool to win as a group, what is the probability? What if there are two or three players? What if only one player is rolling trying to get at least one "1"?
I've driven myself mad (and a little sad I didn't take statistics and probability in school.) I've done the research. I've used www.anydice.com. I'm attempting to understand the math. I'm sure it's obvious to those that have been taught. For those of us reinventing math from scratch, it's a little tougher. :)
Here's the likely outcomes I see. If you have the answer and can explain WHY not just WHAT the answer is, I'd much appreciate it. (Be gentle...)
A) www.AnyDice.com - http://anydice.com/program/8cd9
This shows 48% of a d6 array results in a 0, hence any result that has at least one "1" or more is 52%. Any additional players is multiplied such as 52% or 0.52 * 0.52.
1P = 52%
2P = 27%
3P = 14%
4P = 7%
B) Each die has a 1/6 chance to be the winning result, or 16.67%. To have at least one die a "1" with four dice is: 1/6 + 1/6 + 1/6 + 1/6 = 4/6 or 67%. Additional players are multiplied 0.67 * 0.67.
1P = 67%
2P = 45%
3P = 30%
4P = 20%
C) Four dice have a single chance to be all "1's" out of 6*6*6*6 or 1296 total chances. Or 1/6 * 1/6 *1/6 * 1/6 Or 1/1296. Three dice have a 1/6 * 1/6 * 1/6 chance, or a 1/216, or 6/1296. Two dice have a 1/6 * 1/6 chance, or 1/36, or 36/1296. And one dice has a 1/6 chance, or 216/1296. Adding up the possible winners is 1 + 6 + 36 + 216 = 259. 259/1296 = 20%. Each player has the same chance to contribute at least one "1" die at 20%. So For all players to add in, it's 20%*20%, etc. or...
1P = 20%
2P = 4%
3P = 1%
4P = <1/10%
I think I'm close on C, but it seems super low chance practically looking at it. Is it option A, B, C or a D?
-Adam
Ok, so we're agreed A is correct.
1P = 52%
2P = 27%
3P = 14%
4P = 7%
Yes, each player is a set and has to contribute one success. Think of it as a STAR die face, instead of a number if that helps. The number is irrelevant. A player may spend this special side, at will so the other faces or uses do not matter.
Allowing sharing of successes would make it easier. At least X successes, where X is number of players, from any dice roll would be something like 15-35% or so for 2P-4P.
What would be ideal is a system that scaled with number of players with the same (or nearly so) odds instead of the variance above so that the game mechanic can be balanced.
Essentially this mechanic is for a super power that can be called in, when each player gives up a die to contribute to the party ability. Something like 10-20% occurrence is probably about right. Each player will have 4d6 that are identical as above. A unique 5th die can have any combination of symbols.
If the number of players always goes up, and the percentage of successes is always under 100%, then it would seem to be escalating difficulty to have all successes. Does that make sense? Any suggestions?