Step-die pool mechanic for consideration

[Fallen_Icarus]

Was there a more complicated problem that I'm missing?

No.  Your just a lot smarter than me :)

Thanks Mike.  And also thank you Walt.  Its good to have some numbers in front of me.

[Fallen_Icarus]

Ok.  Mike and Walt, if I could borrow your brains for a another moment.

Something Valamir said got me thinking.  I would like to move, now, from a single die roll resolution method to a "number of successes" multipule dice roll.

The player still chooses which and how many dice to roll and the dice still vary in size.

For example, a player shooting for a target of 5 could need 2 successes (because of the difficulty of the task) so he chooses to roll his d4, d6 and d10.  The d4 succeeds but rolls a 4 and is lost.  The d6 rolls a 5 (fail) and the d10, the long-shot rolls a 3.  Success, but at the cost of his d4.

How much would the probabilities change with this new method?  Lets assume that the most successes needed for now would be 3.

Eric

[Phillip]

Nice die pool system.  To add to what has already been suggested (choosing one die at a time and depleting them, or losing them if max is rolled)
Why not borrow from Button Men and Godlike a little, and have different kinds of dice?  Maybe Luck, Skill, and Determination.  Have different rules for good and bad effects for choosing to use any particular die- for example, Determination depletes if maximum is rolled, representing exhaustion from use.  The Skill die could be similar to the 'hard die' in Godlike- you can call a fixed number, or something similar.  The Luck die can fluctuate from good to bad (Karma swings against you) if max is rolled.  And so on.

[Walt Freitag]

How much would the probabilities change with this new method?  Lets assume that the most successes needed for now would be 3.

The new method has too many variables to tabulate the odds in any useful way. The probability of success would now depend on the number of dice rolled, the size of each die rolled, the target number, and the number of successes needed.

A few things can be said in a general way:

1. Adding more dice to the roll will always increase the chance of succeeding, as long as there are at least as many dice in the pool as the number of successes needed.

2. To calculate the chance of getting 2 successes with 2 dice, multiply the probabilities of rolling a success with one die by the probability of rolling a success with the other. To calculate the chance of getting 3 successes with 3 dice, multiply together the probabilities of rolling a success with each of the individual dice.

3. Adding one to the number of successes needed, and simultaneously compensating by adding an additional die to the roll, will decrease the chance of succeeding overall, unless the newly added die is a "sure thing" to roll under the current target number. If the added die is a sure thing, then the chance of overall success is unchanged.

4. If no sure-thing dice are involved, then the more successes needed, the more extra dice (dice in the rolled pool exceeding the number of successes needed) are needed to reach a given chance of overall success. If each die has a 50-50 chance: To have a 50-50 chance of getting one success, you have to roll only 1 die (0 extra dice). To have a 50-50 chance of getting two successes, you have to roll 3 dice (2 dice needed to have any chance at all of getting two successes, + 1 extra die). To have a 50-50 chance of getting 3 successes, you have to roll 5 dice (3 dice needed to have any chance at all of getting three successes, + 2 extra dice).

5. For a given pool of dice rolled, assuming none of the dice are sure things, the more successes are needed, the more impact decreasing the target number will have on the overall chance of success.

By the way, I made a formatting error in the probability table on the previous page. To make the numbers in the table technically correct, you have to either multiply them by 100 or remove the percent signs. So, where it says "0.25%" (which intepreted literally would mean a one quarter of one percent chance, or one in 400), you should read it as either "0.25" or "25%" indicating a one in four chance.

- Walt