Die modifier mechanics and "value"

Hello,

I'm no mathematician either, but this is basic probability math:

As an example let's assume that both players roll 100 dice. On average both players will roll 50 "hits". Now, let's see what happens when we adjust the values.

A +1 means that you will score 4 out of 6 = 67 hits. A +2 means that you will score 5 out of 6 = 83 hits. A -1 will score 2 out of 6 = 33 hits. A -2 will score 1 out of 6 = 17 hits.

A lot will depend on how many extra dice are rolled. To get the equivalent of a +1 modifier (67 hits) you will need 34% extra dice. So, rolling six dice with a +1 modifier is the same as rolling eight dice without modifier, both would score 4 hits on average.

Rerolling all dice, even the hits, would only make sense when you roll worse than you would statistically expect, or when you are desperate for some reason.

Being allowed to reroll all the failures would give you an average hit % of 75.

Just add the bonus succeses to the average expected hits.

I think the auto-success modifier is the most valuable and re-rolls the least, with the result modifier and extra dice falling somewhere inbetween. But I am no mathamatician so the answer escapes me =(

I really think it depends on the numbers. The result modifier is pretty strong and the small difference between the numbers leave little "wiggle room", but I also find them the most elegant solution. Adding dice is also an elegant mechanic. The others don't seem so cool to me.

I hope this helps some. I'll be happy to help with any further questions.

Here is my attempt to answer your question, with my limited probability skills:

For one die - the order is as follows from best to worst:

1) Automatic success gives you 1 auto success and 1 die roll. The chances of getting 2 successes is 50%, 1 success is of course guaranteed.

2) Getting an extra die (now you have 2), gives you a 25% chance at 2 successes, and a 75% chance at 1 success.

3) +2 Modifier gives you a 83.3% of success - can only fail on a 1.

4) Re-rolling the die gives you a 75% chance at 1 success.

5) +1 Modifier gives you a 66.6% of success.

For 2 dice:

1) Auto success gives you 1 auto success and 2 die rolls. The chances of getting 3 successes is 25%, 2 successes - 75%.

2) Extra die (you have 3), 3 successes - 12.5%, 2 successes - 50%, 1 success - 87.5%

3) +2 Modifer to both dice: 2 successes - 69.4% , 1 success - 97.3%

4) +1 Modifier to both dice: 2 successes - 44%, 1 success - 88.9%

5) Re-rolling dice gives you a 37.5% of 2 successes, and an 87.5% of 1 success.

Without getting into complex mathematics and extrapolating these limited results outward, you can see that Auto success provides the biggest benefit because you always get an extra success.

The extra die always give you a chance to get 1 more success than your opponent - however, already at 3 dice you can see that the chances of getting 1 or 2 successes are better with the modifiers and re-rolling than just getting 1 extra die. Of course if you are to compare getting multiple extra dice - it will always be more powerful than the modifiers.

The +2 Modifier is always more powerful than re-rolling, and the +1 is always better than re-rolling except for 1 die in which re-rolling is the better choice.

Here is a good website that answers some basic questions on dice probabilities that might help you if you want to go more into detail.

http://mathforum.org/library/drmath/sets/select/dm_dice.html

The chart shows the chance of rolling the value OR GREATER.

For the multiple dice percentages, it shows the same thing, but moving left to right, it shows the probability of rolling the result on AT LEAST the number of dice corresponding to the column number. So rolling a Yahtzee of 6s on 5 dice only has a .01% chance of succeeding, but rolling a 4 or greater on 3 of 5 dice has a 50% chance of succeeding.