So, I made a map once and made it D10 and a lot of people got upset for some reason.  I'm not a statistician so I'm not sure why people get so upset over this.  Can someone explain to me, if both sides roll the same dice for attack and defense, isn't it even odds?  I know D6 is the usual but I like the idea of good old fashioned D20 from D&D. I do understand that 1/6 a chance is greater than 1/20 a chance but does it really matter how wide the gap if both sides are rolling the same dice?

I will hang up and listen to your answer now.  Thanks for taking my call.

Remember, we're not rolling 1 die against 1 die here.. In most standard style games the most common battle is 3 dice versus 2 dice (attacker's advantage).  If not for the large slice of ties that go to the defender (rolling 6-sided dice), this would be unacceptable.  Basically, the defender's "tie" advantage is cut into much to severely with 20-sided dice.

I used 10 sided dice in Arm Wrestle.

I needed the extra space to accommodate the +4 attack bonuses that I was using, and the wide variance made it possible for luck to be the winning factor in some impossible attacks.

I however avoid using anything but d6 in more traditional boards.

With 6-sided dice, the odds of each of the following are approximately (I based this on a large number of trials and they are not the exact figures):

Attacker loses 0, Defender loses 2: 37%
Attacker loses 1, Defender loses 1: 34%
Attacker loses 2, Defender loses 0: 29%

And then with 10-sided dice:

Attacker loses 0, Defender loses 2: 43%
Attacker loses 1, Defender loses 1: 32%
Attacker loses 2, Defender loses 0: 25%

And finally with 20-sided dice:

Attacker loses 0, Defender loses 2: 46%
Attacker loses 1, Defender loses 1: 32%
Attacker loses 2, Defender loses 0: 22%

Mainly this is due to the reasons that M57 said above due to the defender winning with ties.  So as you can see, the more sides the dice have, the more the advantage is for the attacker.

So, it looks like I would only use higher sided dice if I wanted a stronger defensive game.  AND I would use lower dice if I wanted a stronger attack game.  (Heck even D2 - flip a coin!)  Thanks for the numbers guys!

Severene wrote:

So, it looks like I would only use higher sided dice if I wanted a stronger defensive game.  AND I would use lower dice if I wanted a stronger attack game.  (Heck even D2 - flip a coin!)  Thanks for the numbers guys!

Actually, it is the other way around... for a stronger offensive game, use higher sided dice as the attacker has the advantage there.

Oops - I got it backwards.  And I was looking right at it too.  Just curious how reducing the number of sides for the attacker would affect the outcome.  Where did you find the dice roll generator for your stats?

I used an Excel spreadsheet to get the trials.  I'm "into" numbers you might say.

The reason the fewer sides on the die, the better it is for the defender is as M57 said above, that the defender wins all ties, so the more numbers on the die, the less chance of a tie.

So if you had 3 sided dice and the attacker and defender each rolled one die, the defender would win anytime he/she rolled a 3 (0% chance for attacker).  If the defender rolled a 2, then the attacker wins if he/she rolls a 3 (33.33% chance for attacker).  If the defender rolled a 1, then the attacker wins if he/she rolls a 1 or a 2 (66.67% chance for attacker).   Adding those up and dividing by 3 (the number of outcomes possible for the defender) means in this scenario, the attacker wins 33.33% of the time.

In contrast, if you had a 2-sided die and the attacker and defender each rolled one die, the defender wins when he/she rolls a 2 (0% chance for attacker), and if he/she rolls a 1, the attacked must roll a 2 (50% chance for attacker).  Here the attacker wins (add them up and divide by 2) only 25% of the time.

I remember this dynamic from the battle matrix at tos.  I think that map used 16 sided dice and it was definitely an attack oriented map.  A few of my friends didn't realize this and played a more defensive game which made things fun for me.  I miss that map, you did a good job on it.

Whose map was battle matrix?  I played that a bit & it was fun.  Seemed like there were a lot of versions & it was always evolving.

I wrote a simple calculator in javascript that you can use to see how changing the dice sides affects the odds:

http://prestopnik.com/wargear/ (on the right side)

@Rope - Thanks, Im glad you liked it.  But when the defensive players noticed the odds they got really pissed off.  I was just using higher dice because I liked the option of using irregular dice.  I was thinking along D&D terms not really RISK odds.

OK Cona, what are the resulting stats for D18 vs D20? OR, what vs D20 defense dice would make it a little more balanced?  (Although, I think a high attack odds map might be OK if I labeled it as such in advance I guess...)

I forgot to mention I also put together a chart with some nice graphs showing how dice odds change as you manipulate the # of sides:

https://spreadsheets.google.com/a/prestopnik.com/pub?key=0AkEShFtV-CJWdEtORmZQYjlUZW51NWtMSjc5ZTFTRlE

#s in the chart are expected attack losses per defending units for standard attack (3 dice vs 2 dice).

One interesting thing to note.   If the attacker has 1 more side than the defender the odds are almost exactly the same regardless of the actual # of sides (.5 attackers lost per defender), and as the # of sides goes to infinity all odds seem to be converging somewhere around .5 regardless of attack/defense bonuses.

Severene wrote:

OK Cona, what are the resulting stats for D18 vs D20? OR, what vs D20 defense dice would make it a little more balanced?  (Although, I think a high attack odds map might be OK if I labeled it as such in advance I guess...)

Assuming my calculator is correct the odds for D18 v D20 are almost exactly the same as D6 v D6.

Wait did I do that backwards again? I meant D18 attack VS D20 Defense.  Is that what you checked on to get similar to D6 results?

Yep that is right.   As # of dice sides go up, the attacker gets an advantage, so knocking the attacker back down 2 evens out the advantage.

If you ever port Battle Matrix to this site, make sure to at least have the 16 sided dice as one of the scenarios.  I really liked it, it made it unique.

Battle Matrix is next on my list.  Just finished Battlestar and am working on an Earth map right now.