Too many dice?

In a game that I recently was designing (a table top war game). I was rolling 20 sided dice versus a particular target number to determine combat results. I started off with rolling 1D20 for each combatent, but soon relised that I was going to be needing to roll many dice as this was a large scale combat game (1000s of troops on each side).

I relised that I could convert the D20 into a percentile die. Each number on the D20 was worth 5% (100%/20).

I determined that if the target number was rolled exactly then 50% of the troops would score a hit. For each number off target (above or below) the number of troops that scored a hit was modified by 5%. So that if you rolled a 15 and the target number was 12 then 65% of the troops would score a hit.

A similar system coudl be worked out for any dice:
for example, with a D6:
100/6=16.666...
Now this isn't exact, but this could be generalised as 16.5% for each number off the target. A simple way to remember this would be with a chart or table. So:
-3 : 0.5%
-2 : 17%
-1 : 33.5
0 : 50%
+1 : 66.5%
+2 : 83%
+3 : 99.5%
if it is off by 4 or more it is either 0% OR 100%. Now these numbers are hard to calculate but you could have a look up chart/table for common number (5, 10, 20, 25, etc) that the players can use.

Under this example if you rolled a 5 and needed a 3 to hit and you had 20 ships then 16.6 (17 or 16 depending how you round) ships will hit. Of course this system works better with a die value that divides cleenly into 100 better (D10 and D20).

This reduces the dice to just 1 die, but does add some calculation into it.

A simple solution would be to set a hard limit as to how many dice may be rolled during a single attack (say, 8 dice). This would encourages players to spread out their forces, rather than concentrate them.

Perhaps, when a player's attack strength is better than 8, he is allowed to reroll that many dice. So, if a player's attack strength is 14, he rolls 8 dice, and then is allowed to reroll up to 6 dice of his choice.

Maybe you could tie this reroll mechanism to one of your other mechanisms. For example, a player may only use the reroll option if he has acquired a certain technology level, or when the attack is in the vicinity of the player's home planet, etc.

I guess you never played Stack?

Back on topic. Risk was mentioned as a way to limit dice, however, one annoyance with that is protracted battle sequences. Since your game is fun and quick, perhaps you can enhance the presentation of the dice as part of the game play (think pop-o-matic).

When we play with lots of dice, the clatter and scatter is annoying. To fix this, we bought a sheet of felt from Wal-mart, placed it in a good-sized plastic container and throw the dice into that.
You could even mark up the felt with a boundary, and dice that fell outside of that boundary would be considered a) long-range attackers b) incoming re-inforcements or c) non-participants.

Mitch

Multiplying the dice by two to cut the number of dice in half does change the probabilities, but is a viable option in some cases as long as you realize what it's doing to the odds. For example, it's like a game where you roll for damage and really big creatures multiply by two rather than roll twice as many dice. The probabilities aren't the same, but it's a reasonable effect.

But I really like the idea of rolling into an area, and based on where the dice end up, e.g. in/out of a circle, they have different effects. I'll have to mull that over.

Of course the probabilities are not exactly the same, but it is some how equivalent.

This is why it is called the law of average. Normally you should make 1 success with 3 dices at 5-6. Sure you can get nothing or you can get 3 success. But if you want to play a more defensive, less risky strategy, you could say: "i'll take the average" instead of rolling dices.

But I really like the idea of rolling into an area, and based on where the dice end up, e.g. in/out of a circle, they have different effects. I'll have to mull that over.

Well, here is something my oldest son and I worked out this morning.
DiceWar on a posterboard

Each player gets eight dice (red for one, blue for the other). Stand so that your SAFE zone is across the table and nearer to your opponent. You can make up any rules you want, but briefly:
Last person with a ship is the winner. When two ships are near each other, you can battle just by pointing to the enemy ship and making a zapping sound. A zap does one pip damage. Roll Ships onto the board, trying to land within the orange circles. This will give the first ship that enters it a blast bonus whenever enemy ships enter the same zone. The bonus is equal to the number of dots in the zone. (So if a level 6 ship is the second to enter a corner zone, the first ship may blast it for 4 damage, then zap it for 1 more!) If a ship =1 and gets another zap, it is removed from the board. Ships that are rolled or knocked off the board are also out of play. Ships that land in your safe zone can not be zapped. Ships that land in the black hole get auto-zapped each round until dead.
When all ships have been rolled, the round is over. For every zone that you control, build one ship (from your out-of-play stock).
If you have no ships available for the next round, you lose.

Sounds dumb, but it's fun! Add your own rules. Have fun!

Mitch