There is a dice game called Button Men. In this game, there are two players, each with a different selection of dice (the number of dice as well as the number of sides on each die varies). For instance, one player may receive four 20-sided dice and his opponent may receive six 6-sided dice.
An oversimplification of the rules: At the beginning of the game, each player rolls all his dice. One player takes his turn by EITHER:[ul][li]Capturing ONE of his opponent’s dice with ONE of his, as long as his die shows a HIGHER number than his opponent’s die.[/li][li]Capturing ONE of his opponent’s dice with ONE OR MORE of his, as long as the sum of his dice (or the number on the single one) EQUAL his opponent’s die.[/ul][/li]
If he can do neither of these, he passes. He MUST do one of these if he can. After the attack is made, the opponent’s die is removed from the game and the attacking player’s die or dice are rerolled.
As I said, this is an oversimplification of the rules…there are special abilities and such which allow for other attacks and things. But on to the question:
Is a small number of high-sided dice better than a large number of low-sided dice? Where is the break-even point?
What is the conversion scale? Do you get dice based on the average dots rolled?
If so, then you could choose between, say, two 20-sided dice, and six 6-sided dice. (The average roll is in both cases 21.) Here I would choose the six 6-sided dice. There will be less waste in taking out his dice. For instance, if you roll a 20 with a 20-sided, but his highest roll is 8, you waste a lot.
I don’t understand your question. If you’re using what’s termed a “power attack,” then your die must be higher than the opponent’s (the first rule I gave). Doesn’t matter if it’s 6>5 or 20>1, their die is taken out of play and yours is rerolled. For the “skill attack” (the second rule), it doesn’t matter if you have 1+1+1+1+1+1=6 or 4+2=6 or 6=6, the opponent’s die is taken out of play and yours is/are rerolled.
I forgot to mention the scoring system, which may have been what you’re asking: You score the total number of SIDES of the opponent’s dice you capture plus HALF of the total number of sides of your own dice that you have left (if any).
For example, if you have four 20-sided dice and your opponent has six 6-sided dice, and he captures three of yours before you eventually capture all of his, you have 66 (the total number of sides of the dice you captured) plus 20/2 (half of the total number of sides of your dice you kept), or 46. He captured three of yours, so he has 203, or 60. He wins, even though you captured all of his dice and had one of your own left.
Basically, I’m trying to determine if it’s generally better to have a larger number of smaller-sized dice or a smaller number of larger-sized dice.
The difficulty here is that there’s strategy involved in the game: In general, a player will have to make choices on his turn, and the outcome will depend on the choices he makes. This means that, in order to determine any probabilities, we’d need to know what strategies each player is using, and to determine the optimal probabilities, we’d need to determine the optimal strategy. This is, in principle, possible, but there’s no law that says it’s going to be easy.
In practical terms, the best way to find out would be to hold a tournament to identify the best players, and track the results of games with varying amounts and types of dice to see which fares better.
Am I correct in understanding that a maximum of one capture can be made per turn? If that’s the case, then my intuitive guess would be that the advantage lies in having more dice than your opponent, since it seems likely to me that you’ll be able to make a capture most turns. But this is just a guess, without any actual experience at playing the game, and probably the standard dice sets already take this into account and are reasonably balanced.
In the actual game, there are semi-rare special abilities out the wazoo, at least one of which allows for multiple captures. However, for the purposes of this post, assume only one capture per turn.
The multiple-dice theory makes sense, but there’s got to be a point at which the higher-valued but smaller pool of dice balances with the smaller-valued but larger pool of dice.