I have often heard "dice" used as a singular, and while many sources reject it, the 1998 New Oxford Dictionary of English apparently accepted it. Wiktionary has details.
I wouldn't be thrown off too badly by this sentence, but I also see how it may be confusing to read "dice" but roll only one die. If the goal is to be as clear and correct as possible, you have at least two very good options.
"A team’s **** **** dictates which of the dice will be used when performing a **** ****. The higher a team’s **** **** the greater chance of rolling a successful ****.
"A team’s **** **** dictates which die or dice will be used when performing a **** ****. The higher a team’s **** **** the greater chance of rolling a successful ****. "
In #1, "the dice" refers to all the types of dice in the game (d6, d8, d10, and d12) and avoids the singular/plural problem entirely. In #2, you cover all bases, explicitly acknowledging the possibility that only one die may be rolled. I personally prefer #2.
We seldom hear the word, because there is a prohibitory proverb– Jim Mack Aug 15 '15 at 15:25