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Is there a method that gets beneficial diminishing returns when adding more dice, yet stays random?

Short Story: I want to find a dice system where multiple dice are rolled and compared at once, but rolling more dice is only slightly more effective than rolling fewer dice, while still being fairly chaotic no matter how many dice are rolled.

Long Story:

I’m designing a game that involves assigning dice to various cards for bonus stats to those cards. Cards fight, victor wins, etc.

The formula right now involves starting at 5d6, getting a die each time you are hit, up to 10d6.

Problem is, it’s hard to balance a card around an expectation of having both one die (a 3.5 average) and 10 dice (35 average). Set an average expectation of "10 points", and now the person with 5 dice is only effective with 1 card, while the person with 10 dice is effective with 3.

We ended up with an issue where it mostly became about dice-trading, where the victor was almost always the one with more dice, as well as the dice mattering more than the card itself. The cards ended up feeling like "placeholders" for stacking dice on rather than strategic choices to invest in.

What we really want is to have the system reward assigning dice to multiple things on the board, so that the game becomes more chaotic and stressful the later into the game it gets, not more predictable or even necessarily much easier for the player with more dice.

We’ve looked at rolling all the dice you would for a card, keeping your highest roll. The good thing about it was that it was relatively balanced, but it was far too predictable.

We’ve looked at exploding dice + keeping high, where you keep the highest value + any dice that match it. It was chaotic, but it basically ended up being an excessive "crit" system that we didn’t like and wasn’t easy to balance.

In case it helps, dice are colored differently for each player.

Does anyone know of a dice resolution system that can do this?

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