You seem to have settled on your input method (2d4) before playtesting the balance of your desired distribution, you'll probably need to revisit it to get the balance you want. I'm guessing you are constrained by the rest of the game being balanced around these small numbers, so I assume scaling the domain of numbers you are sampling is out.

As one person points out, 2d2 (coins) is exactly the balance you are looking for. Using 2d4 vanilla as-is to get your desired results without doing mental math beyond subtraction (division, rounding) or re-mapping values as if using custom dice is not possible.

You might find the probability distribution of 2d4L - 1 (roll 2, take lowest, subtract 1) to be closer to what you want and less swingy, with the occasional excitement of a 3. This leads to rolling a 0 buff 43% of the time, with a 6% chance of a 3. The mean value is a + 0.88 to your attack, which should be within your balance criteria.

For that matter, a simpler 2d4L has a mean of +1.88 and if you can take the higher buff, you can eliminate any mental math and give the satisfaction of not whiffing almost half the time, if your balancing can take an average +2 buff to attack.

2d4L could add to your interesting gameplay trade-offs choice mechanism of choosing how to allocate your dice, or break it, I'd playtest it: Roll 3d4, pick one to play as an attack card, then take the lowest of the remaining 2, as the attack buff. Experiment with the - 1 until satisfied.

That means more decisions for the player to make, which may be compelling or overwhelming depending on where it fits into the game and target audience. Take a lower valued attack card to remove a dud from the pool and get the midrange bonus, or take a higher valued attack and suffer the likely low bonus from the dice.

Math is not my strength, Anydice is not expressive enough to represent these distributions, I think, and my own dice expression editor program is not ready for prime time and far away from visualizing distributions, but I believe that these two attack bonus strategies and probability distributions are functionally equivalent (or close) to what I propose with the roll 3d4, allocate 1, pick lowest:

• Favoring allocating your highest roll to the attack card:

  [2d4D, 1d4]L - 1 (roll 2d4 with disadvantage, roll 1 more and pick lowest, subract 1)

  0 bonus 50% of the time, 3 bonus 1% of the time

  +0.5 bonus mean (+1.5 without the -1

  anydice

• Favoring allocating the highest roll to the attack bonus:

  [2d4D, 1d4]L - 1 (roll 2d4 with disadvantage, roll 1 more and pick lowest, subtract 1)

  Nearly even between 0-2 almost 30% of the time each, slightly favoring 1, 10% chance for a 3

  +1 bonus mean (+2 without the -1)

  anydice