How could I lower the rate of critical successes?

Question

I'm trying to create my own RPG, to play with friends. To be honest, I never played published RPGs before, only home-brewed ones, but I don't feel like spending money on a thing that I may never use, and designing is fun!

I'm basing off my dice system out of Vampire: The Masquerade (5th edition). Each premade character has 7 stats between 1 and 5, averaging at 3. When you roll to accomplish a task, you take two of those stats, add them up, and then throw as many d10. Each die with 6+ is a success, and if you have more successes than the difficulty of that task, it's a success.

If you get two 10, you get 2 extra successes, for a total of 4 on these dice. If your roll is a success, and you got two 10, it's a critical success!

After putting it into code to do some stats, I realized that you have around 10% critical success rate with 6 dice. With 10 dice (the maximum you can have without any bonuses), it goes up to a 25% critical success.

I'm worried such high numbers will undermine the pleasure of getting a critical success out of nowhere.

I tried several systems, but they aren't good enough in my opinion :

• Putting in every roll a colored dice, which would need to be a 10 for the roll to be able to be a critical success. This is unrewarding (having more dice doesn't help you get critical successes), and still too high (10% is too much).
• Using only one die, like a d20, or a d100. This goes too far away from the original system, which I like a lot.

How could I lower the rate of critical successes while not undermining the rolls with very few dice?

Answer 1

After seeing a comment asking for an example, I realized I was asking too much of critical successes, because I wanted every one of them to be a permanent change in the character's personality or skills.

Even if it was rarer, making every critical success game-changing seems impossible.

Instead of lowering the rate of critical successes, I'm choosing to lower their respective effects, and leave those game-changing criticals to already game-changing rolls.

Answer 2

Number of 10s rolled, truncated:

This is what you are experiencing, as you are calculating the odds. While there's a decent spread at 2, the values are higher than you are comfortable with.

Suggestion 1

Rather than 2 10s being a critical success, have it be 3 10s. That way, someone with the worst possible combination of stats, rolling 2 dice, can never roll a critical success, and the odds for everyone else are significantly lower (0.1% for someone with 3 dice, 7% for someone with 10).

If you want everyone to have a chance, then let someone with 2 dice who rolled 2 10s reroll - 2 10s again? Critical success.

Suggestion 2

Make critical successes something the players can aim for, rather than a natural occurrence. Give them some tokens at the start of each session, then they can "invest" that limited resource on rolls where they want their character to give it their all. With that investment, they get an extra die to roll, and with 2 (or 3, see above) 10s rolled, the roll is a critical success.

This has the added bonus of players not feeling they have "wasted" critical successes on rolls where a simple success would do, and raises the odds of critical successes on "invested" rolls slightly, thanks to the extra die.

Suggestion 3

Peter Cordes mentioned in a comment on another answer that you might want everyone to have closer odds of rolling a critical, regardless of number of dice. That made me remember a mechanic, possibly from an older version of the Storyteller system, where each 1 "nullified" a 10 (or success, my memory fails me) rolled, and any remaining 1s at the end of counting would indicate a critical failure.

If you instead in your system have each 1 rolled turn a 10 into a 9, and disregard excess 1s, you will functionally have a system where the average amount of 10s is 0, regardless of number of dice, and getting even a single 10 means beating the odds.

To illustrate:

10d: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10; the 10 -> 9, thanks to the 1 rolled, leaving you with 5 successes, no critical (6, 7, 8, 9 and 9).

3d: 2, 10, 10; 4 successes, critical if successful (10 and 10, both counting twice).

5d: 1, 6, 7, 10, 10; one 10 -> 9, 5 successes, no critical (6, 7, 9, 10, the single remaining 10 counting twice)

The odds of critical success is the same as in your base system at 2d, 1%. At 10d, however, it is 13.5% rather than over 25%. Not enough? Have both 1s and 2s "defeat" 10s, and the curve goes from 1% at 2d to 6.7% at 10d.

Having more than 1s and 2s nullify 10s, though, creates a bit of a curve - the odds rises a bit after 2d, but lowers again when approaching 10d.

At the extreme, when making each non-success (1, 2, 3, 4 and 5) discount a 10, the odds of a critical success peaks at 4d with 1.33%, and then lowers, falling below the 1% of 2d at 7d, and at 10d being a mere 0.69%. A rather flat curve, actually.

I could see that being a bit flavorful - you need some skill to get a critical success, but the more you have mastered what you are doing, the less chance you have of "breaking out of the mold". However, achieving a success (albeit not a critical one) will always be helped by more dice.

Answer 3

Three or more 10s

Instead of a critical being a pair of 10s, make it three 10s. This lowers the chance to about 7% for 10 dice. This is a bit over the 5% crit chance for rolling a natural 20 on a d20. But I expect rolling 10 dice is rare.

You can check other possibilities with an online Binomial calculator:

Once you go down to 9 dice the chance drops to about 5%. For 6 dice the chance is only 1.5%.

For an even more extreme type of critical success perhaps you need 5 or more dice with the same result. So five 10s is a crit. But so is five 2s or five 10s and so forth. This gives about 1.5% crit chance even for 10 dice.

Answer 4

I'm worried such high numbers will undermine the pleasure of getting a critical success out of nowhere.

This fails to take into account a very crucial mechanic which is Hunger.

In Vampire the Masquerade 5th edition, player characters will have a number of Hunger dice in their pool according to how well they have fed. The more hungry they are, the more dice that adds. And in general, for the most of the game vampire characters will have at least 1 Hunger dice¹.

When a vampire scores a critical hit and at least one of the 10s showing is on a Hunger die (regardless of which and how many of the other dice show 10s) this becomes a messy critical. The Beast flares up and lends its "help" to the vampire. The task would be done but maybe not as expected or wanted.

Alicia tries to help her friend who is trapped under a car wreck. Alicia scores a messy critical and instead of merely lifting the scrap with at least some difficulty, she flings it away as if cardboard. The onlookers are sure to notice - now there is a potential Masquerade breach to cover up. Even hysterical strength has its limits as an explanation.

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Robert is trying to get information from a store clerk. The result from the roll is a messy critical. Instead of merely asking in a convincing matter, the Beast takes over, slams the clerk on the counter and, through Robert's mouth, shouts "WHERE IS HE! TELL ME OR I END YOUR MISERABLE LIFE RIGHT NOW!" Robert does get the information wanted. However, other people in the shop are already making calls to the police about the maniac attacking people.

This is what messy criticals can look like².

The larger the dice pool, the higher the chance of scoring a critical as well as the higher the chance of scoring a messy critical. The analysis here is for a single Hunger die, however, it also holds up the more hunger dice there are. In fact for n hunger dice, and dice pool of n+1 every critical is messy. For example, 2 hunger dice and a dice pool of 3.

This means that criticals have a relatively good chance of injecting more complications for characters. It is not just being awesome all the time.

With all that said, even regular criticals are not a bad thing. They fit the narrative framework of the game. The interplay between regular and messy criticals is a good way to portray immortal characters who are better than regular mortals but also the ongoing internal struggle with their inhuman nature.

Even the core rulebook acknowledges the high rate of criticals and also encourages it. From page 122:

CRITICALS IN PLAY

The Storyteller should get used to critical successes showing up in play. With larger dice pools, they become more and more common: a ten-dice pool has a slightly higher than 25% chance of rolling a critical success. Of course, a ten-dice pool represents someone at the absolute pitch of human perfection – or someone who has worked the odds carefully enough, or drawn on enough dark power, to resemble perfection.

Be aware of this when adding extra dice to players’ pools – if a critical seems like it might break suspense or harm the narrative, just lower the Difficulty instead. Mathematically, lowering the Dif- ficulty by 1 equals adding two dice to a character’s pool.

But that said, our advice is to embrace criticals. They allow players to show off their characters, and even when the opposition gets them, they produce rapid, dramatic effects – kind of ideal, we think, for stories of tempestuous predators in conflict.

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¹ _{Sating hunger completely is rare and temporary, as for most player characters it takes killing a human, which is a drastic measure for most vampires.}

2 _{Also worth noting that not all of them need be "loud" but they will cause complications in some form or another.}