# The Math of Valiant Quest

I just wanted to make a quick post about some of the nuances of the way dice rolls work in Valiant Quest. As a quick recap on how dice work in Valiant Quest you roll a die, usually a d20 (most rolls) or a d10 (throwing and saves) and add or subtract a die based on how many boons or maluses are effecting the roll. 1 boon adds a +d4 and every boon beyond 1 upgrades that die one step (d4 -> d6 -> d8 -> d10 -> d12). Maluses counteract boons and if the roll has net more maluses than boons the additional die will be subtracted from the total. Malus dice upgrade the same way boons dice do. If a roll has neither boons nor maluses (or the same number of boons as maluses) no additional dice are rolled.

Boons and Maluses

So you are going to attack an enemy with a medium shield. Your axe can do damage through a shield but you would obviously prefer to roll two dice instead of one. Attempting to slip past a medium shield gives you two maluses (shield 2) which prompts the question:

Just how bad are 2 maluses?

Well it depends.

Situation 1: You are a fighter (1 boon). No other boons or maluses are being applied.

In this situation 2 maluses will swap your from rolling with 1 boon to rolling with 1 malus: d20+agility+d4 to d20+agility-d4. That’s a difference of 2d4, around 5 on average. That is a pretty substantial penalty!

Situation 2: You are a fighter (1 boon) with a polearm. You attack a foe while unthreatened yourself (+1 boon) No other boons or maluses are being applied.

In this situation 2 maluses cancel out your boons. You go from d20+agility+d6 to d20+agility. Losing a d6 is a penalty of 3.5 on average, still substantial but much smaller than the previous situation.

Situation 2b: You are a thief (no boons). No other boons or maluses are being applied.

This is the reverse of the previous situation, instead of losing your d6 bonus from 2 boons you must subtract a d6 from going from neutral to 2 maluses. Another 3.5 penalty.

Situation 3: You are a fighter (1 boon), two of your allies threaten your target (+2 boons), no other boons or maluses are being applied.

In this situation 3 boons are downgraded to 1 boon. A d8 becomes a d4. d4’s average 2.5 and d8’s average 4.5 for a difference of 2 on average. A -2 penalty is not great but it is under half as penalizing as a -5 penalty.

Situation 3b: You are a thief (no boons), threatened by a foe who is not your target (+1 malus). No other boons or maluses are being applied.

Instead of downgrading a boon die from d8 to d4 this situation upgrades a malus die from d4 to d8. The result is a similar -2 penalty on average.

Takeaway

When evaluating a plan of action, whether a roll has net boons, net maluses or is net neutral is more impactful than precisely how many net boons someone has.

In a situation where a priest could bless one of two people, one being a fighter (1 boon) fighting a single opponent and the other being a thief (no boons) fighting a single opponent; the thief will get more (mathematically) out of a single boon as it swaps them from neutral to net boons.

Critical Successes and Failures

In Valiant Quest, you critically succeed a roll if your roll is double or greater the difficulty and you critically fail your roll if your roll is half or less the difficulty. This has some interesting side effects.

Each point of difficulty increases the amount you need to succeed a roll by one, obviously. But it also increases the amount you need to crit by two and every two difficulty increases the likelihood of a critical failure by one. This has a lot of consequences worth considering.

Flat bonuses to a roll substantially lower the likelihood of a critical fail.

The range to critically fail rolls against a flat difficulty of 10 is always 5 or less, this is small enough that any flat bonus will substantially reduce the risk of a critical failure. Lets compare an elf to a dwarf trying to move through difficult terrain. The dwarf rolls d20+3 and the elf rolls d20+5, both roll versus a flat 10 difficulty. The dwarf has a 2-in-20 (1 or 2) chance to critically fail and fall prone. The elf literally cannot critically fail and fall prone unless maluses are applied to the roll.

Boons also go a long way to making rolls much more or much less likely to critically fail, especially on saves. Let’s take the example of a wizard forcing two fighters to make an agility save vs 12 with Acid Blast. Critically failing a save versus acid blast causes sunder 3, which is something no fighter wants to happen. One of the two fighters has evasion (+2 boons on agility saves) and the other does not. They both have 4 agility.

The fighter without evasion has a 20% chance to critically fail, a 50% chance to non-critically fail and a 30% chance to succeed. Not great odds.

The fighter with evasion has a 1.67% chance to critically fail, a 33.33% chance to non-critically fail and a 65% chance to succeed. Substantially better odds. Notably the failure chance is 1/3 lower but the critical chance is less than 1/10th as likely.

Flat bonuses to difficulty substantially decrease the likelihood of a critical success.

An unstaggered wraith is extremely hard to land a critical hit on. This is because the defence roll of a wraith is at bare minimum 9 (7 from agility, 1 from the d20, 1 from the boon on defence rolls). This means that even with the worst possible defence roll the attacker still needs a pretty high roll of 18 to critically hit. The average wraith defence roll (20) is practically uncritable under any ordinary game circumstance.

On the flip side a staggered (no agility), shaken (+1 malus to all rolls) orc can be practically effortless to critically hit. With an average roll of only 8 needing a 16 to critically hit and every point rolled shy of 8 reducing that threshold by 2. Heck, the shaken staggered orc could theoretically roll a 0 or even a negative number to defence at which point you get to score a critical hit for free (provided your own roll isn’t negative).

Hopefully these let you make informed decisions faster at the table. Math plays a big role in most ttrpgs but the math in VQ can be a little obfuscated at times so I wanted to help clear some stuff up.

Any other math quirks I haven’t noted here? Lemme know in the comments!