Magical Math

Magic is random. So, here is some math on the percentages of each magic roll to play Magical Gambits.

Math:

Chance to cast a spell on 1/2/3/4 magic dice:

  • Single Channel (Channel):
    • Normal: 66% / 88% / 96% / 98%
    • With Innate (Channel): Automatic Success
    • With a change 1 dice to (Channel) : Automatic Success
    • With 1 dice re-roll: 88% / 96% / 98% / 99.5%
  • Single Focus (Focus):
    • Normal: 50% / 75% / 87% / 93%
    • With Innate (Focus): Automatic Success
    • With 1 dice re-roll: 75% / 87% / 93% / 96%
  • Double Channel (ChannelChannel):
    • Normal: 0% / 44% / 74% / 88%
    • With Innate (Channel): 66% / 88% / 96% / 98%
    • With a change 1 dice to (Channel) : 0% / 88% / 96% / 98%
    • With 1 dice re-roll: 0% / 74% / 88% / 95%
    • With Power Surge: 16% / 55% / 79% / 91%
  • Double Focus (FocusFocus):
    • Normal: 0% / 25% / 50% / 68%
    • With Innate (Focus): 50% / 75% / 87% / 93%
    • With 1 dice re-roll: 0% / 50% / 68% / 81%
    • With Power Surge: 16% / 41% / 62% / 77%
  • Single Crit (Critical Hit):
    • Normal: 16% / 30% / 42% / 51%
    • With 1 dice re-roll: 30% / 42% / 51% / 59%

Chance to damage yourself on 1/2/3/4 magic dice:

  • Double Crit (Critical HitCritical Hit):
    • Normal: 0% / 2.7% / 7.4% / 13.1%
    • With a change 1 dice to (Channel) ability : 0% / 0% / 0.46% / 1.62%
    • With 1 dice re-roll: 0% / 0.46%

Thoughts:

As you can see, the more magic dice you can get, the easier a time you have of casting magic. Most Warbands only have 2 magic dice, but Theddra with the Godsworn Hunt can become a level 3 Wizard with the universal upgrade Arcane Savant, and the rest can get to 3 magic dice by using the new Gambit ploy card Spirit Sacrifice on a level 2 Wizard to get to 3 dice (and Thedda can use it to get to 4 magic dice!).

  • Arcane Savant: (Upgrade, Wizards only) +1 Wizard level. Apply this upgrade only to a level 1 wizard.
  • Spirit Sacrifice: (Ploy) Choose a friendly wizard. They suffer 1 damage. The first time that fighter attempts to cast a spell, roll an extra dice in the casting roll. This effect persists until that fighter attempts to cast a spell or is out of action, whichever happens first.

Innate abilities are also great, as they make the spells much easier to cast, and also unlock spells that need two successes for level one wizards. Many Warbands have ploys and Upgrades to gain an Innate Channel (Channel), and the universal upgrade Arcane Focus can be activated to grant an innate Focus (Focus) (the Gitz also have Madcap Mushroom).

  • Arcane Focus: (Upgrade, Wizards only) Action: This fighter’s next casting roll in this phase has Innate (Focus).

The “change one result to (Channel)” abilities like that granted by Tome of Incantations make it much easier to cast channel spells, and greatly reduce the chance of hurting yourself with double crits, making them very useful for level 2 wizards. They are not as useful as innate abilities for level 1 Wizards, though, since they don’t grant them access to the two-success spells, just make them better at casting one-success channel spells.

Re-rolls:

Potion of Clarity is an upgrade that lets you react to a spell after the dice are rolled, allowing you to re-roll one dice and discard the upgrade.

Overall, this re-roll gives you the same chance of succeeding as throwing an additional magic dice, so long as you were originally capable of succeeding with the spell. To put it another way, a re-roll can’t can’t help a level 1 wizard roll 2 successes, but it gives a level 2 wizard with a re-roll the same chance of casting a spell as a level 3 wizard without. This makes Potion of Clarity much better than Spirit Sacrifice, as you can wait until the spell fails to decide to use it once it is equipped (though of course it requires a glory to do so).

Because you would only ever use this card if you had failed a spell and needed a single result to succeed, the chance of the re-roll succeeding depends on what result you are looking for:

  • Single Channel (Channel): 66%
  • Single Crit (Critical Hit): 16%
  • Single Focus (Focus): 50%

Power Surge

Power Surge is a ploy card that allows you to add a crit to your magic roll if you’ve already rolled a crit. This will allow any spell in the game to succeed, but also do 1 damage to the caster.

This is only really useful when attempting to cast double success spells, since single success spells would go off with a single crit.

It also becomes less useful the more dice you are throwing, since the chance of rolling a crit and no successes actually goes down the more dice you throw.

However, because it allows you to add a crit to the casting roll, it also allows level 1 wizards to attempt to cast double success spells with a 16% chance of success.

Edit:

Edit: I made a minor correction to the double Channel percentages thanks to Levty on the WU Reddit discord. Thanks!

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