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Glowing Saber

Game Math

Miscellaneous thoughts and tables having to do with the probability of various game mechanics.

Card draw mechanics are calculated using a 54-card "Malifaux" deck. That is a deck with cards valued from 1 to 13 for each of four suits, 1 black joker (value of 0 with no suit) and one red joker (value of 14 with a wild suit).

I have bolded a couple of values in each row and column.

First the lowest value that is 50% or higher. I consider this your average flip. For example when flipping 3 cards your average flip (at least 50% of the time) is an 11. Or if you want to summon a Jorogumo each round, you need to draw a 13+ each round. Looking at the chart you will need to draw 7 cards each round to have an average chance (50.5% in this case) of drawing the 13+ you need.

Second I bolded the lowest value that is 90% or better. I consider this a reliable chance to draw a card. It is also far enough away from 50% to keep the trends separate.

Drawing a Suited Card

This table shows the percentage chance of drawing a suited card or better (vertical axis) when you draw x number of cards (horizontal axis). For example, if you draw six cards you have a 57.8% chance of having an 8 or higher of any given suit.

Drawing an Unsuited Card

This table shows the percentage chance of drawing an unsuited card or better (vertical axis) when you draw x number of cards (horizontal axis). For example, if you draw six cards you have a 98.0% chance of having at least one 8 or higher, of any suit.

How much is a + worth?

On average a single card flip will yield a 7, a + flip will yield a 10, and a + + an 11. Does that mean Ml 5 with + and Df 8 are equivalent?

No. If each player has an unfiltered hand (no holdovers from last round, no Rush of Magic, etc.) of six cards then an attacker with + has 8 cards to choose from and the defender has 7 to choose from. If you look at any given result (e.g. having a 6 +) the attacker has at most a 4.8% advantage and the advantage is less than a 1% for a little over half the results. On average early in the turn the attacker will need to cheat in a card 3 at least higher than the defenders to with the duel.

No assume both players have exhausted their hands are relying on just top decking what they need. The attacker now has a significant advantage. They have a better percentage chance of getting any given result or better, peaking at a 25.3% advantage for a 7+ or 8+. A 13+ only has a 8.5% advantage, but that is nearly double the chances of the defender flipping a 13+. Then again if the defender flips a 10 they need a 13+ just to tie.

I though once I generated these probability tables it would be easy to answer this question, but it definitely is not simple. IMHO, a + is definitely not as good as +3, is probably not as good as +2, and is probably better than +1. I would say a + is roughly equal to +1.5.