I went down the wrong path and was to put the shapes into conway's game of life to see if they converged on something or turned into each other.

I actually have a BA in theatre but game design is a interest of mine and i use data collection and collation in my day job pretty regularly. It does make sense move this to resources if you would like.

There are are 3 Keys that match the 3 Harmonies. However, unlike the 3 Harmonies there are cards with no Keys (the Quantums). There are 12 Phase cards in each Key and 7 cards Transition cards for each Key. You could also count the Half-Circle Transition cards as having a Keyless. Here are the numbers: Phase card in a Keys: 22.2% Any card in a Phase: 35.2% Any true Phaseless: 11.1% Any Phaseless (counting Half-Circle):16.7% The Keys are very similar to the Notes. I think the combination of Keys and Notes is where things get weird I am working on a chart now to get probability for these figured out.

There are 4 true phases. Again similar to Notes we can also consider cards without Notes as 'Phaseless'. This set has quite a lot of variance from phase to phase. There are 12 of each complete Phase cards in New, Partial, and Full Phases. There are 12 Transition cards that include the New Phase, no Transition cards with the Partial Phase, and 9 Transition cards in Full Phase. There are 6 'Phaseless' Quantum cards. You could also count the unmarked half of the 3 Half-Circle Transition as Phaseless. Here are the numbers for each Phase: Non-Transition of a Phase: 22.2% Any Full: 38.9% Any Partial: 22.2% Any New: 44.4% Phaseless (Quantum): 11.1% Any Phaseless (counting Half-Circle): 16.7%

There are 3 different Harmonies. Each Harmony has 16 Non-Quantum cards, 2 Split cards and 1 Blank card. You could look at these as 16 Non-Quantum Harmony cards and 3 Quantum Harmony cards or 17 Full Harmonies and 2 Split Harmonies per Harmony. The 3 Harmonies are High, Mid, Low and have even probabilities (no one Harmony has better chance of being drawn). Here are the numbers for a card from a specific Harmony: Non-Quantum from a Harmony: 29.6% Non-Split from a Harmony: 31.5% Any Card from a Harmony: 35.2% Split cards from a Harmony: 3.7% Of interest here, there is no way to make and exactly 1 in 3 chance of pulling a specific Harmony, it is either slightly above ( If you count splits) or slightly below (if you don't count splits).

There are 4 different true Notes: for the first set these are Circle, Square, Hexagon,and Cross. However, for probability reasons we will also treat Noteless cards as a secret 5th Note. Each true Note exists on 9 different Phase cards and 6 additional Transition cards, except Cross which has 9 phase cards but only 3 Transition cards. There are also 6 Noteless card (the Quantums) and 3 Transition cards that could be considered "Noteless" (the three Transition cards with only half a Circle) Here are the chances of pulling certain Notes (rounded to nearest 10th) Circle Phase:16.7% Circle Transition:11.1% Any Circle:27.8% Square Phase:16.7% Square Transition:11.1% Any Square:27.8% Hexagon Phase:16.7% Hexagon Transition:11.1% Any Hexagon:27.8% Cross Phase:16.7% Cross Transition:5.6% Any Cross:22.2% Noteless (Quantums):11.1% Noteless Transition: 5.6% Any 'Noteless': 16.7% Any Phase card: 66.7% Any card with a Note:88.9% This interesting thing from a game design perspective is that Crosses are effectively handicap, having a 5.5% lower chance of getting drawn than any other note (except Noteless). Also counting or not counting the half-noteless transition cards as "'Noteless' give you and additional way of twerking probability.

There are 54 total cards (not counting the double back card) out of those 6 are Quantum cards and 12 are Transition cards. Drawing a single card from a well shuffled deck ("drawing a card") you would have an ~11% chance of drawing a Quantum card, and an ~22% chance of drawing a Transition card. If you wanted to draw a card that was either Quantum or Transition(a Non-Phase or Non-Standard card) your have an ~33% chance of drawing a that card. 1 in 3 time you draw a card it will be a Non-Phase card. Just the numbers (rounded near tenth): Chance of Quantum: 11.1% Chance of Transition: 22.2% Chance of Non-Phase: 33.3% Chance of Blank: 5.6% Chance of Split: 5.6%