Chance - this spell does not require any spoken, somatic, or material components. once set running, a purely mental act, the spell is largely self-maintaining. in terms of function, the spell alters the variation of acts in its vicinity, seemingly bending probability itself. This is largely an illusion, of course; rather then bending probability, it would be more accurate to say that it adds an additional positive influence to any act with possibility of both success and failure. represented on a game system, it would be more accurate to consider this a bonus to skill checks then a source of rerolls. Some kinds of probability are beyond the spells capabilities to affect; powerful creatures will generally be resistant or immune, even if they enter its fairly-limited base range. Lastly, without Clarity cardinal or a divinatory effect, the spell will be unable to divine the most favourable outcome if it is non-obvious, preventing trivial divination of arbitrary information via repeated coin-tossing.
More skilled use of this Cardinal improves the magnitude of the effect, the range of outcomes it can influence, and the accuracy of its determinations of benefit, but it will almost never reach visible reality-warping unless one has taken hundreds of other Cardinals whos benefits amplify it.
Choosing this Cardinal improves the Limits of the users other Cardinals, altering the upper bound on their power, efficiency, and other qualities. It does not significantly improve the baseline probability of the best effects, but the direct operation of the spell handles that.
Charge - this spell is closer in practice to a metamagic effect. In its base state, it can be used to store up physical energy for a motion while not preforming that particular motion, and then preform that motion with power equal to the users ordinary strength, times the amount of time spent charging. This would generally be an underwhelming effect, hardly worthy of the Cardinal Geometer at all, if it was not also possible to apply to other spells. By multiplying the casting time or energy consumption of a spell, depending on which is the most salient part of the spells cost, the spells overall effectiveness is increased accordingly. There is a certain extent of diminishing returns when multiplying energy consumption past the original size of the users energy pool, as storing energy further is lossy, but this does not apply to casting time multipliers.
sufficiently skilled use of this cardinal allows for control over which costs are multiplied in cases of ambiguity, and reduces the energy loss when casting a spell greater then ones reserves. As well, a skilled user can keep a Charged action indefinitely even while preforming the same action in a non-charged manner, granting significantly improved capabilities even without warning.
Choosing this Cardinal, in addition to its above effects, passively improves the Capacity of other Cardinals and mana-style resources, allowing for greater use in succession or for more mana to be poured into a spell even without activating the Cardinal.
Chi - Ah, the path to shameful muscle wizardry. Inefficient, sweaty, biological, and unpleasant to train, muscle wizards use their bodies and their spells, which means less time on spells overall. Chi grants various abilities, such as energy blasts, flight, and wasteful, brute, physical force, but their utility is far outweighed, not just by the utility of any of the other four Cardinals in this set, but by the sheer virtue of not being a muscle wizard! truly, anyone who takes this Cardinal must have taken leave of their senses.
...perhaps I allowed my prejudice to get a bit ahead of me there. This is supposed to be an impartial account, after all. While I can't personally see the appeal of Chi over the power of Charge, the utility of Chant, or the convenient benefits of Chance, I do have an understanding of their proponents counterarguments. the Chi Cardinal doesn't simply grant access to a separate and inferior pseudo-magic system of Chi, but a sort of mastery. While of course time is still necessary to master the Chi Cardinal itself, users of the Chi Cardinal essentially have supernatural talent in the Chi system, as the Cardinal allows them almost-complete control over their Chi at all times, as well as improving their quantity and quality of Chi, and any other benefits other Cardinals have granted the user. It's also a comparatively simple road to various dedicated utilities, such has superhuman vitality, resilience, rejuvenation of oneself and others, immortality- against age, but not harm, a projectile attack... but it shamefully provides Muscles as well, which is something many people cannot abide. Sufficiently skilled users of the Chi Cardinal can even awaken the system in others, which- if one can stomach the Muscles that will come with it- is yet another reason not to take the Cardinal yourself, as many of its benefits can be passed on.
Choosing this Cardinal improves the Vibrancy of the users other Cardinals, granting all spells an inherent resistance to disruption, dispellation, and deterioration, as well as a small mind maintaining or improving the effects. At sufficiently high levels, this can grant genuine life to some types of spells.
Chant - Perhaps the most versatile of the Cardinals in this set, the Chant cardinal is very simple to activate: you need only chant something, a word, phrase, or sound, to activate it. Its power is fairly lacklustre when you do so, however, no greater then the benefits of the Chance cardinal, and benefiting only towards the accomplishment of things related to the word or phrase, or the symbolism of the sound. Besides which, they require the user to continually Chant, which is not only embarrassing and unsubtle, but difficult to maintain in active combat or during exertion, or during many other spells. The true use of this Cardinal, then, is in groups: The Chants power scales to the number of Chantees, with mundane helpers roughly half as efficient as a first-level Cardinalist. this captures mostly the waste or excess magical energy emanating from the Chanters, so the very greatest Cardinalists, Archmages, etcetra will counter-intuitively provide minimal benefit, and it will not drain the power of the other chanters. It's very difficult to turn this against the members of the Chant, since the goal of the chant will be clear when using words, and it would require more convincing to get people to chant a meaningless sound. When used in groups, Range, magnitude, blatancy, and variety of effect all increase, such that a moderate group chanting "Earth Spike" will be able to conjure a spike roughly the size of a human and launch it, while a single user will only be able to manifest one perhaps the size of their finger, or more likely, slightly increase the likelihood of a nearby stalactite falling.
Choosing this Cardinal improves the Collaboration of the users other Cardinals, making them more powerful or effective when used in combination with another Cardinalist, either as multiple people applying the same effect, or separate effects applied for a single goal, as well as slightly increasing the ease of using multiple Cardinals at once.