While watching this overexplained replay, the player commented on how he chose a particular path with the belief that 'spreading out' elite fights in betwixt your normal enemies would increase the chance of finding more rare card(s).
Slay the spire pulls its card picks by first rolling for a type (common, uncommon, or rare) and then by pulling a random card from said type, with each type member having equal probability. The type roll is weighted random, in the following way:
There's a hidden variable
c, the common counter. Probabilities of cards start at
P = [-2%, 37%, 63%] for rare, uncommon, common cards respectively. Whenever a common card is rolled, in pseudocode:
if(P < 43%) P += 1%; if(P > 0% && P < 43%) P -= 1%;
Whenever a rare card is rolled, the probabilities reset to the base values of
P = [-2%, 37%, 63%] again. On elite fights, the rare chance is modified: it is instead
P + 10% while the common chance is
P - 10%. In shops, it is
P + 6% and
P - 6%
The chart below illustrates the mechanic very insightfully:
At the start of each Act, the chance of finding a Rare card is also reset, due to bosses always dropping a choice between 3 rares.
At the start of the act, the player will typically decide which path to take through the act, which to start from. When planning ahead, it may be insightful to know whether or not the specific sequence of enemies will impact the expected number of rare cards received.
We want to maximize the above. Does a sequence like
rrrErrrE "spreading out the elite fights" compare favourably to one such as
rrrEErrr "bunching them up"?