Clicker Heroes Ruby chance?

Adding to @GiantTree's otherwise great answer:

The expected ruby count, E(R) from a single clickable is:

E(R) = 1 * P(1) + 2 * P(2), (1)

where P(x) is the probability of getting x rubies.

Using @GiantTree's information as source, we see that double ruby is rolled for after the first one, meaning:

P(1) = 0.44 - P(2),

which means the (1) can be expressed as:

E(R) = 0.44 - P(2) + 2 * P(2) = 0.44 + P(2). (2)

Now, P(2) can be calculated by:

P(2) = 0.44 * (0.04 + DRC),

where DRC is your double ruby chance, expressed as a fraction (so 15% means DRC = 0.15).

Finally, we insert this expression into (2):

E(R) = 0.44 + 0.44(0.04 + DRC) = 0.44 * (1.04 + DRC) = 0.4576 + 0.44 * DRC.

Or for short:

E(R) = 0.4576 + 0.44 * DRC.

This means the base expected value is 0.4576 rubies per clickable.

Since the highest value of the DRC-boosting ancient is 15%, we get a maximum value (excluding relics) of:

Emax(R) = 0.4576 + 0.44 * 0.15 = 0.5236,

meaning the maximum expected ruby yield (again, excluding relics) is 0.5236.