Ephemeral Starstone 4
Artifact
T: Add 1 to your mana pool. Flip a coin. If you win the flip, untap Ephmeral Starstone.
Supposedly this series converges to 1, but it gives me a headache to figure out the EV.
Erratic Starstone 4
Artifact
T: Roll a six-sided die twice. Add X colorless mana to your mana pool, where X is the higher value rolled or the value rolled if both rolls have the same value. If both rolls have the same value, sacrifice Erratic Starstone. Play this ability only any time you could play an instant.
Should give an EV of 4.472.
(Sum(i=1 to 6) [i*(2i-1)]) / 36)
It has a 1/6 chance to be sacrificed upon use.
Hermetic Starstone 4
Artifact
You may flip a coin rather than pay Hermetic Starstone's mana cost. If you win the flip, Hermetic Starstone comes onto the battlefield tapped. If you don't, put it into its owner's graveyard.
T: Add 2 to your mana pool.
Ephemeral Starstone 4
Artifact
T: Add 1 to your mana pool. Flip a coin. If you win the flip, untap Ephmeral Starstone.
Supposedly this series converges to 1, but it gives me a headache to figure out the EV.
The expected value is 2. It would converge to 1 if you had to flip the coin to get mana out of it the first time. 1 + 1/2 + 1/4 + 1/8 + ... is a geometric series with r=1/2; the convergent sum is 1/(1-r) which in this case evaluates to 2.
Private Mod Note
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A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.
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Artifact
T: Add 1 to your mana pool. Flip a coin. If you win the flip, untap Ephmeral Starstone.
Supposedly this series converges to 1, but it gives me a headache to figure out the EV.
Erratic Starstone 4
Artifact
T: Roll a six-sided die twice. Add X colorless mana to your mana pool, where X is the higher value rolled or the value rolled if both rolls have the same value. If both rolls have the same value, sacrifice Erratic Starstone. Play this ability only any time you could play an instant.
Should give an EV of 4.472.
(Sum(i=1 to 6) [i*(2i-1)]) / 36)
It has a 1/6 chance to be sacrificed upon use.
Hermetic Starstone 4
Artifact
You may flip a coin rather than pay Hermetic Starstone's mana cost. If you win the flip, Hermetic Starstone comes onto the battlefield tapped. If you don't, put it into its owner's graveyard.
T: Add 2 to your mana pool.
Pretty simple.
The expected value is 2. It would converge to 1 if you had to flip the coin to get mana out of it the first time. 1 + 1/2 + 1/4 + 1/8 + ... is a geometric series with r=1/2; the convergent sum is 1/(1-r) which in this case evaluates to 2.
A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.