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3-Card Monte Simulation

Key Learning:

  • Using seedler Planter, Sprout, and Fire classes
  • Using flags for buds
  • Monte-Carlo probability simulation
  • Re-simulating seeds

Simulation Baseline

The classic 3-card monte game is where the player is presented with 3 face-down cards - two losing, one winning - and must select on card. The standard odds, without cheating is easy to know since 1/3 of cards are winning, which means the player wins 33.33% of the time. However, we can use seedler to run a monte-carlo simulation of the situation to get a similar answer.

from seedler import Planter, Sprout, Fire

sims = 100

PASS = 0
FAIL = 1

class CardMontePlanter(Planter):
    def plant(self, sprout: Sprout):
        cards = [PASS, FAIL, FAIL]
        card = cards[sprout.growth(0, 2)]
        sprout.add_bud(card)

class PurgeFail(Fire):
    def purge(self, sprout: Sprout):
        return sprout.get_bud_count(FAIL) >= 1

class PurgePass(Fire):
    def purge(self, sprout: Sprout):
        return sprout.get_bud_count(PASS) >= 1

lab = CardMontePlanter()
garden_pass = lab.find_seeds(fire=PurgeFail(), maximum=sims)
garden_fail = lab.find_seeds(fire=PurgePass(), maximum=sims)

passes = len(garden_pass)
fails = len(garden_fail)

print(f"{sims} Sims => {passes + fails} Results | {passes} Pass, {fails} Fail")
print(f"Winning odds: {(odds * 100):.2f}%")

100 Sims => 100 Results | 32 Pass, 68 Fail
Winning odds: 32.00%

In this simple example, we calculate our winning odds at 32%, which for 100 tests is very close to the true answer. The power comes when we simulate more complex problems, and simulate thousands or millions of times.

Re-Simulating Single Seeds

Here is a brief example on re-simulating single seeds for results.

sprout = Sprout(seed)
lab.plant(sprout)
is_purged = fire.purge(sprout)

Where lab is a Planter, and fire is a Fire.

Below, we run the 3-card monte, and re-simulate all passing results one-at-a-time to re-check the results.

from seedler import Planter, Sprout, Fire

sims = 100

PASS = 0
FAIL = 1

class CardMontePlanter(Planter):
    def plant(self, sprout: Sprout):
        cards = [PASS, FAIL, FAIL]
        card = cards[sprout.growth(0, 2)]
        sprout.add_bud(card)

class PurgeFail(Fire):
    def purge(self, sprout: Sprout):
        return sprout.get_bud_count(FAIL) >= 1

fire = PurgeFail()
lab = CardMontePlanter()
garden_pass = lab.find_seeds(fire=fire, maximum=sims)

pass_seeds = [seed for seed, _ in garden_pass]

for seed in pass_seeds:
    sprout = Sprout(seed)
    lab.plant(sprout)
    if fire.purge(sprout):
        raise Exception(f"Seed {seed} is supposed to pass, but is purged.")

print("All passing seeds re-passed purging.")

All passing seeds re-passed purging.