with knowledge:     10000000 tries, stay wins  3334274 times, swap wins  6665726 times
without knowledge:  10000000 tries, stay wins  3332947 times, swap wins  3332175 times, and we didn't count  3334878 games because monty happened to open the door that hides the car.
with knowledge:     20000000 tries, stay wins  6669429 times, swap wins 13330571 times
without knowledge:  20000000 tries, stay wins  6666620 times, swap wins  6666379 times, and we didn't count  6667001 games because monty happened to open the door that hides the car.
with knowledge:     30000000 tries, stay wins 10002452 times, swap wins 19997548 times
without knowledge:  30000000 tries, stay wins 10000691 times, swap wins  9998688 times, and we didn't count 10000621 games because monty happened to open the door that hides the car.
with knowledge:     40000000 tries, stay wins 13337424 times, swap wins 26662576 times
without knowledge:  40000000 tries, stay wins 13335449 times, swap wins 13331927 times, and we didn't count 13332624 games because monty happened to open the door that hides the car.
with knowledge:     50000000 tries, stay wins 16668431 times, swap wins 33331569 times
without knowledge:  50000000 tries, stay wins 16669002 times, swap wins 16665316 times, and we didn't count 16665682 games because monty happened to open the door that hides the car.
with knowledge:     60000000 tries, stay wins 20001372 times, swap wins 39998628 times
without knowledge:  60000000 tries, stay wins 20003117 times, swap wins 20000776 times, and we didn't count 19996107 games because monty happened to open the door that hides the car.
with knowledge:     70000000 tries, stay wins 23336691 times, swap wins 46663309 times
without knowledge:  70000000 tries, stay wins 23337282 times, swap wins 23330969 times, and we didn't count 23331749 games because monty happened to open the door that hides the car.
with knowledge:     80000000 tries, stay wins 26671522 times, swap wins 53328478 times
without knowledge:  80000000 tries, stay wins 26669341 times, swap wins 26665020 times, and we didn't count 26665639 games because monty happened to open the door that hides the car.
with knowledge:     90000000 tries, stay wins 30006648 times, swap wins 59993352 times
without knowledge:  90000000 tries, stay wins 30001021 times, swap wins 30000035 times, and we didn't count 29998944 games because monty happened to open the door that hides the car.
with knowledge:    100000000 tries, stay wins 33338997 times, swap wins 66661003 times
without knowledge: 100000000 tries, stay wins 33336749 times, swap wins 33330848 times, and we didn't count 33332403 games because monty happened to open the door that hides the car.
with knowledge:    110000000 tries, stay wins 36670433 times, swap wins 73329567 times
without knowledge: 110000000 tries, stay wins 36670423 times, swap wins 36664718 times, and we didn't count 36664859 games because monty happened to open the door that hides the car.
with knowledge:    120000000 tries, stay wins 40002402 times, swap wins 79997598 times
without knowledge: 120000000 tries, stay wins 40004144 times, swap wins 39996302 times, and we didn't count 39999554 games because monty happened to open the door that hides the car.
with knowledge:    130000000 tries, stay wins 43336203 times, swap wins 86663797 times
without knowledge: 130000000 tries, stay wins 43337738 times, swap wins 43327772 times, and we didn't count 43334490 games because monty happened to open the door that hides the car.
with knowledge:    140000000 tries, stay wins 46669017 times, swap wins 93330983 times
without knowledge: 140000000 tries, stay wins 46673344 times, swap wins 46661949 times, and we didn't count 46664707 games because monty happened to open the door that hides the car.
with knowledge:    150000000 tries, stay wins 50000488 times, swap wins 99999512 times
without knowledge: 150000000 tries, stay wins 50006909 times, swap wins 49995306 times, and we didn't count 49997785 games because monty happened to open the door that hides the car.