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My roommate nerd sniped me and now I am doing mathematics on the back of an envelope

can some mutual double check my math?

Suppose you have a deck of cards with four suits numbered 1-14, and 22 trump cards, making 78 cards in total. Suppose you are dealt 15 cards and then given 1 additional card. What is the probability the additional card is has the same number of some other suited card in your hand?

the result is inconsistent with some brute force simulations I am doing in some code which is telling me that about 35.6% of the time the 16th card is a repeated suited card

There was an extremely funny bug in my simulation code. I fixed it and now it gets the same result up to three decimal points when I run 10,000,000 trials

The bug occurred because I tried to put "VII" and "VIII" in the array but I instead put "VII" and "VII" in the array and these duplicate values cased Bullshit to happen

I logged the array a gazillion times and never noticed there were two "VII"s in it because VII and VIII look similar already lmao

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