Pablo Repetto comments on Duels & D.Sci March 2022: It’s time for D-d-d-d-d-d-d-d-d-d-d-d-d-d-data!

[Pablo Repetto]

Just the obvious contrarian poke:

Are the decks equally likely? We observe that 412050 decks appear just once, 104483 decks appear twice, etc. Is this distribution compatible with random draws?

There are 342396 rows, with 2 decks each. Solving for the number of valid decks one could make, gives me $(\frac{12+12-1}{12})=1352078$ (straightforward application of counting particle arrangements, imagine you have “coins” to place in “card-type boxes”).

Then I just simulated and eyeballed. If I pick 2*342396 random numbers from 1 to 1352078, how many numbers appear just once? How many twice? Eleven runs and the data looks like this:

observation
[412050, 104483, 17805, 2257, 246, 16, 1]

simulations
[411712, 104617, 17885, 2245, 213, 23, 1]
[412504, 104559, 17665, 2240, 212, 20, 5]
[412884, 104509, 17528, 2256, 225, 25, 1]
[413170, 104376, 17629, 2190, 217, 23]
[411926, 104692, 17828, 2209, 202, 23, 2]
[411883, 104746, 17624, 2302, 244, 16, 3]
[411866, 104728, 17779, 2258, 190, 24, 1]
[412771, 104106, 17813, 2294, 210, 24]
[412746, 104561, 17640, 2205, 209, 22, 1]
[412083, 104869, 17627, 2205, 237, 13, 1]
[412093, 104377, 17854, 2287, 224, 18, 1]

Which seems compatible enough.

[aphyer]

I don’t know why I expected anyone to take things for granted just because I told them not to bother looking into them.

[Pablo Repetto]

If there is a place where “pay no attention to that man behind the curtain” is to be disobeyed with prejudice, I’d reckon this is it. ;)