Hearthpwn

I already calculated the probability of that happening, either 1/14950 going 2nd or 1/2995 going 1st (full mulligan when all the cards you see are 2-ofs).

EDIT: Oh you cheeky boy with your Ninja edit ;) The Trump video also had him getting the cards back in the same order, odds of that are much lower, 1/27 * 1/26 * 1/25 = 1/17550, 6 times less likely than just getting the same cards back in any order (And the factor of 6 is because 6 =  3 * 2 * 1 = 3! as I mentioned in my post about the difference between (n choose r) and (n permute r)).

Quote from mungo2613 >>

Speed up the scientific process by making a highlander deck (all 1-ofs). Always mulligan everything. Play the innkeeper and concede after the mulligan.

If the cards were available in the mulligan pool, then if you go 1st the chance to get one of them back would then be 3/30 or 10%. Going 2nd and mulligan everything the chance is 4/30 ~= 13.33%. Those odds are pretty good.

I suspect you'll be waiting a long time for a positive result though ;)

What will happen though is you draw one of the cards you threw away turn 1. Since you threw them all away the probability of getting one back immediately is 3/27 = 1/9 ~= 11.11% when going first or 4/26 ~= 15.38% when going 2nd.