16 cards, 45 hands — can you do it?
Spoiler
Well, yeah, it is possible, but it seems rather unlikely. In over 1000 hands I've succeeded twice for a total of $5.25.
Since there are 16 target cards and it is necessary to get all sixteen, all we need to do to find the chances of completing it is find the chances of not completing it, and subtract from 1.
To not complete it all you have to do is miss one card in 45 draws. of two cards each.
The probability of missing your card on the first draw is 51/52 for the first card, and 50/51 for the second card.
For 45 draws this would be (51/52)^45 which works out to 0.17
So from that it appears that it should be possible to complete the board 83% of the time.
Either I'm extremely unlucky, or I did the math wrong.
I'll write a simulation to see what happens.
