Soltion: Holdin' The Nuts

"Holdin'" is a reference to Texas Hold'em. "The Nuts" means an unbeatable hand, as Boddy's hint text refers to. Given this interpretation, teams are expected to treat each set of five cards as the table cards or "board" in Texas Hold'em and then figure out the one or two cards needed to be sure of winning. Reading down the columns, those cards were:

Hand First Nuts Card Second Nuts Card
1 A A
2 4 5
3 7S 7D
4 AS -
5 8D 10D
6 K Q
7 A A
8 6H 6C
9 A -
10 3S -
11 5C 6C
12 4 5
13 9 10
14 7H 8H
15 7H 7D
16 5D -

The fact that the sum of one or two cards can produce any number 1-26 where A = 1, J=11, Q=12, and K=13 is a pretty good clue that the next step is to sum two one or two nuts cards. This yields:

binaryblackisone

This means that the teams should reinterpret each set of five cards a five digit binary number where black cards and ones and red cards are zero. This yields

Hand Binary Decimal
1 10000 16
2 00001 1
3 01100 12
4 00001 1
5 00011 3
6 00101 5
7 01111 15
8 00110 6
9 00110 6
10 01001 9
11 01110 14
12 00101 5
13 00001 1
14 10010 18
15 10100 20
16 10011 19

Or:

palaceoffinearts

Which says that the next location is the Palace of Fine Arts.

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