"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.