The 5 x 5 Grid Game

Here is a game that I conceived and that Gemini helped me refine and then finally implement for a single player. I got the idea for creating this game while reading "Around the World in 80 Games" by Marcus du Sautoy. He makes no mention of the game I conceived of but the book served as inspiration. It's remarkable how easily Gemini created the game once it was given clear instructions as to what I wanted.

How to Play: The 5x5 Grid Game

Welcome to the grid! This is a game of probability, spatial strategy, and risk management. Your goal is to fill a 5x5 grid with numbers to create specific mathematical sequences across the board.

The Basics

• The Grid: You have an empty 5x5 grid. By the end of the game, every square will contain a single digit (0-9).
• The Dice: Each turn, two six-sided dice are rolled. The sum of the dice determines the digit you must play:
  • Sums 2 through 9 equal their exact face value.
  • A sum of 10 equals 0.
  • A sum of 11 equals 1.
  • A sum of 12 is a Wildcard! You may choose any digit from 0 to 9.
• Placement: You can place your digit in any empty square. Once it is placed, it is locked in forever. Plan carefully!

Scoring Your Grid

When the grid is full (after 25 rolls), the game evaluates 12 different lines for points:

• 5 Horizontal Rows (read left to right)
• 5 Vertical Columns (read top to bottom)
• 2 Diagonals (top-left to bottom-right, and top-right to bottom-left)

The Points System

Tier	Points	Number Types
Tier 1: Base	1	Xenodrome, Non-prime digits only, Balanced number, Cyclops number
Tier 2: Uncommon	3	Balance of prime/non-prime, Balance of odd/even, Mountain number, Odd digits only
Tier 3: Rare	5	Even digits only, Nailpdrome, Plaindrome, Palindrome
Tier 4: Extreme	15	Prime digits only, Katadrome, Metadrome
Tier 5: Jackpot	30	Repdigits, Fibonacci

Glossary of Number Types

• Xenodrome: No digits are repeated (e.g., 17384).
• Plaindrome: Digits ascend, repeats allowed (e.g., 23447).
• Metadrome: Digits strictly ascend, no repeats (e.g., 13468).
• Nailpdrome: Digits descend, repeats allowed (e.g., 97752).
• Katadrome: Digits strictly descend, no repeats (e.g., 86421).
• Palindrome: Reads the same forwards and backwards (e.g., 42724).
• Repdigits: All 5 digits are identical (e.g., 66666).
• Cyclops number: Contains exactly one "0", and it is sitting dead center.
• Mountain number: Digits strictly ascend to a peak, then strictly descend.

• Prime digits only: Only 2, 3, 5, or 7.
• Non-prime digits only: Only 0, 1, 4, 6, 8, or 9.
• Even digits only: Only 0, 2, 4, 6, or 8.
• Odd digits only: Only 1, 3, 5, 7, or 9.
• Balance prime/non-prime: The sum of the prime digits equals the sum of the non-prime digits.
• Balance odd/even: The sum of the odd digits equals the sum of the even digits.
• Balanced number: The sum of the first two digits equals the sum of the last two digits.
• Fibonacci: The 1st & 2nd digits add up to the 3rd. The 2nd & 3rd add to the 4th. The 3rd & 4th add to the 5th.

Play The Game

Rolls Remaining: 25

Press 'Roll Dice' to begin.

Final Score Report

Total Score: 0 Points

The Odds: Know Your Probabilities

Because every square on the grid accepts any number (including zeros), the math is completely uniform across the board. The game is driven by the bell curve of two six-sided dice. Here is the exact chance of rolling each total:

Dice Total	Probability
2	2.78%
3	5.56%
4	8.33%
5	11.11%
6	13.89%
7 (Most Common)	16.67%
8	13.89%
9	11.11%
10 (Digit 0)	8.33%
11 (Digit 1)	5.56%
12 (Wildcard)	2.78%

The True Digit Probabilities

Because rolling a 12 lets you pick any number, the Wildcard effectively adds a tiny fraction of probability (0.28%) to every single digit. When you combine the natural dice rolls with the strategic use of Wildcards, here is how likely you are to actually secure each digit on the grid:

Grid Digit	True Probability	Sourced From
2	3.06%	Roll 2 + Wildcard
1, 3	5.83%	Roll 11 or 3 + Wildcard
0, 4	8.61%	Roll 10 or 4 + Wildcard
5, 9	11.39%	Roll 5 or 9 + Wildcard
6, 8	14.17%	Roll 6 or 8 + Wildcard
7	16.94%	Roll 7 + Wildcard

Strategy Tip: Building lines that require 2s, 1s, or 3s is incredibly risky without relying heavily on Wildcards. High-probability digits like 6, 7, and 8 will quickly flood your board.