I'm working on a game in which players roll dice and race to find the matching symbol on a 3x3 grid of cards, in an "I-spy" mechanic:

3d6 - 1 symbol die (6 symbols) / 1 color die (6 colors) / 1 number die (1/2/3, each twice).

The total number of variations based on these 3 dice is 108 (6x6x3).

Each card has a jumble of icons in different color/number combinations. The active play grid is a 3x3 set of cards, with 12 icon targets per card. The reason for this is: 9 cards x 12 icons = 108. Therefore, there is a reasonable chance that the result of the dice roll will be contained within the cards on the table (but not guaranteed).

When a player finds the symbol/color/number combo on a card, they grab it, replace the card with one from the deck to bring the grid back to 9 cards, then reroll the dice to get the next target. Play continues until a grid of 9 cards can no longer be created. The player with the highest number of cards is the winner.

My question is this...what is the ideal distribution of symbol/color/number combinations in order to make the game reasonably reliable to have the matching result present in the 3x3 card grid on any given roll?

My math has thus far concluded this: 9 cards / 12 symbols each / 108 possibilities always present on the table. There are 108 total possible combinations from the dice roll.

If there are 63 cards in the deck (concluded from a 6P game, with the tenth card won concluding the game - 10/9/9/9/9/9 = 55, plus 8 cards remaining on the table as the end condition), then there must be 7 of every possible symbol/color/number combination (63 cards/12 symbols per=756 total symbols; 756 divided by 108=7 of each combo to balance the deck).

Does any of that make sense? I am admittedly do not call math a particularly strong suit, and before I go to the effort of mocking up these cards, I want to be somewhat confident that the numbers make sense in balancing the deck and the grid of 9 cards on a given draw.

As Jay and others have mentioned, this is the biggest concern; there being no match on the "board" on a given roll. The idea of calling out "no match" is interesting and a simple band-aid for what would otherwise may be considered a broken mechanic...the "Disney Eye Found It" card game does this; if no match is present, flip a new card. Pretty lazy design if you ask me.

Spot It is guaranteed to work every turn as there is only 2 cards ever being matched; it's a brilliant exercise in permutation, but only in its purposefully limited gameplay....as soon as 2 cards becomes 3 or more, the possibility of multiple matches is immediate.

Set is a game I was not aware of, but seems as though some ideas could be gleaned from it. For instance, in Set, if a set cannot be made, the rules say to add cards until a set can be made. In this game idea however, players would just be looking at the one new card, so that exact rule wouldn't work. Replacing a number of cards however, might...something to play with!

As X3M mentioned, there is also the probability of one combo being rolled more than another, thus affecting the likelihood of a smoothly operating game. I was trying to create as much of an equal balance as possible, but with the luck of the roll, it's impossible to control completely...the question is, can it be made to be acceptable?

Anyways this is why I put this idea out to the group! The game is not particularly "gamerly" in its idea, strategy or complexity (it's a super-simple family game idea)...but something I was thinking about.