My math skills are only so-so, and for some reason I can't seem to wrap my head around this fairly simple-seeming math problem.

I have a deck of cards in 5 suits. For each suit there is one of each number card. For example if there were 9 cards in each suit then there'd be a 1 of suit A, a 2 of suit A, etc. through a 9 of suit A. Then there'd be a 1 of suit B, etc. Like normal cards, basically, but with five suits and no face cards.

The question I have is this: How many numbered cards need there be of each suit so that in any given hand of 7 random cards from the deck you'd have an equal chance of being dealt a 3-card set* or a 3-card run** (or for that matter a 4-card set or a 4-card run)? I want the odds of a set and run in a random set of 7 cards to be identical. How many of each suit need there be? Is it possible for them to be equal? How the heck would I figure it out?

Thanks in advance, math gods/goddesses.

(* A set is cards in different suits with the same number, like three of a kind in poker.)

(** A run in cards is cards in a series within the same suit, like a small straight flush in poker.)

Awesome, thanks, I'll take a look now.

I realized after sleeping that there may be no way for them to come out even, but I still need to figure out the odds of a set or a run for a given hand size and given number of cards and suits. At this point my ideal deck is 1 through 9 of five suits... how can I figure the odds? How about if there were, for example, two each of 1 through 5 in five suits?

My brain can't seem to figure out how to break the problem down without simulation (which I could do but seems like cheating).