Poker Hands with Numbered Cards without Suits

I love games like No Thanks, Little Devils, For Sale, 6 Nimmt, and The Game, which use a deck of sequentially numbered cards, no suits, and barely any other components. It’s a wonderful design challenge that I return to from time to time. In that exploration, I came up with a list of “poker” hands that you could put together with a deck of 50 numbered cards numbered 01-50. These should work with any size deck, with some slight tweaks. I’m not sure how or when I’ll use this mechanism, but I share it with you here for your own games if you want to use it.

These hands are ordered from best to worst.

Fool’s Hand
01, 23, 45...
At least three cards with an ascending sequence of digits. If tied, the highest rank in either hand wins. (This is a Star Wars joke for the fans out there.)

Straight Flush
Good:   03, 11, 28, 34, 42
Bad:    03, 24, 05, 36, 17
Ugly:   18, 20, 13, 04, 50
Ascending sequence of five cards. If tied, good beats bad, bad beats ugly. If still tied, the highest digit wins.

Four of a Kind
Good:   10, 13, 14, 18
Ugly:   02, 25, 28, 42
Four cards that share a digit. If tied, good beats bad, bad beats ugly. If still tied, the highest digit wins.

Full House
Good:    10, 13, 14, 35, 38
Bad:     08, 28, 38, 12, 02
Ugly:    12, 23, 28, 48, 24
Three cards that share a digit and two cards that share a digit.  If tied, good beats bad, bad beats ugly. If still tied, the highest digit wins.

Short Straight
Same as a Straight Flush, but fewer cards (two-to-four). If tied, more cards wins. If still tied, highest rank wins.

Three of a Kind
Same as four-of-a-kind, but three cards.

Two Pair*
Good:    10, 13, 45, 48
Ugly:    08, 28, 64, 43
Two cards that share a digit and two cards that share another digit.  If tied, good beats bad, bad beats ugly. If still tied, the highest digit wins.
*These examples assume a deck larger than 50 cards.

Pair
Same as Two Pair, but only one pair sharing a digit.

High Card
Highest ranking card wins.

I like that using the "tens" and "ones" digit or a mix makes an intuitive sub-hierarchy within a traditional poker hand hierarchy. I'm not 100% sold on calling them Good, Bad, and Ugly, they just seemed to make sense to communicate their relative difficulty.

I also figured out the "rarity" of digits in a 01-50 card deck which makes some interesting game design fodder.
Digit  Frequency
0      14
1-4    15
5      6
6-9    5
Interesting that the frequency of 0-5 is almost triple that of 5-9. Should that be reflected in the ranking of these poker hands? Almost any five-card hand worth anything will be built out of 0-4 since they're so much more common. I could be wrong about that assessment though. This is all just conjecture. I'm still trying to find the right game or theme where these rankings would make more sense than just using a more traditional card deck and poker rankings. Maybe you can find a home for this thing. :)