Let's assume we had the following deck:
Suits: ♠♣♥♦▲⬤ Values: 2 - 10, Soldier, Guard, Princess, Queen, King, Ace
Would the ranking of all hands (flush, trilling, etc.) be still in the same order, or would some of the hands change?
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Hand rankings are based on the probability to make a given hand when drawing five cards: the lower the probability, the stronger the hand.
When you add more suits to a deck:
When you add more ranks to a deck:
Other differences may occur in for example the probability of three of a kind being closer to two pairs when you add more and more suits.
One effect countering the other, if you add 2 suits and 6 ranks (~50% of 13) to a deck you would create conditions where rankings are the same (probabilities close to equal), whereas if you add more suits than rank or the reverse you may change how combinations are ordered if you significantly change the deck.
In the example of short deck holde'm, played with 32 cards, since ranks are removed but suits aren't, a flush is significantly less likely to happen than a full-house and as such it is considered a stronger holding.
Some interesting info.
As the number of suits increase, boats/quads drop a lot of value. A deck with more than 16 suits would value straights over boats. If you removed a suit to make a 3-suit deck, straights would outvalue flushes.
As the number of ranks increase, flushes drop value (and conversely gain value when the reverse occurs) while the rest of the 5 hand combos remain somewhat stable. With an 11 rank deck, flushes outvalue boats, and with a 8 rank deck, flushes outvalue quads. With a 6 rank deck, flushes are equal in value to straight flushes.
if you put in 3 more ranks (as per your suggestion), straights would outvalue flushes.
The number of community cards also affects the probabilities (thus the answer assumes only 5 cards are picked, which exclude plo/nlhe community type poker games). As the number of community cards increases, the probability of a flush hits 100% quite quickly (i.e. 17 community + hole cards).
It would have no effect on flushes or straights. Pairs I don't know. Have to work out the math.
A short deck is different in that it increases the likelihood of pairs and triplets and straights. Flushes once again I'm not sure. Have to work out the math.