What would be the main difference to poker if the deck would be extended?

Question

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?

Answer 1

I coded some python to generate every hand. As it seems to work okay for a regular deck (13 ranks, 4 suits), I think I can trust the numbers. For comparison, here's what it says for a regular deck (also, the odds printed are rounded down to an integer).

2598960 hands
1098240 one pair or 1 in 2
123552 two pair or 1 in 21
54912 three of a kind or 1 in 47
10200 straight or 1 in 254
5108 flush or 1 in 508
3744 full house or 1 in 694
624 four of a kind or 1 in 4165
40 straight flush or 1 in 64974
0 five of a kind 

Now, running it on a deck with 15 ranks and 6 suits, we get:

43949268 hands
17690400 one pair or 1 in 2
1842750 two pair or 1 in 23
982800 three of a kind or 1 in 44
93240 straight or 1 in 471
17946 flush or 1 in 2448
63000 full house or 1 in 697
18900 four of a kind or 1 in 2325
72 straight flush or 1 in 610406
90 five of a kind or 1 in 488325

Flushes (and straight flushes) become much more rare compared to other changes. Regular flushes become slightly worse odds than four of a kind (which is about twice as likely as in a regular deck).

Answer 2

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:

• The value of flush increases (i.e. its probability decreases)
• The value of pairs, three of a kind etc decreases
• The value of straight very sightly increase

When you add more ranks to a deck:

• The value of flush decreases
• The value of pairs, three of a kind etc. increases
• The value of straight very sightly decreases

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.

Answer 3

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).

Answer 4

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.