Odds Calculation for 20 card deck

I am trying to figure out what the odds would be for 3 card poker and 5 card poker if the 2-9's are removed from the deck? Thereby only having 20 cards total in the deck. Thanks

3 Card Odds For:
Royal Flush
Straight Flush
Straight
Flush
3 of a kind
Pair

5 Card Odds For:
Royal Flush
Straight Flush
4 of a kind
Full House
Flush
Straight
Three of a Kind
Two Pair
Pair

All your straight flush's would be royals.

Quote: billryan

All your straight flush's would be royals.

For that matter, if the only cards in each suit are 10, J, Q, K, A, then all of the five-card flushes would be royals.

Just to clarify, a Royal Flush is a flush with Spades. A Straight Flush is a without Spades. The odds will be the same for a Royal Flush or a Straight Flush however the payouts are different.

The odds will not be the same then... Given that only 1/4 of straight flushes will count as a Royal Flush. The royal is is that much harder to achieve.

No, the odds are the same for a Royal Flush vs. a Straight Flush based on Twenty cards. Only the payouts will differ.

Quote: TommyZ

No, the odds are the same for a Royal Flush vs. a Straight Flush based on Twenty cards. Only the payouts will differ.

Okay... Let's look at the possible straight flushes for 5 card:

Ad-Kd-Qd-Jd-10d
Ah-Kh-Qh-Jh-10h
Ac-Kc-Qc-Jc-10c

Now let's look at the possible Royal flushes:

As-Ks-Qs-Js-10s

...If you're going to get A-K-Q-J-10 of the same suit, you're 3x as likely to get a straight flush rather than a royal flush. Remember, your royal flush ISN'T 5 suited cards in a row... it's specifically 5 spades in a row. This changes the odds.

Let me also point out that, for the 5 card poker hands, the odds of getting a flush are zero (because its always a straight flush.)

The hand frequencies for the 3 card and 5 card poker with a deck with only 20 cards (ranks T-A) is an easy calculation. I'm on the run at this moment, but, please, someone step up and post the answers.

5 Cards

Total combinations (20 | 5) = 15,504 hands

Royal Flush in spades = 1 = 0.00645%
Straight Flush = Royal Flush in non-spades = 3 = 0.01935%
4 of a kind (5 | 1) (4 | 1) (4 | 1) = 80 = 0.516%
Full House (5 | 1) (4 | 3) (4 | 1) (4 | 2) = 5 * 4 * 4* 12 = 480 = 3.096%
Flush 0
Straight 1 (4 | 1)^5 - 4 = 1,020 = 6.579%
Trips: (5 | 1) (4 | 3) (4 | 2) (4)^2 = 1,920 = 12.384%
Two Pair (5 | 2) (4 | 2) ^2 (3 |1) (4 | 1) = 4,320 = 27.864%
One Pair: (5 | 1) (4 | 2) (4 | 3) (4 | 1) ^ 3 = 7,680 = 49.536%

Total = 15,504.

If you are not doing a draw then a 0 - 0 - 2 - 4- 8 - 25 - 200 - 800 payout for a 97.78% game.
Or a 0-1-2-3-4-20-100-400 game for 99.59% game.

3 Cards

Total combos = 1,140

Royal Flush (AKQ suited) = 4_____ 0.3509 %
Straight Flush = 8_____ 0.7018 %
Trips: = 20_____ 1.7544 %
Flush = 28_____ 2.4561 %
Straight = 180_____ 15.7895 %
One Pair = 480_____ 42.1053 %
High Card = 420_____ 36.8421 %