The Penguin Book of Card Games: Everything You Need to Know to Play Over 250 Games (179 page)

change the relative ranking of hands. They do, however, introduce a

new hand consisting of four of a kind and a wild card counting as

the fifth. By agreement, ‘five of a kind’ either beats everything or is

beaten only by a royal flush. Of tied hands, one with fewer wild

cards beats one with more.

Short-pack Poker

Poker is often played in countries where short packs are the norm.

Like wild cards, short packs change the mathematics but not the

relative ranking of hands.

32-card Poker

The French 32-card pack runs AKQJT987, and Ace counts high or

low in a straight. In this game by far the commonest hand dealt is

one pair. A nothing hand is much rarer, turning up only about three

times in ten. This makes 32-card Poker much more interesting for

Hi-Lo or Lowbal . The most extreme variation occurs with the flush,

which is actual y harder to get than four of a kind. On the face of it,

then, the flush would seem a poor bet and a fourflush not worth

drawing to. On the other hand it is not possible to play with more

than five at a table (or six at Stud), and four is the best number. The

average winning hand is a high two pairs, as in normal Draw Poker,

and the reduced number of players virtual y halves the frequency of

fours and ful houses. The fourflush is therefore in fact a very

reasonable proposition. Players on the lookout for curiosities wil

find plenty of scope here. For instance, how about five-player high-

low stud with two spits common and wild?

Frequency of Poker hands in a 52-card pack with Deuces wild

The commonly reproduced table for this feature (possibly first

published in Culbertson’s Card Games Complete) is wrong, its most

misleading error lying in the rate for straight flushes, quoted as

4,556 instead of the correct 2,552. Only the figures for two pairs,

ful house, and five of a kind are correct in previous tables.

The hands are listed here in order of ascending frequency rather

than in correct ranking order. This makes fours commoner than

than in correct ranking order. This makes fours commoner than

flushes, threes than two pairs, and a nothing hand bet er than one

pair! The figures apply only to a five-card deal as at Five-Card

Draw and Stud, not to Seven-Card Stud. A blank indicates that the

given combination of cards would in practice be more profitably

rated as a hand of higher value. (5S etc. = fives, or five-the-same,

meaning five of a kind. NX is nix, meaning no combination.)

com total

= 1 in 0 wild 1 wild

2 wild

3 wild 4 wild

5S 672

3868 -

48

288

288

48 (a)

SF 2552

1108 32

544

1320

656

- (b)

FH 12672 789

3168

9504

-

-

-(c)

FL 14472 180

3136

7376

3960

-

-(d)

4S 31552 82

528

8448

19008

3568 -(e)

ST 62232 42

8160

34272

19800

-

- (f)

2P 95040 27

95040 -

-

-

-(g)

3S 355080 7

42240 253440 59400

-

- (h)

NX 799680 3

799680 -

-

-

-(i)

1P 1225008 2

760320 464688 -

-

- (j)

total 2598960 =

1712304 +778320 +103776 +4512 +48

Notes

(a), (b) If you prefer to rate a royal flush (RF) above five of a kind,

the figures become: RF=504, 5S=652, SF=2,068. In this case a

hand with four wild cards wil be counted as RF if the natural card

is Ten or higher, or 5S if Nine or lower.

(c) Two pairs and one wild card make a ful house, but with more

than one wild card the hand is at least four of a kind.

(d) A flush with three wild cards is at least four of a kind and may

be a straight flush. Any other flush is weak because on average it is

only half as common as four of a kind.

(e) Four of a kind gets dealt twice as often as a flush.

(f)Astraight with three wild cards is at least four ofa kind and may

be a straight flush.

(g) Two pairs canbemadeonlywith naturalcards andinmost contexts

is worthless.

(h) It fol ows that, if there are seven at a table, at least one player

wil probably be dealt three of a kind.

(i) A nix hand must consist of natural cards except in Hi-Lo or

Lowbal .

(j) Worthless alone, 1P stands good chances of conversion into 3S or

4S in a draw.

40-card Poker

Spanish and Italian packs lack Eights, Nines and Tens, so the ful

sequence runs AKQJ765432. The lowest straightis5432A and the

highest AKQJ7. When a 52-card pack is stripped to 40, it is usual to

discard everything lower than Five, making the lowest straight

A5678. The probabilitiesare

unaf ectedbywhichthreeranksareselectedfor removal. Again, the

commonest hand is one pair, which is dealt about five times in ten

as opposed to four nothing hands and one of anything higher.

Flushes are rarer than ful houses, but commoner than fours. A ful

table would be five or six players at Draw, six or seven at Stud.

48-card Poker

Pinochle enthusiasts have been known to play with a double 24-

card pack, running AKQJT9 in each suit. It produces weird results.

For instance, there are three distinct flush hands other than a

straight flush. A flush containing no duplicated cards is beaten by

any flush containing a pair, and a one-pair flush is beaten by any

two-pair flush. So, for example, a AKQJ9 fal s to KQJJ9,

whichin turn is beaten by JTT99. This seems logical enough until

you calculate the figures and discover that the most commonly dealt

flush is the middle-ranking one pair, and the rarest the no-pair.

These flushes, though ranking as a whole between a straight and a

ful house as in the normal game, are in fact rarer than ful houses.

The top hand is five of a kind, which is only marginal y rarer than

the straight flush. Ace may count high or low for the purpose of a

straight or straight flush, so the three possibilities are: A9TJQ,

9TJQK and TJQKA. The oddest feature of al is the rarity of the

nothing hand. It is not merely rarer than a pair, as in other short

pack games, but in fact is exactly as rare as the straight – there

being 97,920 of each type of hand in the total of 1,712,304 possible

hands in the 48-card. To put it another way, the chances of being

dealt a nothing hand are approximately 17-1 against. Thus, in the

topsy-turvy world of Hi-Lo Pinochle Poker, a nothing is as good as a

straight for the high hand, while the best low hand is a pair of

Nines accompanied by JQK of mixed suits.

20-card Poker

The earliest form of Poker, current in the Mississippi river-boats of

the 1820s, was played with 20 cards ranking AKQJT. The only

admissible hands were one pair, two pairs, and three and four of a

kind, though the ful house soon put in an appearance.

Frequency of Poker hands in short packs

32 cards

40 cards

number odds number odds

SF

20

10068 28

23499

4S 224

898 360

1827

FH 1344 149 2160 304

FL 204

986 980

670

ST

5100 381/2 7140 91

3S 12096 151/2 23040 271/2

2P 24192 71/2 51840 11 1/2

1P 107520 1

322560 1

NC 50676 3

249900 11/2

Total 201376

658008

Odds = odds to 1 against being dealt this hand from a properly

shuf led pack.

Freak-hand Poker

The smart gambler wil play a game he basical y hates if most of

the other

players have more enthusiasm than skil .

Carl Sifakis, Encyclopedia of Gambling (1990)

Freak hands are unorthodox Poker combinations, invented

original y to spice up games like basic Draw where most hands are

won on two pairs, leaving fours and straight flushes so rare as to

risk passing unrecognized when they deign to put in an appearance.

Apart from lowbal hands described above, freak hands have

dropped out of use and are not normal y welcomed in Dealer’s

Choice. This is because it is hard to work out where they should

rank in the hierarchy, hard to remember when you have worked

them out, and consequently apt to give rise to argument. What they

were designed to achieve has been more easily done by introducing