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Poker Odds

The following card odds:

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1. Rank of Hands with Odds

2. Draw Odds

3. Pat-Hand Odds

4. Lowball Odds

5. Hold 'em and Stud Odds

6. Seven-Stud Odds

7. Seven-Stud Catch Odds

8. Two-Pair Odds

9. Wild-Card Odds

10. Comparison of Odds.

1. RANK OF HANDS WITH ODDS

(highest to lowest)

Rank Hand Example Number
of Hands
Possible
* Five Aces (with Bug ) AAAAB 1+
* Five of a Kind 8888W (joker wild) 13+
* Five of a Kind (with Wild Card) (deuces wild) 672
* Skeet Flush 2S 4S 5S 8S 3S 24
1 Royal Straight Flush 10H JH QH KH AH 4
1 Straight Flush 4C 5C 6C 7C 8C 40
2 Four Aces XAAAA 48
2 Four of a Kind X7777 624
* Big Bobtail X 8D 9D JD QD 144
* Blaze Full QQKKK 144
3 Full House 66JJJ 3,744
4 Flush DDDDD 5,108 (n.s.)
* Big Tiger (Big Cat) 8 - - - K 4,096 (i.f.)
* Little Tiger (Little Cat) 3 - - - 8 4,096 (i.f.)
* Big Dog 9 - - - A 4.096 (i.f.)
* Little Dog 2- - -7 4,096 (i.f.)
5 Straight 78910J 10,200 (n.f.)
* Round the Corner Straight 32AKQ 3,060 (n.f.)
* Skip Straight (Dutch Straight) 579JK 8,120 (n-f.)
* Kilter A - - - 9 35,840 (i.f.)
* Five and Dime 5 - - -10 4,096
* Skeet (Pelter, Bracket) 2 - 5 - 9 6,144 (i.f.)
6 Three of a Kind XX10 10 10 54,912
* Little Bobtail XX6C 7C 8C 3,120
* Flash HDSCB 685,464 +
* Blaze PPPPP 792
7 Two Pair X3399 123,552
* Four Flush with a Pair DDD 5D 5 34,320
* Four Flush XHHH 111,540
8 Pair XXX88 1,098,240
9 No Pair (+) XXXXX 1,302,540
9 Ace High (+) - - - - A 502,860
9 King High (+) - - - - K 335,580
9 Queen High (+) - - - - Q 213,180
9 Jack High (+) - - - - J 177,500
9 Ten High (+) - - - - 10 70,360
10 Nine Low (+ +) - - - - 9 71,860
10 Eight Low (+ +) - - - - 8 35.840
10 Seven Low (+ +) - - - - 7 15,360
10 Six Low (+ +) - - - - 6 5,120
10 Five Low (+ +) A2345 1,024

2. DRAW ODDS

Original Hand Cards
Drawn		 Final Hand Approximate*
Draws per
Catch
Ace 4 Two pair or better 14
Ace-King, same suit 3 Two pair or better 14
Pair 3 Any improvement 4
--- 3 Two pair 6
--- 3 Trips 9
--- 3 Full 100
--- 3 Four 380
Two-card flush 3 Flush 100
Pair + kicker 2 Any improvement 4
--- 2 Two pair 6
--- 2 Trips 13
--- 2 Full 125
--- 2 Four 1100
Pair + ace 2 Aces up 9
--- 2 Two pair (lower) 18
Trips 2 Any improvement 10
--- 2 Full 16
--- 2 Four 24
Three-card straight flush, double open 2 Straight or better 12
--- 2 Straight flush 1100
Three-card straight flush, KQJ or 432 2 Straight or better 14
Three-card straight flush, AKQ or 32A 2 Straight or better 21
Three-card straight, double open 2 Straight 24
Three-card flush 2 Flush 25
Two pair 1 Full 12
Trips + kicker 1 Any improvement 12
--- 1 Full l6
--- 1 Four 48
Four-card straight, open both ends 1 Straight 6
Four-card straight, inside or one end 1 Straight 12
Four-card flush 1 Flush 5
Four-card straight flush, open both ends 1 Straight or better 3
--- 1 Straight flush 24
Four-card straight flush, inside or one end 1 Straight or better 4
--- 1 Straight flush 48

3. Pat-Hand Odds

A. Various hands

Hand Hands
Possible		 Pat Hands
per
200,000
Deals		 Deals
per Pat
Hand		 Deals per
Pat Hand
or Better
Royal straight flush 4 .15 649,740 649,740
Straight flush 36 1.4 72,193 64,974
Four of a kind 624 22 4,165 3,914
Full house 3,744 144 694 590
Flush 5,108 196 509 273
Straight 10,200 392 255 132
Three of a kind 54,912 2,113 47 35
Two pair 123,552 4,754 21 13
One pair 1,098,240 42,257 2.4 2
No pair 1,302,540 50,118 2 1
Total 2,598,960 100,000 --- ---

B. High Paris

Hand Hands
Possible		 Pat Hands
per
200,000
Deals		 Deals
per Pat
Hand		 Deals per
Pat Hand
or Better
Aces 84,480 3,250 31 9
Kings 84,480 3,250 31 7
Queens 84,480 3,250 31 6
Jacks 84,480 3,250 31 5

C. Draw Hands to Straights and Flushes

Hand Hands
Possible		 Pat Hands
per
200,000
Deals		 Deals
per Pat
Hand		 Deals per
Pat Hand
or Better
Four-card straight,* any 325,008 12,505 8 ---
Four-card straight,* inside 251,136 9,663 10 ---
Four-card straight,* outside 73,872 2,842 35 ---
Four-card flush* 105,744 4,068 25 ---
Four-card straight flush* 5,796 223 448 ---
Three-card straight flush* 8,064 310 322 ---

4. LOWBALL ODDS

Pat Card Odds on the Deal

Pairless Hands Possible

Highest Card in
five cards		 Including
Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is High
Ace 0 0 502,860
King 508,880 502,860 335,580
Queen 337,920 335,580 213,180
Jack 215,040 213,180 127,500
Ten 129,024 127,500 70,360
Nine 71,680 70,360 34,680
Eight 35,840 34,680 14,280
Seven 15,360 14,280 4,080
Six 5,120 4,080 0
Five 1,024 0 0

B. Draw Odds

One-Card Draws per Catch

Highest Card in
four cards		 Highest Card in
five cards		 Including
Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is High
Ten Ten 2 2.03 2.45
Nine Nine 2.4 2.45 3.10
Eight Eight 3 3.10 4.30
Seven Seven 4 4.30 7.53
Six Six 6 7.53 ---
Five Five 12 --- ---

Two-Card Draws per Catch

Highest Card in
three cards		 Highest Card in
five cards		 Including
Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is High
Eight Eight 7.35 7.59 13.44
Seven Seven 12.50 13.44 30.75
Six Six 24.50 30.75 ---
Five Five 73.50 --- ---

Three-Card Draws per Catch

Highest Card in
two cards		 Highest Card in
five cards		 Including
Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is High
Seven Seven 30.63 31.91 95.15
Six Six 76.56 95.15 ---
Five Five 306.25 --- ---

Four-Card Draws per Catch

Highest Card in
one cards		 Highest Card in
five cards		 Including
Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is Low		 No Straights
and Flushes,
Ace is High
Seven Seven 65.08 70.02 244.96
Six Six 195.24 244.96 ---
Five Five 976.17 --- ---

5. HOLD 'EM AND STUD ODDS

First Two Cards
----------
(stud and hold 'em)		 Deals per Catch
2 aces 221
2 kings, etc. 221
Any pair 17
Any hand with a pair or an ace 5
Ace-king suited 332
Ace-king not suited 111
Any two cards suited 4
First Three Cards (High)
----------
(7 stud & pineapple hold 'em)		 Deals per Catch
3 aces 5525
3 kings, etc. 5525
Any trips 425
Three straight flush 86
Three flush 25
2 aces 77
Any pair 6
First Three Cards (Low)
----------
(Razz)		 Deals per Catch
A-2-3 (lowest) 345
4 and lower 86
5 and lower 34
6 and lower 17
7 and lower 10
8 and lower 6
9 and lower 4

6. SEVEN-STUD ODDS

Hand Hands Possible Approximate Hands
per 100,000 Deals
Straight flush 37,444 28
Four of a kind 224,848 168
Full house 3,473,184 2,590
Flush 4,051,784 3,030
Straight 8,466,876 6,330
Three of a kind 6,374,520 4,760
Two pair 30,834,000 23,050
One pair 56,851,296 42,500
No pair 23,470,608 17,500
Total Hands 133,784,560

7. SEVEN-STUD CATCH ODDS

Start With Misses per Catch of a Straight (outside) Misses per Catch of a Flush Misses per Catch of a Full House or Fours
FFX 66 31 13
FFXX 106 275 19
FFXXX -- --- 38
FFGG 53 137 4
FFGGX --- --- 7
FFGGXX --- --- 11
FFF 4 4.5 1.5
(11 for fours)
FFFX 8 9 1.7
FFFXX 22 23 2
FFFXXX --- --- 4
FFFF 1.5 1 ---
FFFFX 2 2 ---
FFFFXX 5 4 ---

8. TWO-PAIR ODDS

Hand Hands Possible Hands Higher Hands Lower
Aces up 19,008 0 104,544
Kings up 17,424 19,008 87,120
Queens up 15,840 36,432 71,280
Jacks up 14,256 52,272 57,024

9. WILD-CARD ODDS

Deals to Get on First Five Cards

Hand No Wild Cards Joker Wild Deuces Wild Deuces Wild,
Hands Possible
Five of a kind -- 220,745 3,868* 672
Royal straight flush 649,740 119,570 5,370 484
Straight flush 72,193 14,666 575 4,072
Four of a kind 4,165 920 81* 30,816
Full house 694 438 205 12,672
Flush 509 362 159 13,204
Straight 255 221 38 66,236
Trips 47 21* 8* 355,056
Two pair 21 23 27 95,040
One pair 2.4 2.4 2.4 1,222,048
No pair 2 2.2 3.4 798,660
Total --- --- --- 2,598,960

10. COMPARISON OF ODDS

 

 

 

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