Calculations in Poker

In poker the poker players take chances as nothing is guaranteed (hence the betting). Several books are available in the market analyze the calculations of poker. Although a player needs no tools to measure poker, still the experienced player must comprehend numbers.

There are 2,598, 960 different combinations of five-card poker that a player could get with a pack of fifty-two cards. The possibility of receiving these hands when dealt the first five cards are listed below.

KIND OF HAND
 QUANTITY IN DECK
ODDS AGAINST
Royal flush 
4
649,739:1
Straight flush
40
64,973:1
4 of a kind 
624
4164:1
Full house
3,744 
693:1
Flush  
5,108 
508:1
Straight  
10,200
254:1
3 of a kind   
54,912
46:1
2 pairs 
123,552  
20:1
1 pair 
1,098,240
1.25:1
No pair   
1,302,540
Events

Prior to attempting to create the inside straight (whose odds are 11:1), a player must know the poker odds. The chances against enhancing a hand by pulling cards are listed below; these could also assist a player in recognizing his chances in a stud game too.

CARDS KEPT
CARDS DRAWN
IMPROVED HANDS
ODDS AGAINST
1 Pair
3
2 Pairs
5:25:1 
1 Pair
3
3 of a Kind
8:1
1 Pair
3
Full House
97:1
1 Pair
3
4 of a Kind 
359:1
1 Pair
3
Any improvement 
2.5:1
2 Pairs
1
Full House
11:1
3 of a Kind
2
Full House
15.5:1
3 of a Kind
2
4 of a Kind
22.5:1
4 Straight
1
Straight
5:1
(Open ended)
4-Straight
1
Straight
11:1
(Inside)
Four-flush 
1
Flush
4.5:1
Three-flush
2
Flush
23:1
Two-flush
Flush 
96:1