Omaha Odds Calculator

Omaha poker is a type of Hold'em Poker that is popular in recent poker world. To be different than Texas Hold'em ,it uses 2 out of the 4 cards in hand and 3 out of 5 hands on the public board.
The rank of a hands is same as for Stud Poker. (Straight Flush >Quads>Full house>Flush>Straight>Trips>Two Pair>Single Pair>High Card)
For more details about Omaha poker, please check below link: Omaha Hold'em

After several player bet and decide to play their hands (preflop), first three of the board cards is delivered together, this is know as 'the flop'.
When the 'flop' is dealt, one hand can already make a hand by combine either two from their own 4 card hands with the 3 cards on the flop.
After bet round, the fourth card is dealt (the turn), and bet again.
Then, the final card (the river) is dealt and followed the final betting round. The hand with the best rank on the river win this total hand. delivered. This fifth card is called as 'the river'.

Different hand has differnt winning possiblity due to their different nature. For example, AAxx (a hand with a pair of Ace) has the best winning possiblity preflop, which means without dealing any of the board cards, AAxx has the best odds preflop.
You may wonder how likely you can get AAxx ?
below is the code to calculate the possiblity:

options(digits=4)
pAA<-choose(4,2)*choose(52-4,2)/choose(52,4)
print(pAA)

## [1] 0.025

So you can see the odds to get AAxx is about 2.4999538% out of all times.

This tool is developed for calculation of specific odds for below three situation:

• preflop ( when no board card dealt)
• on the flop ( 3 cards dealt)
• on the turn ( 4 cards dealt)
  To give an easy example, when AdAcJdTc (Hand1) against 5s6s7h8h (Hand2) on the board like Ah4h5cKc , any non club 3,6,7,8 will make a straight and none 5,K or A hearts will make a flush (totally 14) and help the Hand2 win the hand , rest does no help for it. So There are totally 52-4-4-4=40 cards left in the deck.
  So the odds Hand1 vs Hand 2 equals

(40-14)/(52-12)

## [1] 0.65

For more complicated calculation, you can use this odds calculation to help.
Thank you^.