Tactics - Omaha: The numbers game

Eurosport - Fri, 12 Sep 09:46:00 2008

After last week's look at the basics of Omaha. We run through some of those vital calculations for pot odds.

28/08 poker vignette - 0

In all forms of poker, understanding pot odds is crucial but even more so in online game and has you have none of the traditional tells.

The main difference between Omaha and Texas Hold'em is that you have four hole cards and this means you will see many stronger hands in Omaha.

There are 270,725 possible starting hand combinations in Omaha; 16,432 distinct starting hands in terms of value and 16 hands in terms of rank. Here are your chances of each:

Four of a Kind - Number of Varieties 1 - Distinct Hands 13 - Odds 20,824:1

Three of a Kind - Number of Varieties 2 - Distinct Hands 312 - Odds 107:1

Two Pair - Number of Varieties 3 - Distinct Hands 234 - Odds 95:1

One Pair - Number of Varieties 5 - Distinct Hands 5134 - Odds 2.3:1

No Pair - Number of Varieties 5 - Distinct Hands 10725 - Odds 0.48:1

Here are some of the more common probabilities for each type of hand in Omaha Hi-Lo.

Omaha High Hand

Royal Flush - Combinations 42807600 Probabilities 0.000092

Straight Flush - Combinations 368486160 Probabilities 0.000795

Four of a Kind - Combinations 2225270496 Probabilities 0.0048

Full House - Combinations 29424798576 Probabilities 0.063475

Flush - Combinations 31216782384 Probabilities 0.067341

Straight - Combinations 52289648688 Probabilities 0.112799

Three of a Kind - Combinations 40712657408 Probabilities 0.087825

Two Pair - Combinations 170775844104 Probabilities 0.368398

Pair - Combinations 122655542152 Probabilities 0.264593

Others - Combinations 13851662832 Probabilities 0.029881

Omaha Low Hand

Five High - Combinations 7439717760 Probabilities 0.016049

Six High - Combinations 25832342400 Probabilities 0.055726

Seven High - Combinations 51687563904 Probabilities 0.111501

Eight High - Combinations 76415359104 Probabilities 0.164843

Nine High - Combinations 90496557312 Probabilities 0.195219

Ten High - Combinations 87800751360 Probabilities 0.189404

Jack High - Combinations 68526662400 Probabilities 0.147826

Queen High - Combinations 39834609408 Probabilities 0.085931

King High - Combinations 13835276928 Probabilities 0.029845

Pair or Higher - Combinations 1694659824 Probabilities 0.003656

Pot odds are the ratio of the current size of the pot to the cost of a contemplated call. So if the pot contains $100 and a player must call $10 to stay in the hand, then the player's pot odds are 10:1 or 10%. Pot odds are often compared to the probability of winning a hand with a future card in order to estimate the call's expected value.

And here are the chances of getting the card you want after each stage of betting. The outs are the number of cards remaining in the deck, which will improve your hand.

Outs: 21 Turn and River: 69.9% Turn Percentage: 44.7% River Percentage: 45.7%

Outs: 20 Turn and River: 67.5% Turn Percentage: 42.6% River Percentage: 43.5%

Outs: 19 Turn and River: 65.0% Turn Percentage: 40.4% River Percentage: 41.3%

Outs: 18 Turn and River: 62.4% Turn Percentage: 38.3% River Percentage: 39.1%

Outs: 17 Turn and River: 59.8% Turn Percentage: 36.2% River Percentage: 37.0%

Outs: 16 Turn and River: 57.0% Turn Percentage: 34.0% River Percentage: 34.8%

Outs: 15 Turn and River: 54.1% Turn Percentage: 31.9% River Percentage: 32.6%

Outs: 14 Turn and River: 51.2% Turn Percentage: 29.8% River Percentage: 30.4%

Outs: 13 Turn and River: 48.1% Turn Percentage: 27.7% River Percentage: 28.3%

Outs: 12 Turn and River: 45.0% Turn Percentage: 25.5% River Percentage: 26.1%

Outs: 11 Turn and River: 41.7% Turn Percentage: 23.4% River Percentage: 23.9%

Outs: 10 Turn and River: 38.4% Turn Percentage: 21.3% River Percentage: 21.7%

Outs: 9 Turn and River: 35.0% Turn Percentage: 19.2% River Percentage: 19.6%

Outs: 8 Turn and River: 31.5% Turn Percentage: 17.0% River Percentage: 17.4%

Outs: 7 Turn and River: 27.9% Turn Percentage: 14.9% River Percentage: 15.2%

Outs: 6 Turn and River: 24.1% Turn Percentage: 12.8% River Percentage: 13.0%

Outs: 5 Turn and River: 20.4% Turn Percentage: 10.6% River Percentage: 10.9%

Outs: 4 Turn and River: 16.5% Turn Percentage: 8.5% River Percentage: 8.7%

Outs: 3 Turn and River: 12.5% Turn Percentage: 6.4% River Percentage: 6.5%

Outs: 2 Turn and River: 8.4% Turn Percentage: 4.3% River Percentage: 4.4%

Outs: 1 Turn and River: 4.3% Turn Percentage: 2.1% River Percentage: 2.2%

Angus MacKenzie / Eurosport

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