My earlier article entitled “Eye-Card Holdings” seemed to generate a lot of reader mail and interest. There were several questions about some related holdings, namely what I will here call the “quartet” and “trio” holdings. Keep in mind that in all of the following we are dealing with holdings which require BOTH the fourth street card AND the last card to complete the straight. Although we all intuitively distrust holdings which require both river cards to complete, nevertheless, there are certain of these two-card-draw holdings which give sufficient odds to be played profitably, especially in combination with other holdings. Since the most critical decision in Omaha is whether to get involved after the flop, it is very advantageous to be familiar with many of these lower percentage holdings.

Recall that the four-card “eye-card holding” (example, 9865 in hand, flop has “eye-card” 7 and two other non-proximate cards, such as a queen and a 2) is the best of all the two card draw holdings. This holding will make a straight over fourteen percent of the time (not even counting last card “gut” straights, which often would cost too much to persue). The three-card eye-card holdings (eg. 986 in hand, flop has Q72) will make a straight slightly under nine percent of the time.

In order to give you a better idea of how these percentages should affect your betting, I would like to introduce a new measurement called the Break-Even-Pot-size (BEP), which for the four-card eye-card holding is about fifty one dollars in a typical five-ten dollar game. The Break-Even-Pot-size, as the name implies, is the projected number of dollars which you should expect to WIN in the final pot, in order to justify your original call after the flop. Otherwise put, if you expect that winning the pot would NET you less than fifty-one dollars, then it would be mathematically correct to fold this four-card eye-card holding after the flop. Since the typical Omaha pot-size at five-ten is around seventy or eighty dollars, you normally call with this holding IF the flop cards are unsuited or if the pot is large - both preferably in a near last position (although this kind of junk flop does not get frequently raised). The BEP for the three-card eye-card holding is approximately eighty-seven dollars, which makes this a very dubious holding that normally would require other equities to play (like suited cards or pairs).

The actual mathematics for computing the BEPs are given below*, but simply stated, the BEP is based on a typical five dollar after flop call, and, IF you get a good fourth street card, a ten dollar call after fourth street (also a ten percent loss guestimate is included). Since the betting action in different poker games varies greatly, of course these BEPs must be viewed as mere hypothetical estimates. But I have found them very valuable to give me a better feel for how the percentages translate into real dollars.

Consider one of the best Omaha hand types, four cards in a row (for example, 9876), which, for lack of a better name, we shall call a “quartet”. Suppose the flop contains a 5 and a disappointing queen and two. There are thirteen fourth street cards (ie. 4,6,7,8) that give a thirteen outs last card straight come, and three cards (ie. 9) that give a nine outs straight come. Overall odds of straightening (not counting “gut” straights) are just under ten percent. The BEP for this holding is approximately seventy-four dollars.

Three cards in a row (eg. 987), which we call a “trio”, with an unsupported 6 in the flop, will make a straight about eight percent of the time. The BEP for this holding is around ninty-eight dollars, and hence clearly requires other equities to play. Finally let us consider the four card holding consisting of a trio plus a card once removed (eg. 9875). Can you think of a good name for this? Let’s temporarily call it a four card split-eye. If the eye-card (here a 6) appears in the flop (with two other bad cards), there are TWENTY good fourth street cards (4 yield 9-way straights, 10 yield 13-way straights, and 6 yield 17-way straights). This is only slightly inferior to the four-card eye (with the hole in the middle) and makes a straight 13.5 percent of the time. The BEP for this nice holding is approximately fifty-five dollars. Note that both four card eye-card holdings are clearly superior to the quartets.

Please remember, as with all straight comes, if the flop contains two suited cards, you must live in FEAR of the third card of that suit, and demote all of your straight comes accordingly. And, of course, if the flop contains a pair, you will usually forget all about this straight nonsense (but river pairs are irrelevant because that simply means you did not hit). Note also that the higher holdings (eg. 9875) are more likely to make the “nut” straight than the low holdings (eg. 9765). But in this situation any “backdoor” straight is usually good enough. Although all of these holdings are relatively low percentage comes, because they come up frequently, it is quite advantageous to be generally (and quickly) aware of what your pot odds are, so that you can squeeze out an extra few percentage points advantage over the uninformed.

SUMMARY OF THESE HOLDINGS:

               Relevant    % of Making   Break Even 

Holding        Flop Card   Straight      Potsize (BEP)

 

4 Card Eye         7        14.3%         $50.94 (73)

(9865)

 

4 Card Trio-Eye    6        13.5%         $55.31 (80)

(9875)

 

 

Quartet            5         9.9%         $73.81 (106)

(9876)

 

 

               Relevant    % of Making   Break Even 

Holding        Flop Card   Straight      Potsize (BEP)

 

3 Card Eye         7         8.9%         $87.50 (126)

(986)

 

Trio               6         8.1%         $98.50 (141)

(987)

*    For the mathematically inclined, the Break Even Potsize (BEP) is calculated based on the most typical Omaha scenario, ie. one bet after the flop, and one bet after the fourth card. Of course in real life there might be raises or you might lose to a higher hand (flush or higher straight). But these dangers are roughly equal with all of the above holdings, so the quantitative  comparisons are still valid. The actual BEP calculation, calculated here for the quartet (eg. 9876 in hand, 5 in flop), goes as follows. First assume that you always drop the hand 1980 times. Since you already have five dollars in each pot, the fold alternative would cost you 1980 times five or minus $9900. However, if you always call the flop, of the forty- five remaining cards (52 minus your 4 and the flop 3), there are sixteen good fourth street cards, hence there are twenty-nine bad fourth street cards which you would fold (although occasionally the pot odds and your position might justify calling with a gut straight come). Hence you lose ten dollars in 1276 hands (1980×29/45) or minus $12760. Of the remaining 704 hands (1980-1276), you make the straight 196 times (169 times from the 13 times 13 outs, 27 times from the 3 times 9 outs). Thus you lose twenty dollars 508 times (704-196) for minus $10160. Therefore, adding $12760 and $10160 and subtracting the $9900 you would have lost by folding, yields the difference $13020 which your wins must offset. Since you will lose a small number of the straights that make, let us subtract 10% from 196 (leaving 176.4), and divide $13020 by 176.4, which gives $73.81, as the average number of dollars that you must NET WIN in the pot to make calling the flop superior to the fold in the long run. In the the above table the BEP numbers given in parentheses project the effects of an approximate 37.5% loss when there are two suited cards in the flop. The reason we use 1980 hands is because there are 45×44 possibilities with the last two cards. You really have to play around with these figures a bit to understand the BEP.