You are playing in a typical four card high Omaha game, where the betting limits are one unit before and after the flop, and two units on the last two betting rounds, for example, “five-ten” (dollars) or “ten-twenty”. Typical house rules impose a three raise limit on any given round of betting. Your four hand cards include the ace and another heart. Several players and you call to see the flop. The good news is that the flop contains two hearts. The bad news is that the flop happens to consist of a queen, ten and nine (assume that your other two cards are useless), thus creating king-jack or jack-eight (beware the low end!) straights.

There is a bet in front of you, which you call, and then there is a raise to your left, and a reraise by the original bettor. All other opposition has wisely folded. You strongly suspect that if you call the two additional “unit” bets, the raiser will take the last raise (”capping it”).

Should you concede the two units that you have already invested, or should you fish along for three more? Keep in mind that if a brick appears on fourth street (ie. not a heart, pair, ace, or king), then, there will probably be a replay of this deadly triangle at twice the price, which would then cost you eight(!) units to see the last card. What price flush draw?

Since there are nine hearts left in the deck (13 minus the two in your hand and the two on board), and the deck has 45 remaining cards (52 minus the 7 cards you can see; hidden cards in the opponent’s hands are equivalent to being in the unused deck), the odds of a heart turning on fourth street are about 9 out of 45, or one fifth. Since you strongly suspect that there are two king-jack combinations held by your opponents, and at least one of those two kings and jacks can not be hearts, there probably are two less unknown cards in the deck.

This slight plus is somewhat offset by the fact that two of the nine remaining hearts will pair the board, and either of the opponents might have two pair or trips with their other two cards. But, all-in-all, one fifth is a reasonable estimate of a heart winning for you on either the fourth or last card.

A simplistic way to calculate whether or not a call is sound in the above situation is to consider what would happen if you played the hand five times. If you folded the hand five consecutive times, you would simply lose the two units you have already put in the pot each time. If you call the three extra units and see the fourth street card five times, you rate to get a heart one of those five times.

Thus, after fourth street, you will be losing 5 units four times, for a total of minus 20, but plus whatever you win on the fifth occasion when a heart turns. On that occasion let us speculate that you win at least 15 units (4 antes, 8 post flop, and a low estimate of 3 on the 4th and last rounds - the opponents can not be sure that you were playing hearts).

Minus 20 plus 15 equals minus 5, or an average of minus one unit per hand. Therefore, your expected value by calling is around minus one unit each time; whereby folding loses two units each time.

Clearly calling to see the fourth street card is better. Note that all of the above was based on the given condition that you had already put in one unit after the flop before the raising started.

Now what happens if you miss (ie. no heart) on fourth street, and the nasty opponents appear ready to stick it to you again in the betting after fourth street. Should you risk the additional 8 units, or should you fold at this point?

If you fold now after fourth street, it would be costing you the five units you have already put in. Using the same approach as earlier, if you fold the hand five consecutive times, it would cost you a total of minus twenty five. In the worst case scenario, if you have to call 8 additional units (of course there is also some chance that one of the opponents will not raise) five times, you rate to lose four out of the five times at minus 13 (5+8) each time, for a total of minus 52 (4×13).

But the one time out of five that you win, you will win about 30 units (4 antes, 8 post flop, 16 after fourth street, and say 2 more after the last card). Thus, minus 52 plus 30 equals a total of minus 22 (an average of minus 4.4 taken over five hands). So even if the opponents DO cap it out on fourth street, it is still slightly preferable to call, since losing minus 4.4 units is better than conceding the minus five units. If one of the opponents declines to raise, your expected value is even better.

Accordingly, in the above situation, it is usually correct to stand and fight, assuming that you are drawing to the nuts. Obviously if you are drawing to a king high or queen high flush, there is the additional danger that one of the opponents also has a better flush draw and you are “drawing dead”. There is an old rule that says you should not put in good money to draw for a card which would give you a second best hand.

All of the above was based on the assumed fact that you had already called the first bet after the flop (or perhaps there was a raise before the flop), and hence had TWO betting units already invested. Does this imply that if you could get out with a loss of only one unit, perhaps folding is better? A combined analysis indicates (using twenty five hands and the above assumptions*) that it is usually slightly preferable to call and fight it out. Your expected loss by calling is about minus half a unit per hand compared to losing one unit by folding.

Perhaps the main lesson to be learned from all this is generally in limit Omaha if you have a good eight card or better draw, which will win the whole pot if it hits, then it is usually good business to withstand the pressure and stick around for the last card.

* Out of 25 hands, you win 5 on 4th street (5×15=+75), on 5th street you win 4 (4×30=+120), and lose 16 (16×13=-208). Hence 75+120-208=-13 units spread over 25 hands.