Several articles back we discussed that “brickology”, the science of counting the “bricks” (that is, cards that do not rate to improve others) that might appear on fifth street, is often the key to making close raises on fourth street. Now I will offer a simple rule-of-thumb, that the appearance of a brick on fifth street is often the key to making “thin” bets on the last card.

“Thin betting” the last card is a term borrowed from holdem, and refers to the classic holdem situation where the driver (lead bettor) not only bets a holding such as top pair after the flop and after fourth street (which is usually considered correct), but also continues to (greedily) bet the same holding after the last card, in order to punish the “keep-you-honest” chasers (who presumably have a smaller pair). Another way of defining a “thin hand” is that it is just good enough that your opponent(s) will never fold if he has you beat. In four card Omaha, since fifth street (the last card) often yields a lock or a likely winner, value betting on any marginal holding is considered “thin betting”, unless you are attempting a bluff.

In the following estimates of the money expectations of thin betting versus checking on the last card, I am using some approximate percentages which you might not agree with. But keep in mind that the main point is simply that if a brick appears on the last card, your winning expectations in Omaha are usually many percentage points better than when a dangerous card appears. And this percentage difference, whatever it is, is clearly more than enough to cover the smaller inaccuracies in my estimates.

The argument against thin betting the last card goes like this. Suppose you have been driving a “thin” hand and it is now your turn to bet after the last card. Let us say that there is one opponent remaining and you judge that your “thin” holding will be the winning hand about sixty-five percent of the time.

First, let’s attempt to estimate the dollar expectency of your last round action if you check. Of the sixty five percent of the time that you actually do have the winner, let’s say that fifty five percent your opponent checks also and you simply win the pot. Let’s say that the other ten percent, your opponent bets, either attempting to bluff or miscalculating his hand. Here you win his bet that ten percent of the time. Although there may well be much to be said for dropping a particular opponent’s bet or raise, for purposes of this discussion we are assuming that either there is enough money in the pot that you are in a “must call” situation or that you are playing against frequent bluffers so that you must “block the plate”.

Of the thirty-five percent of the hands where you have a losing hand, let’s say that your opponent declines to bet ten percent, and that he bets, you call and lose one bet, twenty-five percent of the time. If the above bets were twenty dollar bets (in a ten-twenty game), then your incremental expected value for checking on the last card would be minus three dollars (.1×20-.25×20=-3).

Now, let us assume that instead of checking, you make the “thin” pushy twenty dollar bet. Let’s say optimistically that your opponent will call and lose twenty dollars, twenty percent of the time and will drop out (with no cards) about forty percent of the time. Just for completeness, let’s optimistically say that for the remaining five percent of your winning hands that your opponent tries to raise and bluff you out, which of course, gains you forty dollars. Of the thirty five percent of your losses, let’s say that your opponent raises you twenty-five percent (which you call and lose forty dollars) and merely calls you ten percent (costing you only twenty dollars). Adding it all up statistically, your expected value for betting the twenty dollars is minus six dollars (.2×20+.05×40-.25×40-.1×20=-6). Thus, using the above assumptions, the check is twice as good as the bet.

Note that in the above example, checking is generally to your advantage both when you pick up a gratuitous bluff or when the opponent chooses not to bet his winning cards. Betting mainly gains when your hand is better than your opponent’s AND he has enough to call. But if your opponent raises, you are definitely in a losing situation.

All of the above is based on the assumption that you have approximately a sixty-five percent winning hand. But with all such hands, clearly if the last card is a brick, your winning expectations are often twenty or thirty percent higher than if a dangerous last card hits the table. Thus, the lesson for today is that when a brick graces the table on the last card (especially when trips are the highest possible hand), your significantly higher winning expectencies often make it good business to bet and try to pick up a “keep-you-honest” call. The fact that you make this kind of bet, also helps to protect you should there be a time when you drive a come hand (like a “nut” four flush), which does not make and you resort to bluffing.