Low-High Poker cont..

Every mathematical figure in poker must be modified by later information. The mathematicians work on the basis known as a priori (meaning before the expected event has actually hap­pened). Most of poker would be termed by mathematicians a posteriori (meaning that the calculations are made when actual information is already available). If you are the last hand in a seven-man game and the third man has opened and the fifth man has stayed and the others have dropped, you must know (if the game is reasonably strong) that there is at least a pair of kings out against you. You will not stay on less than two aces or two low pairs, in spite of any number of mathematical tables that tell you that two eights stand a chance to win against two opponents. However, in a wide-open game in which a player cannot bear to throw away a pair of tens or a four-flush, you may choose to stay on a little less.

In a good game, no one bets against a one-card draw with less than three of a kind or aces up, and if the one-card draw bets or raises, no one raises it without a flush. If the one-card draw reraises, he filled at least an A-Q or A-K flush and a pos­sible full house, and his raise cannot be reraised without at least jacks or queens full. The profits in poker come from get­ting a call when you have a slightly better hand than your opponent; they are dissipated chiefly by the occasional chip thrown away in staying on a losing hand or calling on a doubt­ful hand, but they can be as easily dissipated, and much faster, by giving a very strong hand a chance to raise or reraise and then calling.

Here so much depends on appraising your opponent that it is hard to generalize. A poor player will become overly enthusiastic when he has a good hand; he will become almost unrestrainable when he has made that good hand by drawing to it, as for ex­ample when he draws to four diamonds headed by the queen and catches another diamond. It might be the better part of valor merely to call him on a low full house, but it would be stupid to drop a low full house or an A-Q flush on his second raise, on the grounds that an intelligent player would have been fearful even of calling on his hand. A very good player, however, when he raises the bet of a hand that represented two pairs going in and drew one card, should not be called on less than jacks or queens full. Against such a player, there will be a net gain in the long run by throwing away a straight.

I would say that when there is action in the pot, there are three hands worth staying on: Two aces, but no lower pair; if the aces improve, they have an excellent chance of being high. A straight or flush draw if the pot offers substantially more than the odds against filling—that is, 6 or 7 to 1, as against the 4- or 5-to-l odds against filling. And, third, a good hand going in— no less than queens up or a low three of a kind. A lower pair than aces, and especially two low pairs, are candidates for the trash can.

3. The play of two pair. Some authorities have said that 90 percent of one's winnings or losses in poker can be attributed to the play of two low pairs (no higher than tens up). This is undoubtedly an exaggeration, but it serves to emphasize an im­portant point.

The basic principle governing the play of two pair is this: Before the draw, the odds are nearly 2 to 1 (in any draw game) that any two pair will be the highest hand. But the odds are 11 to 1 against improving.

Mathematically, two low pairs have a better-than-average chance of standing up (without improvement) against one or two opponents; they stand to lose if three or more opponents are in the pot. Queens up is the lowest hand that stands to win against three opponents, and aces up against four opponents. This takes into consideration the chance, one in twelve, of im­proving the two pairs you are dealt.

From this knowledge has been derived a general rule that has almost become a poker precept: If you have two pair, raise at once, so as to drive out as many as possible of the other players.

It is true that a raise tends to drive other players out and that you want other players driven out when you have two low pairs. Nevertheless, the rule is faulty. You should raise only when you are the second man (the one next to the opener). You should merely stay when two players are in before you. You should drop two low pairs when there are three players in be­fore you. When I say two low pairs, I mean in this case anything less than queens up. I am also assuming that the pot is offering you no more than 6 to 1. With two low pairs against three preceding players, in a reasonably tight game, the odds are bet­ter than 2 to 1 that one of them will improve and beat you even if none of them has you beaten going in—and my expe­rience is that one of them probably has you beaten going in, because there simply aren't enough high pairs around to give each of three intelligent players a high pair that would justify his playing.

Taking the other side of the medal, much money is lost by failure to back two low pairs strongly enough against one or two players who drew three cards. If you have created doubt in their minds by an occasional unsound one-card draw or bluff, and if you have stayed after both are in, a one-card draw and a bet may get a call from a hand that did not improve. When two opponents draw three cards each, it is better than even that neither of them improved, and when you have a better-than-even shot and can get a call from an unimproved hand, you have a good bet. But if you are known as a man who would not play "on the come" in second position, or if it is known that you would not open on a mere possibility, or if you are in a jackpots game in which you could not legally do so, do not bet; no one will call unless he can beat you. You have to be the third man to speak.

In playing two pair, the thing to watch out for chiefly is the case in which the opponent will not call unless he improved and can beat you if he did. For example, you open on two pair and draw one card. One player stays against you and draws three cards. If you do not improve, a bet is futile. He knows you would not have opened on less than two pair, and he will not call unless he has improved and has at least two pair himself. Against a good player, betting out on the opening hand in such a position leaves you wide open to a reraise, which can be a very successful bluff if your opponent has you figured correctly.

Two low pairs should seldom be opened in a "pass and back in" game. The absence of high cards in the hand makes it more likely that another player will have a high pair and will open; and of all hands, two pair is the hand on which you want if possible to be the last to speak. Queens up or better may be opened, and should be opened if the overhead is high and the antes are worth grabbing, but many good players simply do not open on any two-pair hand under aces up if they are earlier than fourth from the dealer.

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