Cappelletti in Central City

While attending the Fall National Bridge Tournament in Denver over Thanksgiving week, I had several opportunities to check out the local poker action. Although there is no legal gaming in Denver, there are several little former "ghost towns" about a half-hour from downtown Denver that have been resurrected into casino cities. There are more than 20 casinos in the town of Blackhawk, another dozen or so in Cripple Creek, and about half a dozen in Central City.



After the evening session of bridge, shortly before midnight on Thanksgiving Eve, with five large bridge players crammed into my small rental car, I drove out to the Fortune Valley Casino in Central City, which also has a three-star hotel. As I approached the poker room, I was rather surprised to see eight full tables going strong and even a short waiting list. It turned out that all eight tables were $2-$5 limit, because Colorado has a state law prohibiting bets of more than $5 on all casino games. However, I noted that one of my friends was allowed to play four blackjack positions at $5 each.



A jackpot had been hit shortly before my arrival, and everyone at my table was in a festive mood (the free drinks helped). I listened to various amusing and traditional stories about Denver and Central City's past glories, and The Great Turkey War of 1859 (when Denver was a shoot-'em-up gold mining town and still part of the Kansas Territory). But even with the mirth and merriment, and $5 maximum bet, a relatively tight and serious level of hold'em was being played at my table. It was not at all like the "no-fold' em" low-limit hold'em that I have experienced elsewhere. I knew after my first "big-slick" disaster, when an opponent optimally waited until the river to raise with his flopped set, that this might be a tough game.



A bridge buddy who is new to poker was sitting next to me, and he asked me several astute questions about betting a low pair after the flop. Twice I had flopped a low pair in the big blind and he had noted that I bet out one time and check-raised the other. I check-raised into an aggressive preflop raiser (who was a 100 percent post-flop bettor) when there were three low cards in the flop. I led into a meeker preflop raiser (who might check) when there was a dangerous queen in the flop (with two low cards). These decisions require some knowledge of your opponent, as well as good judgment based on the following:



If you flop a low pair with no flush or straight possibilities (for example, you hold Q-5 and the flop is 9-5-2) and the preflop raiser has two overcards but no pair (for example, K-J), you are more than a 3-1 favorite to win the pot if played to completion. Of course, if either hand has a flush or straight draw, that affects the odds. If either hand has secondary (three-card) flush or straight potential, that affects the odds by only 1 percent or 2 percent.



But if your opponent happens to hit the flop or has a bigger pair than yours, you will outdraw him and win the pot only about one time in five. So, what are the chances that a preflop raiser has a higher pair than yours?



That depends mostly on the propensities of the raiser and how often he raises before the flop from various positions. If a very tight player seldom raises preflop, and when he does, he usually has a big pocket pair or A-K, he will have a big pair well over half of the time.



How often will a slightly tight preflop raiser have a big pocket pair? Of course, it depends on exactly what a particular player raises with and from what position. But suppose, for example, that a player is known to raise with pocket pairs of tens or higher, and that he also raises with A-K, A-Q, K-Q, A-J and just a few other holdings.



Of the 1,326 different hold'em hands, six are two aces, six are two kings, and so on. Thus, there are 30 pocket-pair hands of tens or higher. There are 16 A-K hands, 16 A-Q hands, and so on. Thus, if the slightly tight player raises with A-K, A-Q, K-Q, A-J, and only certain other suited holdings (say, A-10 and K-J suited), there would be 72 nonpair holdings: (16 × 4) + (4 × 2) = 72. Thus, this particular raiser would have a pocket pair about 30 percent of the time (30÷102).



Since most players raise with more hands than our slightly tight player, they would have a high pocket pair (aces through tens) somewhat less frequently than one time in four. But these more aggressive raisers also might raise preflop with medium pocket pairs (nines through sevens), and therefore have a low pair beat without using the flop about one time in four (48÷200).



It helps to know that any two cards (for example, A-K) will hit a pair or better on the flop (that is, one or more aces or kings in the flop) less than one time in three. But, of course, the more high cards there are in the flop, the more likely it is that the preflop raiser will have a high pair.



The bottom line? I once wrote that if you flop a pair and the flop contains no ace or king (and no more than one queen, jack, or 10), you probably are a favorite over most preflop raisers. That still sounds about right, but here's one last piece of advice: If the preflop raiser calls your insolent bets after the flop and turn, don't bet the river unless you improve.