Linda Mae saw me waiting for a seat in a $4-8 Hold'Em game and headed my way breathing fire. (I won't describe her again, nor her attire, lest readers with dicky tickers skip a few beats.) She demanded that I explain why I wrote so many columns about Straights.
Straights are less obvious than any other hand type, I responded. Everyone can see the possibility of a Flush with three or more trumps on the table. Everyone can see the possibility of Trips, a Full House, or Quads, with a Pair on the table, I observed, but it takes more imagination to see danger from a Straight in the community cards.
Zero-gap sequences like Q-J-T among the community cards can make a Straight three ways. One-gap sequences like J-T-8 can make a Straight two ways. Two-gap sequences like J-9-7 can make a Straight only one way.
Straights are also more interesting mathematically, I added. Most zero-gap, connected starting hands can make a Straight four ways; most one-gap, connected hands can make one three ways; most two-gap connectors can make one two ways; and, three-gap connectors can make a Straight only one way.
"Why did I write that there were over a thousand Hold'Em starting hands," Linda Mae asked. She said there are only 169 starting hands because suits don't matter: 13 pocket pairs; 78 suited starts; and, 78 unsuited starts. Because those numbers distort the true picture, I answered.
Those numbers imply that suited and unsuited hands occur equally often: they don't, unsuited hands occur three times as often. Those numbers imply that pocket pairs occur once on the average in every thirteen hands: they don't, they occur every seventeen hands. Finally, those numbers don't address connected starts at all.
Linda Mae asked for the definition of "connected." A starting Hold'Em hand is connected, I told her, if it could make a Straight with the right three Flop cards.
There are 1326 (C(52,2)) possible starting hands in Hold'Em. The table above categorizes all 1326 starting hands: suited and unsuited, connected and unconnected. There are 78 (13*C(4,2)) pocket pairs: since they are unsuited and by definition, unconnected, they are counted in the bin, "0 W, Offsuit." Four-way, suited connectors, although much in vogue, are uncommon, about 2% of the possible starting hands. You'll start with a pocket Pair nearly three times more often.
The table above shows those same starting hand numbers expressed as percentages, I informed her. The table shows another reason Straights are interesting: connected starting hands outnumber unconnected hands. About 55% of Hold'Em starting hands are connected. Of course, you shouldn't play some starting hands even though they're connected. For example, 7s-3d is an unattractive start, even though a Flop of 6-5-4 would make a Straight.
Linda Mae asked if I was through writing columns about Straights. "Almost," I told her, "there are a few more in the hopper." She sniffed, and then swayed out of the poker room. I didn't miss a beat.
