One afternoon in early winter at my local poker room, my $4-8 Hold 'Em game was lively with a nice mix of newbies and experienced players. The newbies were playing inferior hands like 8c-2c, "just like on TV," and sometimes cashing with them because even the smallest flush has a 76% chance of being the best when there are exactly three trumps on an unpaired board.
Under the gun I peeked at my hand and saw Kd-5d. I called. Someone downstream raised. The Blinds folded and I called. Four-handed we saw the Flop.
The dealer burned one and placed this Flop on the table, 6d-3d-2d. I had flopped the 2nd-nut Flush, with a Straight Flush re-draw! The odds against flopping a Flush are about 118 to 1, but there it was and it was time to make the most of a great Flop. I checked. Mac checked. A newbie bet $4. Gimpy called. I called and so did Mac. Having someone downstream lead the betting was good because then I could check-raise when the bets doubled. The dealer burned one and placed the Turn on the table, As. No pair on the board, that was good. I had the 5d, so there was no chance of anyone else having a Straight Flush. The Ace on the table was also good because it might marry someone to the hand.
I checked; Mac bet $8; the newbie went all-in for $4; Gimpy called. I raised; Mac called, going all-in. Gimpy thought about it for a few seconds and then called. The dealer burned one and placed the fJ on the River. I led the betting with $8. Gimpy folded. I tabled my hand. Mac showed Td-9d; the beginner showed 8d- 4d. The dealer pushed me the pot.
While I was stacking, I wondered what were the chances, given that two other players had pocket trumps, that the dealer will flop three of the remaining seven? That's one of those rare questions that are both easy to ask and easy to answer. We know that six trumps were dealt, so there remain seven trumps among the remaining 46 cards. Therefore the probability of flopping a Flush is given by C(7,3)/C(46,3), or 7*6*5/(46*45*44). The odds are about 433 to 1 against.
What were my chances of winning with only the 2ndnut Flush, when holding exactly three trumps on an unpaired board? That's a harder question to answer. The column, "Itty-Bitty Flush," published in Poker Player, Vol. 9 Number 16, February 6, 2006, p. 14, has that answer. The table from the column is repeated here and shows that with exactly three trumps on an unpaired board, the 2nd-nut Flush will win 93.6% of the time.
Because they are so rare, we ignored Straight Flushes in developing the numbers in the table. If a Straight Flush is possible, then look for raise(s), and astonishment on her visage, and act accordingly. What about suited starting hands like 8c-4c? I don't see the Flop with them except when it costs me, (a) nothing, or (b), half a small bet with three or more opponents. I do play suited, four-way connectors like 8d-7d in any position providing that I can count on four opponents also paying to see the Flop. When the Flop disappoints, as typically it does, then I muck that cheese without a second thought.
