No More Free Beer

Last night I played in a home cash game.  I’ve played 4 times previously with this group, lots of fun, and won some decent amounts of money each time.

So I decided to be a nice guest, and buy an extra 6-pack for the host.  I emailed to inquire as to his favorite brew, bought some (and another 6-pack for myself with intention of leaving behind the extras in hopes that some would survive until the next game or two there).  When I arrived and handed him the gift, I smiled broadly and explained this was just a small show of appreciation for being invited to join the game, he and his friends are lots of fun to play with and besides they keep giving me their money.

We had a good laugh.

Then started playing poker.  Not too deep into the night, I got AA, raised to $5 (blinds are $1 and $1) and 3 callers.  The flop was 3h 5h 7h.  I have the Ah, so this is not a terrible flop for me.  Everybody checks and I bet $11.  One caller.

Turn:  Jh.  Bingo!  Now I have an Ace-high flush and the only remaining issue is how to extract the most value.  The remaining villain checks, and I’m concerned he might just go away too easily.  By checking behind, I can represent weakness and hopefully induce a bluff on the river.

River:  5d.  Sure, this pairs the board, bringing full houses into the realm of possibility, but I’m really not so worried about that.  He leads out with a bet of $22.  Looks like the bluff I was hoping for.  I don’t want to re-pop him too hard, so I make a barely min-raise to $45.

Now he tanks for awhile, and says the river cards worries him.  I find this a little odd, as if he’s somehow representing the Ah, which I have securely in front of me.  He tanks some more, and looks to be leaning towards folding.

Then he re-raises all-in.  Huh?  My best guess is that he  has convinced himself that I’m the one bluffing here.  I feel pretty pot committed.  Let’s see… there’s about $180 in the pot and I have about $45 behind.  I’m getting 4-to-1 to call.  Gotta call here, and I do.

He says, “Sorry, but I have the nuts!” and turns over 6h 4h for a flopped straight flush.

About an hour later, I get into a hand with Ks Tc, and the board runs out As Js 6s Ac 2s, again giving me the top flush on a paired board.  The same villain leads out on the river, and again I raise – not seeing any possible straight flushes out there.

This time he calls, and says “I suppose you have Ace-Jack.”  Nope, nut flush.  He turns over A-6 for a full house, and takes most of my second $100 buy-in.

Is there a lesson to be learned here?  Probably so.  I tend to think many players are too tight in playing a flush on a paired board.  The percentage of the time that a paired board actually results in someone having a full house (note that in hand #1 above it wasn’t a full house, but a straight flush that did me in, but I digress) is fairly low.  On the other hand, both of my flushes involved 4 same-suit cards on the board, and I had the top possible flush both times.  It is much more likely that someone has a lesser flush than a full house (or quads, or a straight flush).

According to my math, a single player with a random hand will make a full house less than 3% of the time when the board is paired.  Of course, by the river his hand is no longer random.  With about the widest range I can imagine for hand #1, he makes a full house less than 8% of the time.  I’m not going to calculate for hand #2 but it should be higher due to the paired card being an Ace.  Many aces in his range.

I guess in hindsight, I have no issues with the way I played the first hand.  It was just a cooler, my AA turned into an A-high flush and lost to a flopped straight flush.  I’ll enjoy telling and re-telling that story.  The second hand warrants a call and not a raise on the river.  Much easier for the villain to have AJ, A6 or A3 and hit a full house, although I’m pretty sure he checked the turn.

Both times I could have called and not raised on the river, and saved about $120 +/-.

Is that actually the higher EV play?  I’m really not sure.

Please add your thoughts in the comments section.