A Poker Debate - How Many Outs

I may or may not have no clue

My original intention was to start this post by saying that it “felt like a long day today” but struggled to succinctly explain myself, given all days are, of course, the same length. Except, as it turns out, June 30th 2015. Today will be whole second longer than any other day during 2015, as the final minute will be 61 seconds long!

For a fuller explanation of why this is the case, check out this BBC article on the leap second.  Anyhow, I can now close off this intro and drop in the obligatory “read more” link you expect to see on blogs these days….

I wanted to make some reference to how “long” today was, in order to make the reader aware that my judgement might be a little impaired right now. Therefore if this post is riddled with errors, I blame the 10 hours I have spent in a stuffy office/stuck next to a smelly fat man on the way home.

On said train home, I read this Tweet from PokerStars:

I answered “16 outs” but I have since had a couple of replies which make me question this. My answer was based on the following…

Step 1: what do each of the three players hold at the moment?

You – Ace high, drawing to the nut flush or two possible straights
Villain 1 – Pair of Jacks, drawing to a Queen high straight
Villain 2 – Pair of 10s, with an open ended straight draw

As it stands, Villain 1 leads with a pair of Jacks, with Villain 2 in second with his pocket 10s and you trailing with an Ace high.

So what outs do you have? Obviously the nut flush and a couple of straight draws. You also have top pair if the Ace lands, and you have Villain 1 dominated if a Queen hits the board.

Let’s add these up:

– any club gives the nut flush. There are 13 clubs and 5 are already in play, leaving 8 possible outs for the nut flush [8 outs];

– any 10 gives you a Queen high straight, although you would split the pot with Villain 1. There are two 10s in play already, meaning there are two additional outs [2 outs];

– any Ace gives you top pair. There are three Aces left in the deck so that’s another 3 outs [3 outs];

– any Queen gives you top pair with the highest kicker BUT any Queen also gives Villain 2 a Queen high straight, so you don’t benefit from hitting either of the 2 Queens left in the deck [0 outs]; and

– we have already counted the 10s that give rise to a Queen high straight but we have only just seen a flop. We still have the turn and the river to come, meaning we could pick up an Ace high straight if we manage to scrape a 10 and a King over the next two cards. Unlikely, but possible. We have already counted the 10s but we can now count the 3 remaining Kings. Yes, there are 4 Kings remaining but we counted the King of Clubs when considering the nut flush [3 outs].

If we add these up we have:

Nut Flush + Q.high Straight + Top Pair + A.high Straight
= 8 + 2 + 3 + 3
= 16 outs

I had assumed this to be correct but I haven’t yet seen anyone else replying with the same answer. If it wasn’t for the fact PokerStars followers tend to be pretty switched on I would be feeling fairly smug right now but, as it stands, I am starting to doubt my answer.

The majority of replies say there are only 13 outs but I would argue these people have missed the possibility of an Ace high straight and failed to count the three kings. (Or they have failed to realise there are still two cards to come, but that’s essentially the same thing)

Am I missing the point or am I having a rare moment of Poker enlightenment?