Pocket Rockets Killer?

Imagine the following scenario:  you are on the bubble in the World Series of Poker Main Event and, for some reason, you let your chip stack get so low that you are now all-in in the big blind.  If you are eliminated right now, you go home with nothing.  Win the hand and you will almost assuredly outlast one more player to make the money and pocket at least $20,000.  Everybody folds to the small blind, who, for the puny cost of one more small blind, officially puts your tournament life on the line.  Your heart sinks as he flips over pocket Aces.  You haven’t looked at your cards yet. 

What do you want your hole cards to be?

The absolute novice would probably think for a tenth of a second and say, “Pocket Kings!”  After all, that is the next best hand to Aces.  But after a moment of thought, most any person who has played the slightest bit of poker would realize that this is the wrong answer, as Kings only have two direct outs to beat Aces (I say direct because, of course, the Kings could still turn into a straight or flush with the right four cards on the board). 

Let’s move on, as I have spent way too long on a clearly incorrect hole card choice.  Without much more analysis, most players should eventually come to the realization that suited connectors, while still a big underdog to Aces, would be a good hand to hold.  With suited connectors, you can make straights and flushes that could beat the Aces, even if your opponent hits a set.  Of course, you also have a chance to hit two pair, three-of-a-kind, and other winning hands.  But which connectors?  K-Q sounds reasonable at first, since they are high cards, but in reality, the Aces take away straight possibilities from that hand and other cards that would help (T-J-Q-K) could also help the Aces make a straight (this is also why there are smaller pairs that would have a better chance than Kings to beat Aces). 

So, we’ve narrowed it down to middle or small suited connectors – the ones that are the least dependent and least affected by the two Aces that are gone.  Everything from 5-6 through 9-T is fairly similar, with each pair of hole cards giving you approximately 22% equity against pocket Aces, when rounded to the nearest percent.  When we look further, it turns out that 5-6 suited just barely nudges out 6-7 for the best hand to have against pocket Aces.

The difference is negligible, and for all intents and purposes, virtually non-existent, but it’s there.  After running the hands through a simulator over one billion times, we find that both will beat pocket Aces 22.29% of the time.  Technically, 6-7 will win slightly more often, about .0023% more, because the two Aces that are already used take away straight outs from the 5-6, but this difference is so small it’s silly.  The real difference, and remember, this is still a minute difference, is in the tie percentages.  5-6 suited has a .21% chance to tie A-A, while 6-7 suited “only” has a .18% chance.  Therefore, because the gap between ties for the two hands is significantly greater than the gap between wins, 5-6 suited has the better chance of surviving the all-in confrontation with Aces.  In the end, 5-6 suited has 22.499% equity against A-A, all-in pre-flop, with no other players in the hand.

But why does 5-6 tie more often than 6-7?  Because of the straight combinations.  There are seven combinations of five community cards that would put a straight on the board and result in a chopped pot between 5-6 and A-A: 2-3-4-5-6, 3-4-5-6-7, and so on, through 8-9-T-J-Q.  All of these would also result in a chop between 6-7 and A-A except for 2-3-4-5-6, because that board would give you, with 6-7, a higher straight than your opponent.  Because there are only six straight board combinations for 6-7, compared to seven for 5-6, the probability is lower that 6-7 will chop with A-A than it is for 5-6.

Additionally, amongst the straight boards that the 5-6 and 6-7 have in common, two of them (6-7-8-9-T and 7-8-9-T-J) are less likely to occur for the 6-7 hand because either one or both of the cards required have already been dealt.  Thus, the chances of chopping with 6-7 are further reduced.

So what does this all mean?  It means that you should definitely go all-in with 5-6 suited against pocket Aces!  Just kidding.  You will still be a huge underdog, with just over a 22% chance to survive the confrontation.  But if you knew you were against only one player, that player had Aces, you had to put all your chips on the line pre-flop, and could choose any two hole cards you wanted, 5-6 suited would be the hand of choice.