This is an interesting hand that can be played in Hold ’em poker, either limit or no-limit, which I’ve not read about in all of the poker books I own, but I think many players use it sort of intuitively if for no other reason than a King’s involved. What I’m talking about is a hand of King-something that is suited (usually shown as K-xs, with x standing for any other cards and the s meaning suited). Obviously, K-Qs is a good hand that can be played almost any time – but understand I’m not talking about K-As here – that’s an A-xs hand, not a King hand. What I’m mainly going to talk about is K-Q suited and lower, all the way down to K-2s.
It’s obvious that K-xs will make the second-best flush available for any suit, which is the basis for this article. Naturally, if you’re up against A-xs of the same suit or even just the Ace of your suit, the probability of losing a big pot is pretty high, should three or four cards of the suit in question appear on the board. It’s only by understanding the various odds in this situation can we make an intelligent decision on playing this hand, so that’s what I’ll cover.
A hand of K-xs can turn into a nice trapping hand, particularly against all of those “Ace huggers” out there who will play A-x offsuit as though it were A-A or A-K. Consider this: Your opponent limps with, say, Ac-6d and several other players limp in as well. Let’s further say you’re in the Big Blind with Kh-8h and call. (If your hand is Kh-10h or better, you’d likely raise; I know I would). But with K-8 suited, you’re just happy to see a cheap flop and let’s say it comes As,10h, 5h. Your opponent has hit top pair with a poor kicker and, if they’re smart, they’ll bet out because that might win the hand straight away, plus they want to charge those on a flush draw (namely us) a higher price. Of course, the “Ace hugger” is, or should be, aware that other A-x hands may be out there (see Lesson 25 for the probabilities on that), so their lower kicker might slow them down some and they’ll just check to see where they stand. Either is okay for us, so long as any bet made isn’t too big because we now have a 35% probability of completing our Flush. It may not be the nut flush, mind you, but the odds of us ending with the 2nd best flush can also be calculated, which I’ll show you in a bit. For now, let’s continue with the hand.
Okay, various bets are made and, so long as the pot is offering you at least 2 to 1 on your $$$, you can proceed, especially when you consider the “implied” odds of this hand as I envision it playing out. Let’s say the Ah comes on the turn, thus giving you the nut flush and your opponent trip Aces. While your opponent knows s/he may be up against a flush and you know s/he could make a full house if the board pairs, do you really think either of you is going to fold on the river? That’s why the implied odds are so big for this hand, assuming your opponent has a stack size equal to or larger than yours – one is going to bust the other, most likely – and you’re the favorite at this point with a probability of 77%. Your opponent has some outs, of course: one Ace, three 10s, three 6s and three 5s. With 44 cards remaining, those 10 outs make a 23% probability, so you’re not home yet but it’s looking good. Should the board pair on the river – that is, a 10 or 5 falls, you might be able to get away from the hand, but if a 6 falls, lets face it; you’re toast. Actually, the best thing that could happen would be for the fourth Ace to fall on the river. Because you don’t have a pair, you can pretty well figure your hand isn’t the best and fold with good conscience.
Through the magic of the written word, I made this hand easy by having the Ah fall on the turn, but if your luck is like mine, that’s not going to happen so we must rely upon the basic mathematics of the hand to tell us how to proceed. As usual, I turn to Excel at times like this, so let’s do a little review of how it can be used in this situation. First of all, if you hold the Kh-6h, the odds of flopping two more hearts is 10.94%. We know that because with 50 cards remaining, there are COMBIN(50,3) = 19,600 possible three-card flops. With 11 hearts (of 13) left, we know there are COMBIN (11,2) = 55 possible two-heart hands, which can combine with any of the 39 remaining (non-heart) cards to create 55 x 39 = 2145 possible flops. If you divide 2145 by 19,600, you get 10.94%. The perfect situation, of course would be to have the Ace of your suit (in this case, hearts) and another card of that suit come on the flop, so you know you have a nut flush draw. (If all three flop cards are of your suit, you probably won’t make a lot of $$$.) Unfortunately, the odds of the Ah-xh coming on the flop are pretty small. Flopping two more cards of your suit is a 10.9% probability, but for one of those cards to be the Ace, the probability drops to just about 1%.
The odds of seeing the Ah come on the turn, if it didn’t come on the flop is 1 of 47 or 2.12%; any heart on the turn is 11 of 47 or 23.4%, which will give you a made flush but not necessarily the nut flush. Assuming no hearts fell on the turn, there are nine of them left in the deck when the river card is dealt. Because we’ve seen six cards to this point (our two pocket cards, the three cards on the flop and the turn card) that means 46 cards remain to be played. Nine of those are hearts if we haven’t already made our flush so the odds of hitting the Ace of hearts on the river is 1 of 46 or 2.17% and the odds of hitting any heart is 9 of 46 or 19.56%.
The probabilities of making a flush on the turn or river might not look all that important, but they give us the means to calculate the odds of a “loss” out, something you don’t see mentioned in most poker books. A loss out (or, as one author who does talk about in his book calls it, a “dout”) comes into play here because while you’d like to see just three more hearts come on the board, if a fourth hits and your opponent is holding the Ace of hearts instead of the Ace of clubs, s/he now has the nut flush! Let’s say you made a flush on the turn, which obviously places three hearts on the board. If your Ace-hugging opponent has the Ace of hearts, we know there are eight hearts remaining but your opponent believes there are 10 left, because s/he cannot know what cards you hold. From your opponent’s point of view the odds of making a flush on the river are 10 of 46 or 21.74%, but we know it’s actually 8 of 46 or 17.39%. A good average to use in the “heat of battle” is 20%, which means your opponent must be getting pot odds of 4 to 1 for betting the draw to be a proper play. (Understand? if s/he bets $10 five times for $50 in total action and loses four of them, the loss is $40. If the fifth hand wins $40, it’s break even.) In a limit game, the pot odds could easily be that high. But in a no-limit game you can destroy the pot odds for such a draw by
making a pot-sized bet and that will give your opponent only 2 to 1 odds
for what we know is a 17.39% probability, which is a 4.88 to 1 shot, to be
I’m getting ahead of myself here, because the reality is that most of the time you won’t have a flush draw and you could very well be up against an A-x, so your hand will have to improve in order to win. Preflop, a hand of Kh-8h versus Ac-6d has a 44% chance of winning or odds of about 5 to 4 against, which isn’t that bad. Pot odds of 1.25 to 1 or better make getting involved worth the risk, but the real story will come on the flop. Here are some probabilities of improving a hand of K-8s on the flop, along with the Excel formulas for calculating them:
|Three more flush cards flop:||0.84%||=COMBIN(11,3)/19600)|
|Two more flush cards flop:||10.90%||=COMBIN(11,2)*39/19600|
|Make Full House (K, K, 8 flops):||0.045%||=COMBIN(3,2)*3/19600|
|Make Full House (K, 8, 8 flops):||0.045%||=COMBIN(3,2)*3/19600|
|Make Trips (K, K, x flops):||0.73%||=COMBIN(3,2)*48/19600|
|Make Trips (8, 8, x flops):||0.73%||=COMBIN(3,2)*48/19600|
|Make 2-pair (K, 8, x flops):||2.02%||=PRODUCT(COMBIN(6,2)-(6),44)/19600|
|Make a high pair (K, x, x flops):||16.22%||see comments below|
|Make a low pair (8, x, x flops):||16.22%||see comments below|
(Comment on the formula for making a pair on the flop: The three remaining Kings will combine with the other 47 cards left, which is shown as
=3*COMBIN(47,2) or 3243 flops out of the 19,600 that are possible. This does not calculate to 16.22% because some of the flops will be KKx, which are obviously Trips and one will be KKK, thus giving you four Kings – you should be so lucky. Anyway, those other hands should be subtracted but it makes for a very complicated formula that shows a probability of 16.22%.)
The only way I would continue playing aggressively with the hand is if I were to make two-pair or one of the “made” hands like a flush or full house. Remember, a pair of Kings or 8s alone probably won’t win this hand, so I’d be more in a check-and-call mode with those and a 4-card flush draw. Naturally, every hand is different and a lot depends upon how you view your opponent(s), but easy does it seems to be the best play unless and until you’re sure your hand is best. After the flop, you’ll have a 16.5% chance of improving two-pair to a full house, a 35% probability of making a flush from a 4-card flush draw and an 8.4% probability of turning a pair into Trips if you stay in the hand all the way to a showdown. Depending upon what the board looks like after the turn card is dealt, you need some pretty big pot odds to stay in and I cannot cover every possible situation here. If you miss the flush on the turn, you’re down to 9 outs from the 46 cards remaining or a 19.5% probability, like I talked about before. If I had at least a pair, be they Kings or 8s, I’ll have 6 outs (13% probability) for Trips, which calls for 7.5 to 1 pot odds. If I have a pair and a four-card flush, my combined probability is 32.5%, assuming I feel trips or a flush will win the hand. All that takes is 2 to 1 pot odds for me to call. If I get those odds, I’m calling, otherwise I’ll probably fold.
For what it’s worth, I began thinking about this play – the King’s Gambit – after I found myself with K-2 suited in the Big Blind at the final table of a multi-table tournament.
I was the short stack (as usual) and the player to my right, the big stack at the table, was making just the minimum raise with A-x; at least that’s what he had when he knocked out two other players. I pegged him for an Ace hugger in earlier matches (I take a lot of notes wherever I play), so when he min-raised again while on the Button, I called from the Small Blind with Kd-2d. Well, as luck would have it, the flop came Ad, 6h, 9d. I checked and he made a big bet – about 2 times the pot, which I called more out of desperation than anything else. The turn brought the 3d, giving me the nut flush. He went all-in and I naturally beat him into the pot. He had As-6s for two-pair, but didn’t improve on the river so I took a nice chunk of his chips. I later went out in third place, but you can’t win them all.
I’ll see you here next time.