Let’s say you’re playing a variation of Deuces Wild. Assume you are asked to look at the following two hands: Q♠ J♠ K♦ T♦ 4♠ and Q♠ J♠ K♦ T♦ 3♠. Assume further that you are told that in one of the hands you hold Q♠ J♠ and the other one you throw all five cards away. The question is which is which? And why?
For those of you wondering why the 4-card straight QJKT isn’t held on these hands, this game is a variety of Double Bonus Deuces Wild — where you just get your money back for 5-card straights. In these games, 4-card straights are never held. For those who simply must know (it actually isn’t important), the actual variation I am referring to is where straight flushes return 12-for-1 and returns 99.81% with perfect play. But having never played the game is not a sufficient reason to not get the answer to the puzzle correct. And, surprisingly, even players who play this game all the time will not have an easier time answering this puzzle than those who have never played the game before.
This is a very close play — too close to be on all but the most complete strategy cards. Players whose philosophy is to learn strategies without understanding the nuances behind the strategies have little chance to get this correct.
For players new to penalty cards, the difference between Q♠ J♠ K♦ T♦ 3♠ and Q♠ J♠ K♦ T♦ 3♥ is much easier to explain. The 3♠ is a “flush penalty” to holding Q♠ J♠ because it makes it harder to make a flush simply because there are fewer spades still in the deck when we throw one away. A flush penalty in this particular case is worth about 4.6¢ to the 5-coin dollar player. But the problem today has nothing to do with flush penalties. It doesn’t even have anything to do with the value of Q♠ J♠. In both hands presented in the first paragraph, the value of Q♠ J♠ is $1.48135.
Do you find it surprising that the difference in the play of the hands has nothing to do with the value of Q♠ J♠? After all, we said that in one case we held Q♠ J♠ and in the other case we threw everything away. If it’s not about the value of Q♠ J♠, what could it be about?
It’s actually about the value of drawing five new cards. In games involving a 52-card deck, there are more than 1.5 million combinations of cards that you can draw when you throw away all five cards. This time, it includes two chances for a royal flush (namely clubs and hearts). You can’t get a royal in either spades or diamonds this particular time because at least one royal card in each of those suits was originally dealt, and if you throw it away it’s not going to be coming back on the same hand.
There is a theory I call “Power of the Pack” that Liam W. Daily and I first wrote about in our Winner’s Guides series. We used the term “pack” to represent the 47 cards remaining after the initial five cards were dealt. We used the term “deck” when we were referring to all 52 cards.
In Deuces Wild, consider the continuum AKQJT9876543. Notice it does not include the deuce (which is wild). In non-wild games the continuum is AKQJT98765432. Since the ace can be high or low, sometimes the continua are extended to include the ace at the bottom. There’s a reason I don’t do this, which will be discussed later.
In general, when cards are at the extremes (i.e. 3 is more of an extreme than a 4 — A is more of an extreme than a K) the value of drawing five new cards goes up. You should verify this for yourself. Go to ANY Deuces Wild pay schedule on your computer and enter in a random hand including a single 3 but not a 4. Write down the value of drawing five new cards. Then change that 3 to be a 4 and write down the value of drawing five new cards. You’ll see the value has gone down.
This is all that has happened here. It was a close play between Q♠ J♠ and drawing five new cards and changing the 4♠ to a 3♠ was enough of a difference to move the value of drawing five new cards from barely below the value of Q♠ J♠ to barely above. This is not something any of us can figure out in our heads, but when you do see it, now you know why.
For players who attempt to play perfectly, this kind of Power of the Pack distinction is not such a rare event. In Full Pay Deuces Wild, for example, compare K♣ Q♣ 3♥ 4♠ 6♦ with K♣ Q♣ 3♥ 5♠ 6♦. After understanding today’s article you should have no trouble deciding in which hand you should hold K♣ Q♣ and in which case you should draw five new cards.
In NSU, a similar difference may be found comparing K♦ Q♦ J♣ 7♣ 3♦ to K♦ Q♦ J♣ 7♣ 4♦. Or K♥ T♥ A♠ 9♠ 5♥ (correct play: draw 5) versus K♥ T♥ A♠ 9♠ 8♥ (correct play: K♥ T♥). Hopefully you recognize 5♥ as being more extreme than the 8♥.
The Power of the Pack isn’t limited to drawing five new cards. In Deuces Wild it can explain drawing however many non-deuce cards are needed. In Full Pay Deuces Wild (where W indicates a wild card — specifically a deuce), the difference between W W W T♥ T♣ and W W W 9♥ 9♣ is a Power of the Pack consideration, although in this case we are looking at the potential to end up with a wild royal flush. (Even though it doesn’t change the play, the value of drawing to three deuces is quite a bit higher from W W W 3♥ 3♣ and W W W 6♥ 6♣). An example from NSU is that from W 5♥ 6♣ 7♦ A♠ we hold the deuce by itself while from W 5♥ 6♣ 7♦ T♠ we hold W 5♥ 6♣ 7♦. This is a Power of the Pack consideration because the A is far more extreme than the T.
If we changed one of the original hands to Q♠ J♠ K♦ T♥ 3♠ from Q♠ J♠ K♦ T♦ 3♠, we would have found that the play goes from Q♠ J♠ to draw 5 new cards. How is this case different? (Try to answer it for yourself. It’s much simpler than the earlier question.)
The difference here is that throwing the T♥ away instead of the T♦ kills the chances for a royal flush in hearts. Now there would only be one chance out of 1.5 million to get a royal rather than two. That’s enough to change the play! And this is the reason that I include the ace only at the top end of the Power of the Pack continuum. Compared to a king, the ace is more extreme. compared to a 3, it is more extreme but there are also royal considerations.
I don’t expect any recreational player to concern himself very much with these factors. Most professional players don’t either. But I do. Including the Q♠ T♠ K♦ J♦ 3♠ variation of the same hand it costs an eighth of a cent to hold the two honor cards and it happens every 108,290 hands. In and of itself this is way too miniscule to worry about — even for me. But there are LOTS of these hands. Along the way to learning to distinguish between these fine points, I practice all of the not-so-rare hands a lot too. This makes it less likely I’ll be making mistakes that are not so miniscule.