So, yeah, the Savant Deck. Murphy’s is now hawking a gaff deck from Craig and Lloyd whose core purpose is to make you look like a mathematical genius or a Grandmaster of Memory (as they call them in the competitive memory sports arena). And, you know what? I don’t mind it. It’s a plot that deserves a little more attention, given that there are a lot of fun things you can do with it presentationally if you choose not to go down the easy “human calculator” route. Plots where you are temporarily given the ability to think faster via some meditation or an experimental hypnosis technique involving perfectly timed flashes of perfectly colored light. Plots where you can discern the values of cards by the differing magnetic forces of the ink in them. There’s some room here for creativity, and a deck that does most of the work for you so you can just play in that space is worthwhile.

On the other hand, it’ll run you 35 bucks, or else an hour or so making up the gaffs yourself if you don’t need the tutorial and want to customize it using your favorite deck. And either way, I lay even odds you’re just going to toss the deck in a drawer after only a couple of performances. So, in the spirit of offering alternatives, I’m offering you a way to perform an effect very similar to the basic Savant Deck trick using just a regular deck of cards.

Of course, thanks to a four-month delay in posts being published here (Quoth the editor: “Shut up about publishing posts. My shoulders won’t massage themselves!”), I’ve been scooped by Andy over at the Jerx. Our methods are completely different, so right up front, before we even get into my method, I’ll give you a little chart comparing the pros and cons of all the Savants, with the best option for each category highlighted:

(Sorry that this looks bad on mobile.)

	Savant Deck (Barnes and Petty)	Idiot Savant (Jerxmann)	21 Savant (Franklin)
What kind of shuffle can be done?	Riffle or multi-packet table cut	Any	Riffle, rosette, or faro
How many times can the participant(s) shuffle?	Any number	1	1
When can shuffling be done?	Anytime	At the beginning	Anytime
How much of the deck does the participant shuffle at once?	Whole deck	Packets	“Whole” deck
Who cuts the deck for the shuffle?	Participant	Magician	Magician
How long does it take to set-up/reset the deck?	Instantly	Time-consuming	Time-consuming
Is the deck examinable at the beginning?	Yes	No	Yes
Is the deck examinable at the end?	Yes	Yes	Yes
Is the deck a normal 54-card deck?	No	Yes	No
How many phases can be done?	Any number	1	Many
How many cards can the participant cut off?	Any number	Any number (within a range)	Any multiple of 6
Does the magician need to see how many cards were cut?	Yes	No	Yes
What information does the magician need to know to compute the sum?	Number of cards	Value of card cut to	Number of cards and sometimes number of high cards
How many steps does it take to compute the sum?	2	3	0-3+
Does the magician need information about the values of the summed cards to compute the sum?	No	No	Sometimes
Does it cost more than a deck of cards?	Yes	No	No

In short: Savant Deck is clearly the most commercial product with its instant resets and infinite repeats in exchange for restricting shuffles. Idiot Savant allows the most freedom in shuffling style in exchange for having to be a bit more cagey with the handling at the start of the effect. And the method presented below falls somewhere in between on both counts.

One Possible Presentation

Having done something bizarre to “temporarily heighten your mathematical abilities,” you shuffle and display a deck. From this deck that’s clearly been shuffled, you deal six cards face-down around a table. Together, you and a participant turn all six face up as quickly as possible. Within two seconds, you report the sum of the cards. With the help of a calculator if necessary, the participant checks the sum.

Next, you turn away and stare at your watch while the participant starts dealing cards face-up around the table. You shout “Stop!” and then turn around, glance at the table for two seconds, turn away again, then report the sum of the cards. Once again, the sum checks out.

“Now, I have to admit, I did accidentally catch a glimpse of a couple of the cards near the top earlier. I promise I didn’t remember them or add them up in advance, but I want you to see that this isn’t just some memory trick.”

You display the cards again, still clearly shuffled, separate them into two face-down piles, and ask the participant to push them back together, randomizing the order. Again, you turn away while they deal cards face-up, but this time you let them deal a lot more. Once again, you stop them, turn around, and, after a couple of seconds, report the sum. Everything, of course, can be examined.

The Core Method

The deck is, of course, stacked. The stack looks very random (and kind of is) and so can be freely displayed. But stacked it is.

And the central property of the stack is that in every group of 6 cards, the sum of the card values is equal to 7(3+h), where h is the number of high cards (cards greater than 7).¹ So, all you need to do is make sure six cards are dealt, count how many high cards there are, add 3, then multiply by 7.²

Now, what about that participant shuffle? Well, actually, we’re going to start with the part of the stack at the bottom of the deck reversed. That way, as long as we split the deck at the place where the two stacks meet, they can be riffled or rosette shuffled together and, thanks to the Second Gilbreath Principle, the property will still hold for every group of six cards starting from the top of the deck.

So, for the effect described above: in phase one, you deal six cards. In phase 2, you stop the participant after dealing six cards (by listening to their deal). And in phase 3, after they shuffle, you stop them after dealing 12 cards.

Twelve cards? Well, it turns out that we can ensure that the sum of 12 cards will always be 84, so there’s nothing here to calculate. But we’ll get to that when we talk about the stack.

Examples

Before we do that, let’s work some examples.

In this example, there’s only a single high card, so the sum must be 4*7=28.

In this example, there are three high cards, so the sum must be 6*7=42.

Of course, as mentioned previously, the sum of 12 cards will always be 84.

Now let’s look at how I stacked a deck to produce deals like these.

The Stack

To construct the stack, remove the Jokers and the 7s from the deck. Yes, you won’t be playing with a full deck.³

Make six piles of 8 cards each. The first pile contains the Aces and 8s. The second has 2s and 9s. And so on up to the sixth pile which has the 6s and Kings. Make sure that within each pile, the values alternate low-high-low-high, but the suit order should be randomized.

Pick up the packets in a random order. Deal this deck out into 8 piles and stack them up again in order.

At this point, you’ll have alternating groups of 6 high cards, then 6 low cards, always in the same order numerically. (Or maybe 6 low cards then 6 high cards—either is fine.) So if you were to leave the deck like this, dealing 6 cards at a time would give you alternating sums of 21 and 63. However, you can cut a few cards and get a different pattern: alternating 28 and 56, alternating 35 and 49, or even a sum of 42 for every set of 6. Go ahead—it’s your life!

Finally, turn the deck face-up and deal 18 cards into a pile, thus reversing the order of the bottom 18 cards. Memorize the card that is on the bottom of the deck after this deal before dropping the dealt pile back on top of it again. This memorized card marks the place where the two stacks meet. You will cut the deck below it when offering it to the participant to shuffle.

The end result might look something like this:

It looks pretty random, right? If you stare at it, you might notice a 12 card repeating pattern that stops at the Jack of Spades and is reversed below that, but no one will notice that. So if you start your performance with a few false shuffles and then openly fan out the cards for your participant to see, they won’t have any reason to believe they aren’t, in fact, fairly shuffled.

Alternative Procedures

1: Participant Cuts

What if you don’t want to have to cut for the participant before they shuffle? Try this: Skip the last step of the setup so that the bottom of the deck is not reversed.

In phase 1, have the participant cut to a random spot and deal face-down into your hand while you close your eyes and look away. Stop them after six cards, turn them over and fan them towards you, calculate, and immediately report the sum. Drop the fan on the table, careful to preserve the order, and have the sum checked.

In phase 2, have them continue dealing (this time without a cut), but stop after 12 cards. Continue as before, though of course, this time you already know the sum without looking.

Gather up the two fans, stack them with the first smaller fan going on the face of the larger fan, and turn them face-down. Ask the participant to set their pile next to your pile, and set up a rosette shuffle for them.

Do one more phase as before, but with 18 cards this time.⁴ This way, despite all 3 phases working identically, each looks more difficult than the last. Or, if that’s too much dealing for you, use 12 cards dealt again, but do something completely different for the third phase.

2: Only the High Cards

For example, have the participant deal 12 cards, tossing the low values out face-up and keeping the high values hidden “to make the sum as difficult as possible”. Starting from 84, subtract the cards you see as they are tossed out. Once they stop dealing, you can have them flash the hidden cards for less than a second, and then immediately report the number you already computed.

3: The “Free” Cut

Holding the deck, ask the participant to cut off about half of the deck. Have them count the cards by dealing to the table.

If the number of cards is 24 (exactly half), you know the total is exactly 168. If they cut, say, two cards past 24, have them spread the cards face-up. Glimpse the back two cards and add their values to 168. If they cut, say, two cards short of 24, either peek the top two cards of the deck and subtract them from 168, or just bluff: “Oh, I bet I can do better than that. Here, take a few more.” And then hand them two more cards to make it total exactly 168.

If they cut wildly off of halfway, improvise so that you only have to sum a multiple of 12 cards. For example, if they count to 29, pick up the last five dealt and turn them over. Challenge them to add those as quickly as they can. (See next subsection.) And now you know the face-down ones sum to 168.

Note that if you do this handling before the participant shuffle, the counting of the cards will reverse them just perfectly for shuffling them back in for another phase.

4: Race the Participant.

Have the participant deal out two piles of 6 cards. Then, you let them choose a pile.

Then you let them go first. Have them add up the cards they picked, estimate how long it took, and then check the result with them. Once you know the result, subtract it from 84. You can do this mentally while they’re double-checking their work or entering it into the calculator.

“Know that I’m not cheating here. You were the only one who saw these cards as you were separating them out. This will be my first time seeing them.” Then spread out the other pile face up and instantly say the number you precomputed. And, almost as an afterthought, report the original sum: “Oh, and when I add that total to yours, I get 84.”

5: Thought Reading

Hand the participant 6 cards from atop the deck. Ask them to look at them and secretly pick one. Then, while carefully studying the wall rather than the participant, do something like the following:

“Is your card high—seven or higher—or low—six or lower?”

“Low.”

“In that case, name all the high cards in your hand—just the values, ignore the suits.”

“A Queen and an eight.”

“Alright, name all the low cards in your hand that are a different color than your card.”

“A six and a four.”

“Interesting, so there’s only one low card that’s the same color as yours. Which is it?”

“A three.”

“Now, I haven’t seen any of those cards, of course, but I now know all of them except for the one you’re thinking of. And based on the ones you declined to choose, I bet you picked the very lowest card. You picked a two, didn’t you?”

(In case it’s not obvious, the calculation here is (3+2)*7=35 minus 20 (the Queen and the eight) is 15 minus 10 (the six and the four) is 5 minus 3 is 2.)

Conclusion

Craig and Lloyd are really onto something with popularizing this sort of plot again. There are so many things you can do with these ideas, so I would suggest giving this gimmick-free methodology a spin in the real-world a couple of times to see if this kind of trick jibes with you. If you really enjoy it, then it might be worth your time and money to grab a Savant Deck and benefit from the added flexibility it yields. After all, the Savant Deck does allow arbitrary riffle shuffling, and allows you to do any trick that makes use of a key card, not just this value-summing plot, and it also allows easy forcing of any multiple of 13 if you need a number for something, not just 84.⁵ But if none of this seems like your thing, then you can thank me for limiting the rate at which you fill your junk drawer.

1. You’ll note that you could also compute this as 21+7h, hence the title of this post. Nothing to do with any public figures. ↩︎
2. If you pencil dot the corners of all the high cards in the deck, you could actually pre-compute the sum in advance of turning the cards face-up. And then afterwards, use the same deck to demolish your friends at blackjack. ↩︎
3. Actually, you could also do this trick using a 56 card deck too. Add two more Jokers, pairing the Jokers with the 7s when you’re setting it up. The only other differences are 1) you’ll have them deal groups of 7 cards instead of six; and 2) you’ll reverse the bottom 21 cards when constructing the stack instead of the bottom 18. For the calculation, you’ll consider 7 as a high card. I don’t do this version because having cards worth nothing (the Jokers) only makes the sums look easier from the participant’s perspective. ↩︎
4. You only need to do the usual calculation for the back 6 cards. The other 12 you already know add to 84, so just add that to the result. ↩︎
5. Of course, if you need to use cards to force a number, you could also consider the Number Forcing Stack. ↩︎