The Omega Bet
By Matt Baker - Wednesday, January 13, 2021
The Omega Bet is a delightfully devious mathematical magic concept devised by Karl Fulves. In this post, I’ll explain what the Omega Bet is, discuss why it works (including its relationship to the Gilbreath Principle), and then teach an original routine based on it.
The Omega Bet: An Interactive Explanation
Go grab a deck of cards. Oh wait, you’re a magician, so you already have one within arms reach - perfect! Take out 6 red cards and 6 black cards and alternate them R-B-R-B-R-B-R-B-R-B-R-B in a face-down pile on the table.
Now take the top card, turn it face-up, and insert it wherever you like into the middle of the face-down packet. Pick up the packet, hold it in dealer’s grip, and begin dealing the cards in pairs onto the table. Keep going until you reach the pair which contains the card you inserted; place this pair, consisting of a face-down card and a face-up card, in front of you. We know that the face-up card is red, but what about the face-down card?
Matt the Magnificent will tell you: it’s black.
Take a look, and then shout at your screen, “How did you know that, Matt?”
It’s math, silly. Here’s one way to understand why it works. Once you remove the top (red) card, the packet looks like this: B-R-B-R-B-...-R-B. Turn the card you removed face-up and insert it somewhere in the middle. When you deal the cards in pairs onto the table, all the pairs you deal off BEFORE you reach the one containing the face-up card will be B-R. Suppose you’ve now gotten to the point where the NEXT pair is the one containing the face-up card. There are two possibilities: (1) the top card (of what remains of the packet) is face-up; or (2) the card second from the top is face-up. Let’s consider each of these cases separately.
In case (1), the top (face-up) card is the one you inserted, and the next (face- down) card is the one which came AFTER the previous B-R pair in the original packet. Since it came after a red card, the face-down card must be black.
In case (2), the top (face-down) card is the one which came after the previous B- R pair in the original packet and the next card is the (face-up) card you inserted. Therefore the face-down card is black in this case as well.
Here’s a slicker way to see why this works. Suppose we deal the WHOLE PACKET out into pairs. It’s pretty much obvious that every pair EXCEPT for the one containing the face-up card consists of one red card and one black card, because the cards in any such pair were consecutive in the original packet. But since we started with the same number of red and black cards, the pair containing the face-up card must ALSO consist of one red card and one black card.
The Omega Bet and the Gilbreath Principle
Here’s a THIRD way to understand why the Omega Bet works (mathematicians love explaining the same thing in multiple ways). If you’re a regular reader of this column then you’re already an expert on the (First) Gilbreath Principle. If not, here’s an executive summary: If a deck consisting of an even number of cards with alternating colors is cut so that the bottom cards of the two piles have OPPOSITE colors, the two halves are riffle-shuffled together, and then the cards are deal out in pairs, each of these pairs will consist of exactly one red card and one black card (though not necessarily in the same order each time).
What does this have to do with the Omega Bet? Well, one way to cut the deck so that the bottom cards of the two piles have opposite colors is to cut off just a SINGLE card. And what happens when you riffle shuffle one card into a larger packet? It’s the same as simply inserting this card somewhere into the packet. Now imagine that we turn this single card face-up before inserting it. This is precisely the situation of the Omega Bet! Gilbreath’s First Principle therefore implies what we’ve already seen through different reasoning: if we deal the cards out in pairs, each pair will consist of one red card and one black card. In particular, the special face-up/face-down pair will have this property.
I’m a decent mind reader, but I can’t quite tell what you’re thinking right now. You might be thinking “Wow, that’s super cool”, but you also might be thinking “That doesn’t seem like a very good magic trick.” In either case, though, you’re correct! It IS super cool, but as just described it’s a rather lame trick.
First of all, you knew that the cards started in alternating red-black order, because I had you stack them that way! If you want to use this in an actual card trick, you’re probably going to want to keep this little detail a secret. (Think of the difference between Out of This World as it’s meant to be performed and Out of This World where you know in advance about the red-black separation...)
Second, the procedure as presented so far is rather unmotivated — why are we turning the top card face-up and sticking it in the middle? And why do we deal the cards in pairs? Karl Fulves’s idea was to present the routine as a wager. In his own inimitable words: “Properly presented, this wager will establish your reputation as a master of betting games.”
Finally, if you just do it once, the Omega Bet is merely a 50-50 proposition. In order to make it feel magical, you’re going to have to repeat the wager multiple times. Therefore we’re going to need some variations on the basic procedure, as well as a dramatic structure which builds tension and excitement. I’ll present a few variations first, and then I’ll describe a routine designed with theatricality and entertainment in mind.
Some Variations
Variation #1: Do the same thing, but use the bottom card instead of the top card. This time, the face-down card will be RED. (Note that in both the original method and this variation, the face-up and face-down cards in the special pair have opposite colors.)
Variation #2: Deal the top card to your left and the next card to your right. Now spread the rest of the packet face-down. Ask a participant to pick up either one of the cards you set aside, turn it face-up, and insert it somewhere into the face- down spread. Close the spread, pick up the packet, and go through the Omega Bet procedure, dealing the cards to the table in pairs until you come to the pair containing the face-up card. If the participant picked up the card to your LEFT, the two cards in this pair will have the SAME color; if she picked up the card to your RIGHT they’ll have OPPOSITE colors. This is interesting, because it means you can predict the outcome of the wager but the outcome changes depending on which card the participant chose.
Variation #3: Deal the top card to your left and the next card to your right. Now spread the rest of the packet face-down from right to left. Have one participant pick up the card to your left and have another pick up the card to your right. Instruct the first participant to insert their card face-up into the left-hand portion of the spread (from your point of view), and have the second do the same but into the right-hand portion. Close the spread, pick up the packet, and go through the Omega Bet procedure, dealing the cards to the table in pairs until you come to the pair containing the first face-up card. Set this pair aside and then continue dealing the cards in pairs until you come to the pair containing the second face-up card. Set this pair aside as well. If you inspect the two pairs which were set aside, you’ll find that each of them consists of cards of the SAME color. However, had you spread the cards from left to right instead of right to left, you’d find that each of the pairs which were set aside consisted of cards having OPPOSITE colors!
There are many other variations possible, but hopefully you’re starting to see that there the Omega Bet procedure is flexible enough that it should be possible to do some pretty interesting card magic with it.
A Routine for The Omega Bet
The first performance I ever saw of The Omega Bet was on Geoff Williams’s excellent DVD set “Miracles for Mortals”. I was immediately enchanted by the possibilities. Geoff’s routine for the Omega Bet is based on a five-phase routine from Bob Wagner.
I like the overall structure of Bob’s routine, but I wanted to make a few changes to suit my own taste. First of all, in Bob’s routine you don’t know in advance how the first few phases will turn out — it depends on the spectator’s choices. For dramatic purposes, I wanted to be able to control this better, so in my routine Phase 1 is always a ‘Match’, Phase 2 is always a ‘No Match’, and Phase 3 is always a ‘Match’. Also, in Bob’s and Geoff’s routines (as well as in Karl Fulves’s original), the conceit is that the magician is able to correctly predict in advance what the spectator will do every time and thus wins every round of the game. Rather than presenting it as a competition between the magician and spectator, I prefer to present it as a game in which the spectator is repeatedly given a chance to win more and more money, but she continually fails. I’ve also added a new methodological ingredient to the last two phases, and I’ve incorporated a lovely procedure of Steve Beam’s to help with the clean-up after each phase.
With those preliminaries out of the way, let’s dive into the routine! I’ll first describe the overall presentation, omitting the (important) details of how to reset the stack after each phase. Then I’ll go back over everything and explain the nitty gritty details. You can, and should, frequently give the packet a false shuffle throughout the routine. There are many possibilities here, and I’ll let you decide what works best for you. However, let me suggest that a Charlier shuffle works quite well, because it’s a fairly logical thing to do with a small packet and it doesn’t matter for this routine how often the packet is cut.
Setup
Begin with an even number of cards (around 18 works well for me) in alternating R-B order on top of the deck. Make sure none of these cards is a 7. Also, make sure you have some cash in your wallet; I use two $1s, a $5, a $10, and a $20.
Presentation
“Have you heard of the game show ‘Deal or No Deal’? Well, we’re going to play a game which I call ‘Match or No Match’. We'll only use about a third of the deck.” Remove the preset stack and place it face-down in front of you; place the remainder of the deck into the card box and set it aside.
“I'll also remove some good luck cards for later, just in case we need them. But it's unlikely we’ll actually need to use them.” Look through the remainder of the deck and remove the four 7s. Place them to the side in a face-down pile in alternating R-B order.
Phase 1: “Let me demonstrate how the game works.” Place a $1 bill on the table as you ask the spectator to cut and complete. Deal first two cards together (not one at a time) face-down to the table. Spread the remaining cards face- down.
Take the top card of the tabled pair as a demonstration card, and hand the other card to the participant. Turn your card face-up and casually insert it somewhere into the face-down spread. “Your goal is to get a match.” Square up the spread, pick it up and hold it in dealer’s grip, and begin dealing the cards in pairs onto the table. Keep going until you reach the pair which contains the card you inserted. Show the spectator that the cards in this pair have matching colors.
“That’s what a match looks like. Now it’s your turn... If you get a match, you win the dollar!” Indicate that the participant should do the same thing with the card you handed to her. Repeat the procedure; unfortunately for the participant, her cards will not match. “Ooh, sorry about that.”
Phase 2: “Alright, I guess you're more of a ‘no match’ kind of person. We’ll go for a ‘No Match’ this time, and I’ll add another dollar to the pot, so if you win you'll get $2. Here, let me demonstrate what a ‘No Match’ looks like.”
Allow the participant to cut and complete. This time, deal the top two cards one at a time face-down onto the table, reverse-counting them in the process. Otherwise this phase is the same as Phase 1, except this time you will get a ‘No Match’ and the participant will get a ‘Match’. (There are some small differences in the handling of the reset in Phases 1 and 2, though — see below for details.) “Such a pity... I really wanted you to win!”
Phase 3: “Hmmm, I guess I was wrong... You seem to be a ‘Match’ person after all, so let's go back to ‘Match’. I’ll add $5 to the pot to give you an incentive to try a little harder. And to make this as fair as possible, you’ll do everything in your own hands. That way there’s no possibility for me to cheat.” Have the participate take the face-down packet and give it a complete cut under the table. Ask her to remove either the top card or the bottom card, reverse it, and place it face-up somewhere in the middle of the face-down packet. Now take the packet back from her and go through the standard Omega Bet procedure once again, being very clean and fair with the dealing of pairs. It will end up as a ‘No Match’. “Shoot, that’s really bad luck.”
Phase 4: “Maybe you just need more opportunities to win. I tell you what, this time we’ll add $10 to the pot and I’ll give you TWO chances.” Have the participant cut and complete. Deal the top two cards face-down onto the table, reverse-counting them in the process. “And this time, I’ll let YOU choose Match or No Match. Which do you prefer?”
If they say ‘Match’, flip the top card of the two-card pile which you just dealt face-up and hand it to them; if they say ‘No Match’, flip BOTH cards face-up and then hand them the face-up top card. (This is the main technical innovation in my routine; I haven’t seen this form of equivoque used in connection with the Omega Bet before.)
“Some people think I’m doing the Charlie Miller Spread Pass when I pick up the spread from the table, so we’ll do things a bit differently this time.”
Just kidding. Don’t say that unless you’re sessioning with magician friends. Instead, say, “Some people think I cheat when I spread the cards on the table. So we’ll do things a bit differently this time... I want everything to be as fair as possible.”
Begin to deal the cards one at a time into a face-down pile on the table. Ask the participant to insert the face-up card they’re holding whenever they like. Once they’ve done this, continue dealing cards face-down into the same pile. Ask the participant to pick up the remaining card (and turn it face-up if it’s currently face- down) and insert it whenever they like. After the spectator inserts the second face-up card, finish dealing through the remainder of the face-down packet as you comment on how they could have placed the cards anyway they wanted...
“You chose to go for a ‘Match’ (resp. ‘No Match’). If EITHER of these is a ‘Match’ (resp. ‘No Match’), you win all the money in the pot!” Needless to say, the participant will lose both times.
Phase 5: Have the participant cut and complete one last time. Peek the face card of the packet once the cut is made and remember its color. “I was hoping we wouldn’t have to resort to using the lucky cards we set aside at the beginning, but you’ve been extraordinarily unlucky so far so I think you're going to need them. Tell you what, I’ll add $20 to the pot, which makes $37 in total. And this time I’ll give you FOUR chances to win the whole thing! Again, it’s your choice: would you like to go for ‘MATCH’ or ‘NO MATCH’?”
You need to know which color is on the FACE of the four-card ‘lucky packet’, so peek this as you’re placing the four-card packet of 7s face-down in front of the spectator.
If they say ‘Match’, and the two colors you peeked also match, flip the four lucky cards face-up as a group. Same if they say ‘No Match’ and the two colors you peeked don’t match. But if they say ‘Match’ and the peeked colors don’t match, or vice-versa, don’t flip over the lucky packet. In either case, they take the 7s one at a time from the lucky packet; in the latter case they also flip them face-up as they do.
The rest of this phase is just like Phase 4, but with four chances for the participant to win instead of two. After they insert the four 7s, spread the packet and give them a chance to move any one of the face-up 7s either one card to the left or one card to the right. If you’ve been paying attention, you know by now that this doesn’t matter at all, but feels like you’re giving the participant one last important choice. The participant will fail four times in a row to win the $37 pot.
Place the money back in your wallet. “Well, thanks for playing ‘Match or No Match’... You didn’t win this time, but I’m sure that next time you’ll be a big winner!”
Notes on resetting after each phase
That’s basically the whole routine, other than the fact that the packet needs to be reset into alternating R-B (or B-R, it doesn’t matter) order after each phase. Since everything is supposed to appear casual and fair, you can’t look through the faces and adjust cards after every phase — you need to have an effortless way to reset.
Luckily, Steve Beam has already solved this problem for us. With Steve’s permission, here is his handling for the reset which works perfectly in my routine. It’s nearly the same handling in each phase, but there are a few small (yet crucial) differences. So I’ll explain things phase-by-phase. For explanatory purposes, I’ll assume that the participant is sitting across the table from you.
Phase 1: When you deal through the packet in pairs to demonstrate a match, deal into a pile (we’ll call it Pile 1a) on your right. Place the special pair, consisting of one face-up card and one face-down card, into Pile 1b above (i.e., closer to the spectator) Pile 1a. The remaining cards (Pile 2a) are placed down to the left of Pile 1a.
When you turn the face-down card from Pile 1b face-up to show a ‘Match’, place it face-up on top of Pile 1a:
To reset for the next phase, pick up Pile 2a, flip the face-up card which is on top of Pile 1a onto the cards in your hand, and then place rest of Pile 1a onto this combined packet. Finally, place the remaining face-up card in Pile 1b onto the BOTTOM of the packet.
When it’s the participant’s turn to play the game, the handling is exactly the same as for the demonstration phase. You should now be back in alternating order.
Phase 2: The handling for the demonstration part of Phase 2 is exactly the same as in Phase 1. However, after the demo portion, there will be two cards of the same color on the bottom; don’t worry, we’ll fix that in a minute.
In the participant’s portion of Phase 2, because there are two cards of the same color on the bottom, you can’t let the participant insert their card at the very bottom or one card up from the bottom. There are various ways to handle this restriction. One is to simply say, “Place your card somewhere in the middle”, and if they insert the card near the end just say, “I said the middle, you moron!” (or possibly a more polite variant of this).
For the clean-up, it’s basically the same as before, except that instead of placing the final card on the bottom, it goes SECOND from bottom. (I do a pinky pull- down plus a ‘bottom tilt’ move, but you really don’t need any sophisticated sleight of hand to accomplish this. Just put the damn card second from bottom.) We’re once again back in alternating order.
Phase 3: The dealing into pairs and reset in this phase are handled exactly as in the participant’s portion of Phase 1.
Phase 4: This is basically the same as Phase 1, except there will now be five piles instead of three. When you deal through the packet in pairs, deal the pairs into a pile (Pile 1a) on your right until you come to the first special pair consisting of one face-up card and one face-down card. Place this pair into Pile 1b above Pile 1a. Continue dealing pairs into Pile 2a to the left of Pile 1a. When you get to the second special pair, it goes into Pile 2b above pile 2a. The remaining cards are placed into Pile 3a to the left of Pile 2a.
When you turn the face-down card from Pile 2b face-up to show that it matches (or doesn't match, as the case may be), place it face-up on top of Pile 2a, and do the same with Piles 1b and 1a.
For the clean-up, pick up Pile 3a, flip the face-up card on Pile 2a face-down onto the cards in your hand, and then place rest of Pile 2a onto this combined packet. Now flip the face-up card on Pile 1a onto the combined packet in your hands and place rest of Pile 1a onto top. Finally, if they said 'Match', place the face-up cards in row b face down on the bottom of the combined packet from left to right; if they said 'No Match', place the face-up cards in row b face down on the bottom from right to left.
Phase 5: If you’re table-hopping and need to reset everything, repeat the handling from Phase 4 (just with more piles, and the 7s can go anywhere into the remainder of the deck). If you don’t care about resetting, then for visual purposes you should still probably handle the dealing in a similar manner to Phase 4. However, in this case there’s no need at the end to keep track of which piles to pick up in which order. In fact, it’s better if you just haphazardly pick everything up at the end because this will destroy all the evidence of your stack!
That’s it. It’s a self-working trick, but you do need to remember the handling differences between the different phases to avoid accidental mishaps. I recommend practicing the routine thoroughly, just as you would for a trick which involves sleight of hand — especially if you’ll be wagering actual money on the outcome! (Don’t say I didn’t warn you...)
A Simplification
I should point out that Phase 5 is strictly optional. I personally think it's a wonderful climax for the routine, but it's also the most difficult phase to remember and it does make an already long routine even longer. For a more streamlined version, don't bother removing the 7s at the beginning and simply conclude your performance with Phase 4. In this case, you don't have to worry about the clean-up after Phase 4 either. These simplifications will make learning the routine quite a bit easier, so I recommend that the first time(s) you perform the routine you do it this way. As a bonus, it will also cost you less money this way if you screw up! ??
As an additional note, aside from enhancing the dramatic structure of the routine, the other reason I remove the four 7s at the beginning and then use them in the final phase is that I can secretly arrange the alternating R-B setup on the fly from a shuffled deck in use under the guise of removing the four 7s. There are numerous ways to accomplish this, including: (a) Kostya Kimlat's "Roadrunner Cull"; (b) Harry Lorayne's "Great Divide" or Lennart Green's "Angle Separation"; and (c) the method Juan Tamariz teaches in the context of the routine "Impromptu Neither Deaf Nor Stupid" on Disc One of "Magic From My Heart".
Credits
As I mentioned earlier, the Omega Bet is the creation of Karl Fulves. His original routine was called “Odds On Favorite”, from the 1973 booklet Riffle Shuffle Set-ups. Fulves also published the idea as “The Omega Bet” in his 1984 book More Self-Working Card Tricks. Nick Trost published a full-deck version called “The Omega Bet - Updated” in the 1997 book The Card Magic of Nick Trost (written with Al Thatcher), and in his 2019 book Nick Trost’s Subtle Card Creations he employs a blackjack theme rather than using red and black cards.
Bob Wagner was the first that I know of to employ the simultaneous insertion of more than one card; his routine was published in his Master Notebook of Magic. Geoff Williams’s presentation for the Wagner routine appears on his DVD “Miracles for Mortals” (Vol. 1), and also in his Penguin Lecture.
Steve Beam published numerous version of the Omega Bet in his Semi-Automatic Card Tricks series. In particular, “The Omega Particle” (Vol. IV) provides an encyclopedic treatment of different multiple-card insertions, and my clean-up procedure is essentially the same one Steve teaches there. Check out “The Charm” (Vol. XII) as well, which builds on Nick Trost’s blackjack concept and has a fun presentation revolving around a “lucky charm”.
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