Tuesday, April 28, 2020

The Red and the Black

If you’re interested in mathematical and gambling material you might find it worth it trawling through the following. It’s the history of a red/black proposition bet and a collection of various published ideas leading to what I think is an entertaining betting routine that seems to have been forgotten. I’ll describe the various aspects of the trick and interrupt along the way to let know a little more about the background and history

My minor addition to this is that you use some marked cards to give you an edge in this game that probability will not. Only two black spot cards in the deck need to be marked in a way that you can distinguish them.  If you want to use them in all the routines that follow, then I suggest you mark them at the corners. Alternatively, you can use a one-way deck, the black cards turned in the opposite direction to the red cards.

Let’s say the two black cards are the 8C and 9S.  Begin the routine by taking out four playing cards from the deck. Two are red spot cards and two are your marked black spot cards.  Explain that you are going to demonstrate a gambling hustle.

Show the cards and then let the spectator shuffle them. When the cards are mixed so that neither of you know the order, ask him to deal the four cards face down in a row across the table. I’ll give some basic patter so you can follow the plot.

‘Here is the bet. There are four cards, two reds and two blacks. And all you have to do is select two of them. If the two cards are the same colour, you win.’

‘It’s an even money proposition. Doesn’t matter whether you select black or red. You can select two red cards. Or two black cards. You only lose if you select one of each. Sound fair?’

The spectator agrees that it does sound fair.

‘It’s not fair at all,’ you say. ‘And I’ll show you why.’

Ask the spectator to turn one of the cards over. He does. Then say, ‘Now all you have to do is turn another card over and if the colour matches, you win. Which card would you like?’

Ask him to point to one of the three remaining face-down cards. Because the cards are marked you know whether he has pointed to a card of the same colour. If he hasn’t, ask him to turn the card over. It doesn’t match and he’s lost, just as you predicted.

He will lose two times out of three. This is a mathematical hustle. Using red and black cards to explain probability goes back hundreds of years but a significant date in magic history was December 1970 when Martin Gardner explained the swindle in his Scientific American column. Which is why this source is often given when trying to date the scam. For example, Gardner gets the credit in The Red-Black Swindle described in Karl Fulves’ The Big Book of Magic Tricks (1977).

If the player loses, you can offer to play again and this time you explain that athis isn’t actually a 50/50 bet. Once he has turned over a card he has nailed his colour to the mast. For example, if he turned over red, there are three cards left face-down on the table but two of them are black. The odds are against him.

But let’s assume that things don’t go your way and the spectator is pointing to a card that matches the colour of his first choice. At this point you’d prefer he changes his mind. So you now explain the swindle to him. And ask whether he would now like to change his mind. He can change his mind in one of two ways. He can point to another card. Or he can turn his original card face-down and pick another. Either way by laying out the real odds and offering additional options you are trying to psychologically force him into a losing situation. Think how Chan Canasta might handle it.

If he changes, wonderful. Turn the card over and reveal that he lost.

If he doesn’t change his mind, congratulate him on his intuition, ‘You are really good at this. No one ever beat this hustle before. I think you are ready for the big time.’

What is that? I hear you ask.

Well, you have several options and, interestingly, for one of them we travel back in time long before Martin Gardner wrote his column. In The Conjurors’ Magazine for April 1946 Walter Gibson suggests a similar proposition bet, Check Payer, this time played with seven cards, five reds and two blacks.

Take three more red spot cards from the deck and add them to the four already in play. Lay the cards face-up on the table as you explain how the odds have increased in the spectator’s favour.  The game is to pick out three cards in a row. But look how the odds favour him.

‘On the first try you have five reds to two blacks. That’s 2.5 -1 in your favour.’

Pick up one of the red cards.

‘On the second try there are four red and two black cards. That’s 2-1 in your favour.’

Pick up another red card.

‘On the third try there are still three reds to two blacks. That’s a 3-2 edge for you. Looks fair right?

He says it does. And you tell him he’s wrong and you’ll explain why.

Shuffle the cards and then lay them out in a face-down row. The odds of him choosing three red cards in a row are 2.5 -1 against him. Walter Gibson says he ran the idea past Royal Vale Heath who wrote Mathemagic. Heath said that in two-hundred and ten tries there were only sixty possibilities of the spectator picking out three red cards. I have no idea how or why he arrived at those numbers.

Let the spectator choose cards by first pointing to them and then turning them over. The cards are marked so you know how well his choices are going and are able to use a bit of psychology and double-talk to get him to change his mind along the way.

Nick Trost described this routine as the Seven Card Wager in the September 1967 issue of The New Tops.  He doesn’t mention it but I imagine he might have read Walter Gibson’s article.

In the December 1965 issue of M.U.M magazine there is a description of a performance by Al Thatcher that took place at the U.F. Grant Assembly of the S.A.M in Columbus Ohio.

Al Thatcher began his routine of ‘Gambler’s Odds’ with two red cards and two black cards. He points out that the odds are even and presumably proceeds with a demonstration similar to that Martin Gardner later described in Scientific American magazine.

Thatcher then added three more black cards to arrive at the situation in Gibson’s Check Payer. Here the spectator shuffles the cards and then deals them into a face-down row.  The bet was that the spectator couldn’t turn up three black cards without turning a red card first.

Al won the bet and than added two more black cards and a new game. He arranged the nine cards into a 3 x 3 matrix, all cards face down. Al challenged the spectator to turn over three black cards before he hit a red card. It was a bet that Al won.

This betting matrix really piqued my interest and for a while I thought it was unpublished. But then I discovered that Nick Trost had put it in print.

You’ll find it in Gambling Tricks with Cards – Part 2 (circa 1975). Trost doesn’t credit Al Thatcher. They were acquainted. But the three stages of the bet are described, the finale with nine cards being titled the Tic Tac Toe Bet.

Let’s think about this with the cards we started with. In our version we’d add two more red cards. Now we have seven red cards and our two corner-marked black cards.

The challenge is for the spectator to turn over three red cards. However, he can only turn over cards that are in a row, column or diagonal.

I don’t know if Al Thatcher controlled the position of the black cards in his version and Trost doesn’t mention the idea. But it gives you are considerable advantage if you position the two black cards, one at a corner and one in the centre.

There are eight possible lines in the matrix but if you put the black cards at the centre and corner that leaves only two winning lines for the spectator. Add that to any psychological persuasion you might bring to bear and it’s a good bet for you.

If you have a group of spectators, then one way of overturning a correct decision is to give someone else the option of changing a card. Playing one player’s choices against another can also add to the entertainment value.

Another interesting aspect of Thatcher’s routine is that he was performing it in 1965, five years before Martin Gardner published his article in Scientific American and ten years before Nick Trost put it in print.

Trost returned to the theme of the red black bet when he published his Seven Card Wager with a Kicker in the March 1971 issue of The New Tops. This is a magical version of the hustle in which the spectator loses repeatedly and then all the cards in the packet change to black cards. This is a good idea but Trost’s solution involves duplicate cards and false counts. An easier and better solution might be to secretly swap the packet of cards entirely for one in which every card is black.

Assuming that’s done the spectator gets unlucky by picking out a black card on his first choice. Feeling generous you say, ‘Well, we’ll consider it a win if you pick out two red cards.’ He tries again and picks out another black card. At this point he has lost the wager. But you offer him a third chance saying, ‘Okay, if you pick out an even value red card we’ll consider it a win.’ To his surprise he picks out another black card. Finish by turning over the remaining cards to reveal that every card is black. End of trick.

Here is a different way of adding a kicker to the bet that makes use of the corner-marked black cards.

The deck must be set up with the red cards on top of the black cards. Go through the entire routine starting with the Red Black Proposition Bet, then the Seven Card Wager and then Tic Tac Toe Bet.

Pick up the cards from the table and replace them in the deck as follows. Insert one of the black cards into the lower portion of the deck. Let’s assume it’s the 8C. Insert the rest of the cards, including the 9S, into the upper portion of the deck. Then give the deck a false shuffle that retains the order or at least the separation between the upper half of the deck and the lower half.

Table the deck and offer the spectator one last bet. First ask him to cut off a portion of cards. You want him to cut a little less than half the deck but enough so it includes your corner-marked black card. If he cuts too few half him deal off a few more. You want the largest packet you can get. This packet will consist of all red cards except for one marked black card.

Put the rest of the deck away and, if you think the spectator can shuffle the cards, have him mix them otherwise do it yourself. Then take the packet and spread it face-down across the table.

‘Here is the bet. A challenge for both of us. All you have to do is pick out a red card. And all I have to do is pick out a black card. 50/50 odds for both of us. Let’s see how we do.’

The reality is that all the cards in the spread but one are red. Let the spectator make his choice first. If by chance he picks the black card, make the most of it. Turn the spread over and reveal that all the rest of the cards are red. ‘You just never seem to get a break. That’s my card.’

Most of the time he will take a red card. Don’t turn that card over for the moment. Instead, you choose a card from the spread, picking out the corner-marked black card.

‘Let’s see how I did.’

Turn over your card to reveal it’s a black card.

‘And now you.’

The spectator turns over his red card.

You then say, ‘I guess we’re both winners. Although to be fair, I think you had it easy.’

Turn over all the cards in the spread and show that they are all red.

I think there’s a lot of fun to be had with the red black proposition bet. I personally don’t like the idea of playing it as a gotcha against the spectator. I’d rather explain it as the mathematical game it is. But Tamariz has a wonderful presentation in which he pitches one spectator against another in a game of Three Card Monte. I think it’d be possible to do something similar with the red black proposition bet. That way you’re not the one showing off.

There’s another interesting version of the bet in the June 1984 issue of The New Tops. It is in John Sherwood’s Lost in the Forest column. He credits Nick Trost’s Seven Card Wager with the inspiration. In Sherwood’s version five men and two women are asked to stand in a circle. A blindfolded volunteer stands at the centre of the circle. The challenge is for him to point to three men in a row. If he points to a man, that man leaves the circle. If he points to a woman, that woman gives him a kiss. Since there are more men than women he is convinced by the performer that he can eliminate the men from the game and if he misses he’ll get a kiss. It’s an interesting premise. There’s no kicker but it would be very tempting to rearrange that circle of people once the spectator has his blindfold on.

Finally, I recommend you take a look at Al Thatcher’s card magic. He has many wonderful ideas and routines in print. Thoroughly practical and clever card magic. There is also a book available that contains 73 of Al Thatcher’s tricks and 13 contributed by his friends:

Al Thatcher – After Hours Card Magic. Below is an Amazon Affiliate link for the Kindle edition of the book.

In Check Payer I said I didn't understand how Royal Vale Heath arrived at the calculation that in 210 tries the spectator would only pick three red cards in a row in 60 of them. Well, Alain Gesbert emailed the following which makes the calculations clear:

The three games have the following number of red cards in them

1: 5 red cards among 7 cards
2: 4 red cards among 6 cards
3: 3 red cards among 5 cards

To calculate the probability of the spectator winning the bet you multiply the three ratios:

5/7 x 4/6 x 3/5 = 60/210

Thank you Alain!