The Mysterious Misdeal

Having ¡thoroughly shuffled a full pack of 52 cards, shuffled them to your full satisfaction, hold them face down ready to deal. Now here is what you do. Deal the cards out, face down, as though for whist, first card to the West, second card to the North, then the East and finally yourself, the dealer, South. But before you commence to deal note this. During any one of the rounds, and at any one of the players' hands, you skip a card, going on to the next. In other words, you misdeal , once. You may do this on the first round, say, at your opponent Nor;th (thus you would deal West, miss North, deal East, then South) or at any one of the rounds right up to the thirteenth.

Having misdealt at your chosen hand, you carry on dealing with the rest of the cards in a proper manner, and if you trouble to figure it out you will find tha|t, having missed one hand somewhere in the deal, the last card will not go to the dealer, as it normally would, but to the player on your left, West. In dealing, fake care to drop the cards fairly evenly on their heaps, in other words, avoid the cards sliding off, and becoming misplaced, for the heaps have to be picked up again.

Now you have four face down heaps on the table. Gather ,them up in any order you like without disturbing the heaps themselves, and commence to deaf out four hands, exactly as before BUT WITHOUT MISDEALING TO ANY PLAYER. In other words, a fair, square deal. Now examine the four hands, in their turn, and, IN ONE OF THE HANDS YOU WILL FIND A SINGLETON, that is, one solitary card of any of the suits. It can be a single diamond in an otherwise mixed hand of clubs, hearts and spades. I,t can be a single spade in an otherwise mixed hand of diamonds, clubs and hearts. BUT, WHY A MISDEAL ON ANY ONE OF THE HANDS IN DEALING OUT ALL 52 CARDS, FOLLOWED BY A PROPER DEAL

OF FOUR HANDS OF THIRTEEN CARDS EACH, SHOULD CAUSE A SINGLETON TO APPEAR IN ONE OR OTHER OF THE HANDS, WELL, I JUST DON'T KNOW. All I know is that it does happen, and that I will gamble on. I'll take any pack of cards, which I have never seen before, I'll have it shuffled and I'll deal, MISDEALING AT ANY HAND YOU CARE TO DESIGNATE IN THE PROGRESS, I will then ga,ther up the hands in any order you suggest, and re-deal them, properly, this time. You shall then examine the hands, one by one, and I'll wager you anything that-one of the hands contains a singleton. You shall then deal them yourself, just as I did above, misdealing where you fancy, you gather up the cards in your own desired order, and you shall re-deal them correctly, and again I'll guarantee that you find a singleton in one of the hands.

I have shown this to dozens and dozens of people, all interested in cards, and no-one has offered a reason, let ajone a solution, as to why this happens. I have placed the problem before clever mathematicians, and not one can vouch a reason as to why a simple misdeal can in any way effect the suits and their order of appearing in any one of the hands.

One puzzled spectator made a good suggestion. He advised me to get a pack of blank cards, colour 13 faces red, thirteen green, thirteen yellow and thirteen blue. Mix them up and misdeal and deal as I had done with the playing cards . I promised that someday I would do this, but have never got down to it What I have done, however, is to get FOUR PACKS HAVING DIFFERENT COLOURED BACKS, and to take 13 cards from each pack. Thus I have made up a pack of 52 cards having four coloured backs thirteen times repeated throughout the pack. I have shuffled them and dealt them face down as directed above, and in every case I have found one solitary coloured card mixed among the other twelve designs. In other words, a CARD BACK SINGLETON. And I still don't know why it works.

At this stage in typing out this script, a friend has just called upon me and naturally wanted to know what all this is about. I took him through the routine of the misdeal and re-deal, and he goes away happy but puzzled and he promises to bring me some sort of solution next week. I hope he does but— they've all said that!

I am assuming by now that you have had a pack of cards out, and have tried out the

Mysterious Misdeal, and by now you will be as intrigued as I am. You will also be wondering how this problem can be turned into something worth while. Here's how. Discussing this darned thing some time ago with a well-known London magician, between us we found that, at the end of the misdeal, or the majority of them, the hand on your left had one more card than he should have, in fact fourteen cards. On this fact we were able to cut out the first dealing of the cards, and this is how the routine would appear to the layman.

Have him bring out his cards and shuffle them, then taking them from him, emphasise the fact that you have never handled the cards before, that they are freely shuffled and you cannot possibly know the position of any card or cards. "Now" you say, "I am going to ask you to deal out these cards into four heaps, as for whist or solo, something like this, each hand getting his thirteen cards". Here you count off thirteen cards from the top of the pack by the running count, merely sliding all cards to the right about half an inch and never disturbing their order. You do this four times, placing the heaps, West, North, East and South.

"Now", you continue, "please gather the cards up in any order, and then deal them out, not as I did, of course, but in proper rounds a card at a time". When this is done, ask him to examine the hands, one at a time, and offer to wager with him that IN ONE OF THE HANDS THERE WILL BE A SINGLETON. There will be, never fear. Sometimes there will be more than one, but one can almost be guaranteed, and additional ones I take to be incidental to the dealing.

The how? When you take the pack in your hands, face down, you illustrate (?) what you want the spectator to do, that is, deal the pack into four heaps, but YOU hurriedly run them off into heaps. Exactly, and for a purpose. The first heap you run off and place to the left contains, not thirteen cards but fourteen. This is accomplished by taking two as one at the beginning of the run off, or at any stage of the count to suit yourself. The second heap, North, gets exactly thirteen cards, counted as before, but correctly. The third heap gets thirteen, and the fourth heap, nearest yourself, naturally gets the remainder —twelve. You either dump this remaining dozen cards on the table on the natural assumption that there must be thirteen, seeing that all other hands have got (?) thirteen, or, you count them off just as you did the others, counting one card twice to make up the odd one. The running count is the most useful for this.

Now the job is done. The spectator gathers up the cards in any order, (or you can do it for him, handing him the full pack) and deals them out, to find later on that, had he taken on your wager, you would have won, with a singleton!

Are there any clever mathematicians amongst my readers? I have just turned up some data regarding the game of Poker. This data gives the number of variations there are to the many playing hands, and follows with the odds against a player getting such a hand from a shuffled pack of 53 cards. The formula

is as follows:—

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