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# Shell Game (Thimblerig)

Shell game – aka Thimblerig or Three shells and a pea – is a well-known gambling game with a simple principle. The shell man puts a small ball under one of the three shells and then shuffles them. The player tries to guess under which shell the ball is located and if successful he is paid 1:1. The game has a hallmark of dishonesty and this was also confirmed by a court.

## Odds of Winning

Before looking at the assumed dishonesty of the Shell game and the court arguments that led to this ruling, let us do a simple mathematical analysis of the Thimblerig game. We have got three shells and a small ball. If we supposed an honest shell man (aka thimblerigger or operator), no matter how illusive it would be, then we could find easily that the odds of winning are 1/3 and the odds of losing 2/3.

Thus the long-term expected return would be 1/3 or 33.33% of the wagers. That is a nice one in deed, however not the biggest one that can be achieved (legally) in the gambling industry, but let us set this aside for a while. Moreover the return could be lower, if the shell man was little handy (very unlikely), or the return could be much higher, if the shell man was cheating (very likely).

## Cheating and Tricks in the Shell Game

Cheating and psychological tricks are a common practice in the Shell game. It is a mixture of skill of the shell man, who is able to hide the ball in his fingers or palm and then place it under any shell at his will, but it is a well prepared show as well.

The shell man does not play alone, but there are several "helpers" or so called shills. The Shell game is usually played on the streets, marketplaces, funfairs and other busy places. The shills are to attract passers-by to the game and encourage them to wager. "Wanna bet, sir? I have just won twice in a row, bet as I do..."

Even more crafty way to attract new souls is to deliberately play poorly and lose. The shill counts on the player's thinking: "This guy is playing terribly, the small ball must be right here..." so the player wagers on his own. As we said before, it is the shell man who controls the situation. One needs to bear this in mind constantly.

The shell man often lets the player taste the flavor of easy winning and then take everything away from him, if he allows him to do so. The atmosphere is completed by the shell man himself as he often waves bank notes in his hand. Thereby he strikes the player's subconscious mind: Here's the money, come and take it.

## Ruling of the Czech Supreme Court

This story and the ruling might be similar in other countries too. In 2007 the Czech Supreme Court ruled about an appeal of a thimblerigger, who had been given a suspended sentence for an operation of the shell game in a fair back in the year 2005.

Among other things the judge stated that the Shell game was an unfair game as the participants had unequal chances, that the shell man had a double odds of winning (2/3 against 1/3) and that a common man was not able to follow the shuffle of the shells.

The Court dismissed the appeal, despite the thimblerigger argued that there was actually no game of even chances and that there could be no game like that as the gambling business could not exist in the long run.

First of all to dispel all doubts we say that we do not support any form of cheating. Nonetheless the arguments of the Czech Supreme Court are very dubious, troublesome and unconvincing. Let us have a closer look.

No even chances
And what game gives even chances for the players? It is the substance of gambling games that their operators have some edge over the players. And it is understandable as it would not be possible to run this kind of business profitably.

The operator's edge in the shell game is 33.33% (if he was honest...). For example in French Roulette it is 2.7%, in American Roulette it is a double of that, in Sic Bo, the dice game, the house edge can reach up to 30% too, but for instance lottery games often consume about 50% of the wagers (while at that time there was the Czech lottery game called Sportka, which was operated by state)!

A common man is not able to follow the shuffling of shells...
First of all, why that would be necessary? The game could also be offered in a way that the bettor would be turned around. The shell man would place a ball under one of the shells. The bettor would pick up one and if successful he would be paid even, that is \$10 bet would bring \$10 net. As regards the honesty, this game could be imagined as a slot machine and it would bring its operator a long-term margin of 33.33%. And again, this margin is much more adequate than in case of lotteries.

Secondly, the ruling may manifest (at least an apparent) misunderstanding of the game by the judge. The shuffling of the shells is completely irrelevant. On the other hand it is true that it creates an illusion (or a delusion?) of how easy it is to win and it is usually followed by a deception – the shell man's manipulation with the small ball at will. However in the countries with the rule of law it is needed to prove the deception, even though it is almost impossible in this case. However we should not become reconciled to someone saying that "this game is simply deceptive" and therefore it will be outlawed. This is quite problematic and dangerous (conviction without evidence).

What was left for the Supreme Court, was there a better argument? We believe so and are surprised that the main argument was not an illegal operation of a gambling game without a license or something like that. In that case there would be nothing to argue.

## The Best Shell Game Player? A Cat!

A little bit of fun before the conclusion. Watch the following video of a cat playing the Shell game. The cat called Kido reveals with 100% success under which shell the "small ball" is hidden. And it manages to do so even with four shells. The question is, whether the cat sees or hears the movement of the small ball. However there are two amazing things: first, the cat understands what is going on in the game and second, it is willing to play. Have fun.

## Conclusion

Playing of the Shell game (Thimblerig) cannot be recommended and not only because it is illegal, despite, according to our opinion, the dishonesty was based on dubious arguments of the Czech Supreme Court. From our side it was just a theoretic consideration and an attempt to objectively compare it to other games. By no means it was a defense of deceptions that are very frequent at the Shell game. The players themselves should resist the temptation of an easy profit and simply not play the Shell game as no law can protect from human naivety or silliness.

Thimblerig is also unsuitable for an entertainment amongst friends as there are other games where the edge of the "banker" or the operator is much lower. Friends do not need to rip each other off, be it play for money or for short drinks. However we have already dealt with the profit (or margin) adequacy.

You can only lose on the street. Even though you might win by chance or you would actually be allowed to win in the first games, you may lose the money behind the corner anyway.

Based on the original Czech article: Skořápky – pravděpodobnost výhry, podvody, soudní rozhodnutí.