Gangster penguin (mathematics)

The problem known as of the gangster penguin can be schematized in the following way:

One is opposite two machines with under
One, $A$ , is in functioning order. It thus brings back 1 euro by token with a known probability $p_0$ .
the other, $B$ , is ruined, and thus brings back 1 euro by token with an unknown probability $p_1$ .
One has $N$ tokens. What to make to maximize its profit reasonably?

To trim the problem

Some considerations make it possible to avoid the combinative Explosion:

Seule a setting on $B$ can bring information to us and only a contribution of information can lead us to change opinion. Thus as soon as one ceases miser on $B$ , one is certain never to have reason to return on it .
the problem is summarized consequently with knowing how much tokens one will misera on $B$ , according to the results, before commutating (definitively) on $A$ or not. It is the traditional problem of the Experimental design .

Practical application

The most typical application of the problem of the gangster penguin is that of the choice between old and a new posology of a Vaccin or Médicament (or between two different): it is necessary to determine as quickly as possible if the new product must be adopted or the old one maintained. Any error would be translated into lost human lives (or, at least, as people suffering from consecutive disorders either to an incomplete treatment, or with excessive side effects).

See too

Inference bayésienne
Theorem of Experimental design Bayes

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