### Installation

You need to authorize the installation from unknown sources, as prompted by Android when you try to install.

### Descriprion

There are two Gaussain random generators, labelled as hypothesis A and hypothesis B, each characterized my μ and σ (m and s in the app). A generator is extracted at random (equally likelly) and a number (Outcome) is generator. The question is to 'guess' where the outcome comes from, with some probability, and to play accordingly.

Android proposes a bet on either hypothesis, also fixing the odds, i.e. the ratio of probabilities. For example, 2.0 means "2 to 1". Then if you bet on such an event ('Pro'), then you 'pay' 2, the adversary (Android) 'pays' 1, and the winner gets 3. In this case you have a net gain of 1/2 of what you payed.

For 'simplification' (anyway a choice...) the total amount is fixed to 100 Euros, so that the amount to pay is decided by the odds and you win always 100 (if you win), or lose what you paid (the administration is done internally, so you don't have to worry). The gain will be the difference.

For example, imagine the odds are 3 and you bet 'Pro'. This implies that you pay 75 and your opponent 25. If you win you will have a net gain of 25, otherwise you lose 75.
If you instead bet 'Con', then it is the other way around and you can gain 75 or lose 25.
You have the possibility not to bet ('check') and you will see anyway the right hypotheses.

Where is the game? The odds proposed by Android are not exactly those obtained from probability theory, although not very far (apart from 'level 0', see later). This gives you and advantage if you are able to evaluate correctly the odds. So, although with fluctuations, because we are dealing with uncertain events, you can win "in average", a statement which reflects the long term performances.

'Levels':

• 0: The two Gaussians have always the same parameters; the proposed odds are given at random. Then it is rather easy to win.
• 1: The two Gaussians have always the same parameters; the proposed odds are around the correct ones.
• 2: like 1, but the two Gaussians have standard deviations generated at random, although they remain constant until 'reset'; the proposed odds are around the correct ones.
• 3: Gaussian parameters change at every bets; the proposed odds are around the correct ones.

You can ask the advice of "an expert" capable to evaluate rapidely and correctly the odds and to suggest the "best" move, although "best" does not mean you are necessarly going to win at each move, because it is an expert and not a 'magician'. (To be precise, it uses exactly the same pieces of information availabel to you.)

There are two kind of experts, the 'aggressive' and the 'conservative':

• the 'aggressive' tries to exploit any little difference between proposed and correct odds;
• the 'conservative' only suggests to bet (Pro or Con) if there is a 'remarkable' difference between proposed and correct odds, otherwise it recommends to 'check'.
Performances of different strategies are shown in 100 histories of 1000 simulated bets.

# Enjoy!

### [ “May the odds be ever in your favor”...(*) ]

(*)Pay attention to the extended meaning of 'odds'.

### Credits

App written with App Inventor 2.
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