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How to create a "merciful" game for us?

     In this article we explain how to build a game in a way to get an advantage, that is - if the number of bets will be high enough you can manipulate how much percentage will find a way to your pocket.

Our game will be really simple and based on one dice. But the rules explained here are general. The point is that in this small example it is easy to understand what is going on.

O.K., so lets start.
Initial conditions are:
1. we have one BIASED dice and you are a dealer,
2. if result is 1, gamer gets 3€, it means you loose 3€
3. if result is 2, you get 1€, it means - gamer looses 1€
4. if result is 3, gamer gets 3€
5. if result is 4, you get 6€
6. if result is 5, gamer gets 5€
7. if result is 6, gamer gets 3€

     In "neutral" dice all possibilities - to get 1, 2 etc., are the same an equal to 1/6 and it would be very easy to predict results for big enough sample. However in general games are more complicated, and this is the reason we use in our example biased dice, to make it more difficult for "common" prediction, as in real game.

     How do you think - how much could you expect in the game based on a sample, lets say, 1000 throws? Well, the game looks a real disaster for you as a dealer. "Common reason" says that you could loose: if you add negatives and positives separately you will get -14€ and +7€ respectively. So is the game good for you as a dealer?
The term called "probability expectancy" can answer. The formula is below:
Multiply probability of the event by corresponding value for the event and add up results for all events:
expectancy = (-3€)*0.1 + (+1€)* 0.1 + (-3€)*0.1 + (+6€) *(0.4) +(-5€)*0.2 +(-3€)*0.1 = +0.6€
It means on average you could get from one game/bet +0.6€, so for 1000 throws it would be, most probably, 600€.

Obviously, if you can MANIPULATE the probabilities and money, you can get almost exactly the amount of money you want, provided the sample, that is the number of bets, will be high enough.