A member sent me a pm asking about the Andruchi system (google it). It's been exposed as a scam numerous times but I don't think the dodgy calculations on the website have been exposed for what they are (the member was asking specifically about those).
Basically the system involves waiting for 20 unique numbers to appear, the procedure is to then bet for the next 3 spins (or until a hit) on the remaining 17 numbers using a progression.
Andruchi uses some weird calculation to find the probability of getting at least one hit in the 3 spins, which, according to him, is 91.49%. This gives the probability of a progression bust of 100% - 91.49% = 8.51%. The average win is 8.33 units and a progression loss of will cost you 68 units, and on this basis the total expectation is positive (see calculation below in the image).
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The correct calculation to find the probability of at least one hit in the 3 spins is as follows (I'll start from first principles so it's easy to follow):
You are betting on 17 numbers, and if you win it will either be on the first, second, or third spin.
The chance of a win is 17/37 and the chance of a loss is 1 - 17/37 = 20/37
Win on spin 1: The probability is just 17/37
Win on spin 2: You lose on the first spin and win on the second, so the probability is 20/37 * 17/37
Win on spin 3: You lose on the first and second spins and win on the third, so the probability is 20/37 * 20/37 * 17/37
Since if you win it must be on either spin 1 or spin 2 or spin 3, and since these results are mutually exclusive, we just add them to get the probability of at least one hit in the 3 spins.
17/37 + 20/37*17/37 + 20/37*20/37*17/37 = 0.8421 or 84.21% (rather less than Andruchi's result).
Now this gives the probability of a complete loss as 100% - 84.21% = 15.79% (rather more than Andruchi's result).
Now if we repeat his calculation using these probabilities, the expectation is:
0.8421*8.33 - 0.1579*68 =
-3.723Not positive after all.
![:(]( "Sad")
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