A player can choose his own set of a maximum of 10 numbers and, depending on the number of selected and guessed numbers, his bet is multiplied by a different factor.For example, the player chose 3 numbers.Then his chances are:
- guess 0 numbers: 41,093%
- guess the 1st number: 44.028%
- guess 2 numbers: 13,664%
- guess 3 numbers: 1.215%
For each of the outcomes, we consider the coefficient using the formula
100/probability.It turns out:
- if you guessed 0 numbers: 0
- if you guessed 1 number: 2.271
- if you guessed 2 numbers: 7,319
- if you guessed 3 numbers: 82,305
But with such ratios, the"casino" turns out to be a big loser.For example, 100 players bet $1.Of them, according to probability, 1 number will win 44.028 and be picked up, at a rate of 2.271
2.271 * 44.028=$99.9- i.e., the whole prize fund is already.And 2 and 3 more numbers will guess - there, too, each option spends $100.Of this, payments are 3 times higher than the bets made.
How to calculate the odds so that “casino"Remained in the black, and did the rates reflect the real probability of winning?
Also tell me, please, the literature about this kind of games and their mathematics: both probabilistic and financial.