Jacob Bernoulli 1654-1705
Bernoulli and Chebyshev proved different versions of the law of large numbers.
Chebyshev's method is used in modern textbooks, so it is well known, but not many have seen Bernoulli's method.
Here you will find a modernized version of Bernoulli's proof in which the structure of the proof is the same.
You will also find Bernoulli's infinity argument and his scholium argument. just click on the links below.
Bernoulli's Infinity Argument Betting Systems
Bernoulli's Scholium Chebyshev's Law of Large Numbers
More on Lemma 7 MultiLine Slot Machines
The Russian Improvement external link to appendix 6
The Modern Form of Bernoulli's Theorem Probability Formula
Bernoulli's actual proof is in Chapter V of part 4 of Ars Conjectandi.
Here is an external link to an english translation Ars Conjectandi
If you have any questions or comments my e mail address is ddaniels1622@yahoo.com