Difference between single and multiple bets. Suppose we have 100 dollars and we need to bet a total of 100 dollars before we can get this money.
On each bet the bookmaker takes 5% on our winnings.
Does it have the same expected value to make a single 100dollars bet or let's say 20 bets of 5 dollars each?
I'm not a math expert (to be honest this should be quite elementar but I'd like to hear your opinion) but to me it should be the same since if we make a 100 bet we'll lose 5 dollars; instead if we make 20 5dollars bet we will lose 0.25 dollar each which is 5 dollars. Right? 
So is it reasonable to make many little bets to reduce the variance?
 A: Well, first of all, you have not specified the chance of winning a bet and the amount granted if you win. Also, 'the bookmaker takes 5% of our winnings' means that we should know exactly how much the 'winnings' are.
If you have to bet exactly \$100, and don't want to bet any more, there is no difference in the money made by the bookmaker, whether you put one bet or many.
The only difference is how much risk you want to take. The smaller the bets are, the more close your final outcome will be to the predicted one. For example, if the predicted outcome says that you are at a disadvantage by 5%, then you are most likely going to lose about 5% of your money, if you place 1000 \$0.1 bets. However, if you place lesser bets, your outcome can vary more from the predicted outcome.
Mathematically, the distribution of bets does not affect the fact that who is at an advantage (you or the bookmaker), and by how much. What matters is how much you are willing to risk losing, to try gaining a proportional amount. That depends on other factors (how rich you are, how attached are you to your money, etc.) that involve maths only when specific data is given.
