Please be gentle, I am no statistician.
Imagine that I offered you a coin toss bet in which you have to call heads or tails. If you call the toss correctly, I give you £200. If you call the toss incorrectly, you have to give me £100.
By my understanding you have a 50% chance of winning the bet at odds of 2-1. However, you refuse to take my bet.
I then say, "How about we toss the coin 100 times at the same odds?". You now take my bet.
Am I right to believe that you are no more likely to win money in the single toss game or the 100 toss games and that the probability of you winning or losing money is exactly the same in both scenarios?
I would really appreciate an authoritative answer – many thanks