Perhaps I've misjudged you, Thomas, because it seems you are unwilling or unable to entertain the slightest possibility there might be a different perspective on these games other than your own version of the "one time" "single dvent" kind.
Odds never change. People confuse the words odds and probability. Using your example of the "Coin Toss" dvent, in your version of this game no one can predict the outcome and I agree. The odds are always 50/50.
In the version I was trying to present to you for discussion was of a different kind. Here's an example:
We can use the old Charles Dickens story of "A Christmas Carol," only this time when the ghost of Christmas past picks up Mr. Scrooge to take him back in time they drop by your house and pick you up as well. Now in this new version you and Scrooge are taken to several different places in time. Each time the three of you descend out of the clouds you are ask to bet on 2 or 3 tosses. The Ghost tells both you and Scrooge you may ask him one question just prior to the Coin Toss and he will whisper the answer to each of your single questions. Not the result of the contest, but any other question. Thomas, because of his beliefs, declines the offer and Scrooge does not! At the end of the day Thomas has ended up broke and Scrooge is rich. What question did scrooge ask that helped him win over 90% of his bets?
The answer the ghost gave to Scrooge each time was the key and the answers he whispered to him were different each time and they were, 8, 7, 6, 9, 12, 14,12,19,18, etc. These were the answers that Scrooge used to win more than he lost. He made a killing asking the Ghost the same question. "Is this an on-going game and if it is, what has been the result just before we got here? The Ghost would always answer "The guy on the left or right has just thrown 8,7,6,9, 12....etc. heads or tails in a row" Scrooge, being an experienced betting man would always bet the next toss to go the opposite way!
In a single dvent coin toss the odds never change. The probability that someone can throw heads more than 5,6,7,8, etc. in an unbroken chain. Well, that's a horse of a different color! Thats why I always like to know what these numbers have done ijust prior.
If, one day you buy a quick pick with 123 on it and someone advises you exchange it because 123 had just come in that order the last 2 days in a row, do it. The odds are the same each day ofcourse and anything is possible, but probability says your chances are almost nill. Chances not odds.