What is Probability?

There is something seriously missing in probability theory. Say for example, what is the probability of rolling a dice and getting a face 5? General answer is 1/6. But what does this exactly mean? One way is to say we have 0.17% chance of getting face 5. But probability theory also suggests if we roll the dice 6 times we expect to have one observation of a face 5 - i.e. 1 in 6. But this is not guaranteed is it? so clearly 1/6 is completely misleading. In fact probability of NOT getting a face 5 rolloing the dice 6 times in a row is (5/6)^6 = 0.0001. Basically zero or assured that there will be a face 5. How confident are you with theory? 

I recall Paul Wilmott gave a good example. Imagine a magician with a pack of cards asks you to name a card at random. Lets say you picked Ace of Spade. He then shuffles the pack and then picks out a card at random. What's the probability that it will be Ace of Spde? One can say 1/52, agree? but oh wait he's a magician so it must be 100%? or actually what if the magician is capable of making an error in his work? 

I once thought of some events capable of taking place at certain points in time and others not. I emailed Nassim Taleb to get his thought on how time can influence outcomes and his reply was basically that time acts like variance. What!?

I once found an automated Poker game on the net at http://games.betfair.com/. The game is continuous, you don't actually get a hand, you're presented with 4 hands and you can back or lay (go against) any of them with a bet. Impressive I thought. After watching few games go by I quickly thought of martingaling a hand (double up on losses) as an experiment, since the game *apparently* is computer generated. Suddenly I lost when a *rare* event occurred - when one hand that I laid against won 7/8 times in a row. But I kept watching. For weeks. I noticed this rare event does happen in this game but doesn't follow from another. I didn't pursue as it required too much attention and the pay-off if successful does not make it worthwhile. But very interesting if you want to put probability to test. They have similar games that follow the same behaviours. i.e. it follows man's idea of what probability is. It's artificial. And I truly believe there is someone sitting behind their server who can change an outcome of any game at an instance if a serious wager is made on any single hand. Betfair offers you to download historical results of all games and do any analysis in Excel. You can also access the game via an API if you can build a bot and the minimum you can wage is even lower then. 

More on probability later..