Gamblers Fallacy is subjective. it is the appearance to the gambler that the next event in a chain of event is more or less likely to happen then it actually is. His math is correct as it shows the % chance of a string of events to happen in sequence operating on the assumption that each individual possible result of each event is equally likely. Say I flip a coin, I have a 1/2 chance that it will be heads. Lets say I flip 3 coins in a row, the chance that they are all going to be heads is 1/8; that is 1/2 * 1/2 * 1/2 = 1/8. Gamblers fallacy would be someone saying "Hey, I got heads 3 times in a row, tails has got to be coming up soon. I mean what are the chances of it being heads again?" The chances of each new flip being heads or tails is 1/2 each time the coin is flipped. What happened last flip does not somehow make heads or tails more likely then the other on each new flip.