Isnt it annoying? You abandon a casino machine or table disgusted at (or broke from) the game being colder than Fidos nose on a rainy midnight. Then you watch someone take your seat, play no differently than you did, and rake in the dough. Or you stroll by subsequently and some smug never-say-die remarks, "You should have stayed, pal. It really got hot right after you quit."
Or this: You fall into a deep hole, grind your way back to a respectable partial recovery, and high-tail it to the cashiers cage. Youve cut your losses and declared a moral victory. Youre pleased with yourself. That is, until you wonder, since you were on enough of a roll to recoup as much as you did, would you have broken even or gone over the top had you continued a bit longer?
These enigmas are meaningful in some gambling situations. Like speculating in the stock market. There, unless youre so big that your trades sway prices and experts ratings of an equity, your purchase or sale doesnt affect its value. So you dump stock you bought for $8 when it drops to $5, figuring the firm is bound for bankruptcy and you might as well salvage what you can. The next week, it rises to $9 and would have done so regardless of what you did. You know how much you sacrificed by being impetuous.
Not so in a casino. Your leaving, and your place being taken at a machine or table or the action proceeding without you, alters what would have been the future. This isnt due to an etiological link between your move and ensuing events. Rather, it results from some of the agents that inject chance into the games.
Consider the machines. Many believe their favorite slots cycle through pre-selected series of steps, somehow randomized in advance and etched on computer chips. Not so. The internal computers generate new random numbers continuously. When the machine is activated for a wager, the most recent number to be produced determines the current decision. So unless a new player triggers succeeding rounds at precisely the same instants you would have, those results wont be the same as yours would have been. And, of course, theres no way to know.
Similarly on tables. Take a game in which an individuals presence and participation has no overt bearing on results, like the big six or roulette. But picture what happens when someone comes or goes. The dealer exchanges chips for cash or makes check change, colors-up for a bettor, waits for an OK from the floor, accepts a toke, says hi or bye, cleans house, and so forth. These things take time. So the next spin occurs later than it otherwise would. Such being the case (and dealers not being finely calibrated robots), the force applied to the wheel or ball, and for roulette the position and speed of the wheel when the ball is released arent the same as they would have been even a split second sooner on the next round, the one after that, and on into the great beyond.
How about blackjack? Change the number of hands per round by leaving, and its a whole new game. But perhaps you drop out in mid-shoe. Someone who plays exactly as you do takes over without missing a hand, and the dealer isnt relieved before the shuffle. Assuming everyone else at the table plays as they would had you stayed (a plausible but not assured condition), you can see how you would have fared during that one shoe.
But theres still a timing deviation. If a relief dealer appears, it wont be at the same point in the shoe as it previously might have been. Another card will therefore be "burned," so different hands are dealt for the rest of the shoe. Its also likely that the dealer wont shuffle the cards in exactly the same way, or that whoever cuts the shoe will hit the identical point, from one instant to the next. Chance accordingly writes an alternate ending to the story.
It all boils down to Lesson 106 of what you learn in the casino that you can use in the real world. You cant predict the future reliably when you know what influences it. You certainly cant when you dont.
What you can do, however, is heed the hortatory of the venerated versifier, Sumner A. Ingmark:
Lament not on what might have been,
But focus on the way to win.