Independent event an probability?

Question

A person is playing a slot machine. He makes the comment “I have been playing this d**n thing for over three hours and haven’t won yet! I will keep playing because I am bound to hit soon!” What’s wrong with what he said? Explain your answer using independent events and probability.

Answer 1

Basically the slot machine is memoryless.

To illustrate what this means, consider flipping a coin: Say you just flipped 5 tails in a row. What are the odds of flipping heads on the next flip? Still 50/50. The coin does not somehow "remember" that you flipped 5 tails in a row. It's not that smart. Every flip has the same probability of coming up heads, regardless of what happened in the past.

The slot machine will continue to lay you the same odds each spin because each spin is an independent event which doesn't depend on / remember what happened in previous spins.

Answer 2

every time the player pulls the lever of the slot machine it is an independent event.  this means the out come of the previous tries has no impact on the current attempt to win.  while it is unlikely to "never win" it is possible and it has no impact on what will happen in the future.

Answer 3

There is one problem with the above answers. Casinos are obliged by law to return a certain percentage of their "take". In order to do so, slot machines are programmed to return a percentage of the money that has been played. However, determining WHEN the machine will pay out is very, very difficult.  Even when not being played the slot machine is actively generating random numbers that change every millisecond or faster. You win when the correct sequence of numbers corresponds precisely to the time you pull.  The percentage payout is calculated over the long term. Even if you leave a slot, and the next player gets the jackpot, it does not mean that you would have won it had you stayed. Being a fraction of a second off would have meant the difference between winning and losing. It's timing, not the number of coins you play. Thus indeed, each "pull" is a random event. Once, however, at the Casino in Montreal, there was a defective machine, and two guys realized that they could determine when the machine would pay out. They made millions of dollars over a period of time, until the Casino realized what was going on. The Casino sued them and I believe the case is still in court.