Ask the Slot Expert: How can slot machines be random if I can't win five spins in a row?

Question: One of the things I'm curious about is in regard to the term "random."

You have mentioned, many times, that every pull on a slot machine is completely random from the next. After playing the slots for over 45 years, I have noticed that it is very rare to have a win on more than three consecutive spins. Even three itself is infrequent.

In playing mostly dollar and five-dollars slots, and in keeping detailed records, and in having played in 109 different casinos across the country, I have recorded five straight wins only a handful of times. I have also recorded a personal record of 82 consecutive losses in one session.

I cannot figure out why, in most every case, it's nearly impossible to win five times in a row. This is random?

Answer: Let's toss a completely fair die. What is the probability that we will throw a 6 five times in a row?

The probability of a 6 on the first throw is 1/6, and it is also 1/6 on the second, third, fourth and fifth throws. The probability is 1 over 6 to the 6th or 0.0000214 or about once in every 47,000 groups of five tosses. Not very likely.

Many years ago I played a low hit frequency slot machine and tracked the results of each spin. I too had a long streak of losing spins, about 80 spins. I had seen the PAR sheet for the game so I knew the hit frequency was 7%. On the average, only seven spins out of 100 will be winners. Put another way, 93 spins out of 100 will be losers. Doesn't it seem more likely that a player will get 82 consecutive losing spins than five consecutive winning spins?

The probability of winning a spin is 0.07, so the probability of winning five spins in a row is (0.07)(0.07)(0.07)(0.07)(0.07) or 0.0000016807. The probability of losing a spin is 0.93, so the probability of five losers in a row is 0.696. The probability of 80 losing spins in a row is 0.003, much more likely than five winning spins in a row.

An unlikely event, getting five wins in a row, not happening in a player's experience does not cast any doubts on the randomness of the outcomes.

Consider this kiosk game. Players choose one of six cards on the kiosk screen to reveal their mystery multiplier for the day. The multiplier values range from 5x to 10x. After playing the game dozens of times, I have gotten the 10x only once. My friends have a similar experience of having gotten the 10x once or twice or never. If we were randomly choosing one out of six cards, I'd expect to get the 10x 1 in 6 times.

I'd also expect to get the 5x 1 in 6 times, but I've gotten it only two or three times. Most of the time I get 6x, far more than 1 in 6 times.

My friends and I always compare the multipliers we get. I get 6x, Jean gets 6x, Tom gets 6x, Dominic gets 6x, Pat gets 6x, Henry gets 6x, Wilma gets 6x, Elaine gets 6x and Linda gets 6x. We all get 6x, but it should be more like 1 in 6 getting 6x if we were truly choosing a value at random.

The probability that six players get 6x in a truly random choice is (1/6) to the 6th or 0.0000214, yet it happens to us most times we play the game. This is a case where something that should happen rarely is happening frequently and our experiences do cast doubt on the randomness of the game.

The multiplier is chosen at random, but the randomizers aren't the distibution of the values on the screen and the choice that the player makes. What is actually happening in this kiosk game is that the system is randomly choosing the player's multiplier value after the player starts the game. The multipliers are weighted so the system is more likely to choose 6x or 5x than the higher multipliers. It doesn't matter which card the player chooses. The system has already chosen the multiplier. (I always choose the bottom right-hand corner and I almost always get 6x.) Even though the kiosk reveals the multipliers under the cards not chosen, the revelation is a sham. No matter which card the players choose, they get the multiplier chosen by the system.

In the case of five wins in a row, an unlikely event not happening does not make us question the randomness of the outcomes. In the case of the kiosk game, on the other hand, what should be an unlikely event happening frequently does make us question the randomness of the outcomes or, at least, how the outcomes are determined.