Cold streaks outweigh hot streaks

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Today’s topic comes courtesy of a friend of mine who asked me over dinner if he was way off base by saying sometimes it seems like video poker machines get into hot streaks. You hit a bunch of solid hands and feel like you’re going to get a Four of a Kind then all of a sudden you do. My friend wanted to know if he was imagining things.

Hot and cold streaks are a part of gambling. This does not mean games are rigged. Games would be rigged if the casino knew when these streaks were going to occur or made them occur for certain people. Streaks are simply what happens with random events.

Tossing coins

To explain this a bit better, I took the ultimate random event – a coin toss, and analyzed the results. I created a computer program that would flip a coin 10 million times. I kept track of the length of each streak and whether it was heads or tails. No surprise that there was little difference between these two potential outcomes.

But, if the chance of a head or a tail is exactly 50/50, what type of streaks should form? Okay, maybe you get two or three in a row of one type or the other, but there is always a 50% chance the streak will end, so how can this coin toss machine really get hot or cold?

Well, the longest streak I got was 25 consecutive heads. I had eight others (split between heads and tails) that were 20 or longer. There were a total of just over 5 million streaks, so these were very rare, but they did occur. One in 500 streaks were of 10 or more flips of the same outcome.

Now, imagine if this were a video poker machine where 50% of the hands end up as a winner and 50% end up as a loser.

You would see streaks of similar length of winning hands. You would also go, on occasion, 10-15 hands in a row without winning anything. But, these are not the true odds for video poker.

The probability of a losing hand in video poker (jacks or better) is closer to 55%. Let’s see what happens if we assume a 45% probability of winning and a 55% probability of losing.

Longest runs

Now, the longest streak of winning hands is 20. There are only 36 streaks of 15 or more. On the losing hand side, the longest streak is 27 and there are 571 streaks of 15 or more. With just a 5% swing in losing probability, long losing streaks become longer and far more frequent than winning streaks.

This situation is still not a representation of video poker. Of the 45% hands in video poker that are winners, about 35% of them are a High Pair (which is really a push) or a Two Pair (2-for-1/even money). It is only Trips or better that you remember at all.

So, what happens if we break this into three possible outcomes? Big winner of Trips or better, a losing hand and High Pair/Two Pair hands? The frequencies are 10%, 55% and 35% respectively.

The longest streak of big winners was 7. There were only two of these. There were only 78 streaks of 5 or more. So, real hot streaks are very rare. Getting 10 hands in a row of Trips or better, basically, doesn’t happen. More on this in a second.

In the meantime, streaks of hands in the middle zone max out at 15. There are less than 200 of 10 or more. Also, nothing changed about our losing streaks. There are more and longer streaks of losing hands. So, in short, cold streaks will be longer and more common than even mildly hot streaks and significantly longer and more frequent than true hot streaks.

Selective memory

So, if the longest streak of Trips or better was 7, how can we hear stories of someone hitting a Straight Flush, 2 Quads, a Full House, a Straight, etc., in a row? More than likely if the streak sounds less than believable that’s because it is. The person isn’t lying, they’re just using selective memory.

People don’t remember mundane outcomes. If in between these high paying hands you get a High Pair and a losing hand, you’ll probably forget about those hands. In reality, you had seven big winners, one small winner and one losing hand.

This is a totally different probability than seven big winning hands in a row. What you perceived as a smoking hot streak turns out to be a bit milder than you thought.

The beauty of video poker is these hot and cold streaks are just part of the randomness of a 5-card draw game. Machines will go hot and cold. You just can’t predict them.

But why does it seem like the hot streaks always end and the cold streaks, which you expect to end, sometimes go on and on. Well, as I’ve shown, the cold streaks will be longer and more frequent. The hot streaks will come to an end much quicker.

The lesson to be learned is when to get out after that hot streak, knowing a cold streak is likely around the corner.

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Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].

About the Author

Elliot Frome

Elliot Frome’s roots run deep into gaming theory and analysis. His father, Lenny, was a pioneer in developing video poker strategy in the 1980s and is credited with raising its popularity to dizzying heights. Elliot is a second generation gaming author and analyst with nearly 20 years of programming experience.

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