# Streak odds

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On one hand, saying that there are hot and cold streaks in video poker (or any casino game) could be considered to be contrary to the belief that math controls all the outcomes. This simply isn’t so. Streaks will exist – in fact the math tells us this. You become a ‘non-believer’ when you start thinking that you can predict what streak is about to happen instead of merely recognizing the streak that has just happened. In other words, the past doesn’t predict the future, only the math does.

It is these ups and downs that increase the thrill that can be had when playing in a casino. It is what is generally called the volatility of the game. To put it in simpler terms, some games are like a Ferris wheel, some are like a little roller coaster and some are like the monster roller coaster with your feet dangling that turns you upside down at 70 MPH. When you go to an amusement park they have all types of rides. When you go to a casino they have all types of games. Different strokes for different folks.

There is a mathematical formula that can be used to calculate ‘volatility,’ but I’ve never been one to bring out complex math formulas for the masses to use. If I tell you one game has a volatility of 3.56 and the other 5.73, what do you learn from this? Instead, I prefer to simulate the game and talk about some real-world style results that you can expect.

For jacks or better video poker, I ran 100-game ‘sessions’ and tallied how many the player won and lost and how big the win or loss was. I did not find the results surprising, and you should keep in mind that 100 games may only be 10-20 minutes worth of play. The goal here was to get a sense of streaks and not to see how you would do in a 3-hour session.

It should be little surprise that about 60% of the sessions ended in a loss; 44% of our sessions ended in a loss of 1-20 units, while 15% of the sessions ended in a loss of 21-40 units. A very tiny number of sessions had larger losses. On the winning side of things, 27% of the sessions had wins in the range of 1-20 and 9% had wins of 21-40%. In both cases, these are considerably smaller in quantity than their losing counterparts. However, 3.6% of our sessions end up as winners of 41 or more. If a Royal came up within the session, then the win was in the 800 unit range.

This is the true essence of volatility for casino games. We’re going to lose more often than we win, but there will be a handful of really large wins and the losses can only get so big over a period of time. If you’re playing 100 games of video poker then the absolute most you can lose is 100 units (assuming a single-coin play). However, in reality, you’re not very likely to lose more than about 30 units no matter how bad of a streak you hit. At the same time, the upside has a lot more room in it. Hit a Royal and you’ve got a win of nearly 800 guaranteed. Hit a Straight Flush and you’re up 50 in a single hand. Quads will all but guarantee you a winning session. There will also be a fair amount of times when you’ll amass enough Trips and High Pairs to eke out a small gain.

What is quite interesting in all this is that only 1.7% of the sessions ended in a ‘tie’ – no win or loss. Despite playing a game that is 99.6% payback and is nearly dead-even, you’re just not going to wind up even very often.

For comparison purposes, if we use a simple coin-flip game (heads you win, tails you lose), we find that only 1% of the sessions would end with a win or loss of greater than 20 coins vs. a 25% frequency for video poker.

Until we analyze all the casino games, it might be hard to decide which is what type of ride, but I think we can all agree that a coin-flip game would be something less exciting than the ticket booth.

You can try out your strategy by playing our video poker game.

### 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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