Game Volatility - What does it Affect

For sure you know what volatile game is like compared to a non volatile game. But do you know what exactly volatility is and how you can use it in your everyday operations?

Game Volatility

Volatility is a measure how much the game random outcomes vary. In general you get high volatility by high payouts for some results that are very unlikely to occur. On the other hand you get low volatility with low payouts for results that occur frequently.

You can measure volatility with "standard deviation". The latter is usually marked with small greek letter sigma 𝜎.

Roulette example

A nice example is the game of roulette. The outside bets have very low volatility, one of the lowest volatilities in gaming. For example the bet on red has quite high probability of winning (48% in single zero roulette) and the payouts are only even money. For this bet the standard deviation is 1.00.

Another bet to look at is a single number bet. Here, the probability of winning is lower (2.7% in single zero roulette) and payouts are 35 to 1. This bet has standard deviation of 5.84.

The roulette game is also a good example that a single game may have several bets available with different volatility.

Do note that most EGMs have even higher volatilities than single number bets in roulette.

Deviation during several games

The most important aspect of variation is that it reduces with the number of games played. So, the more games your players play, the less deviation is expected in the final outcome. This is critically important because it is highly unlikely for your table or EGM to have a loss. That is true after enough games played - in the long run the casino wins. The central limit theorem from statistics explains this phenomenon.

Let's continue with the roulette example. By using standard error the casino result after a single 10€ bet would be 0.27€ ± 10€ (from -9.73 to +10.27€).  The lower end of the range is the mean (house edge times the bet) reduced by standard deviation times the bet. Upper end is the mean plus the standard deviation times the bet. All this with 68% of certainty. That is, in 68% of the games, the outcome should be in this range and 32% of the games should be outside of that range. This result for one game does not make much sense because the standard error formulas are valid only after several games played.

A bit later there were 100 games played with 10€ bet for a total bet of 1,000€. Now the expected casino result is 27€ ± 100€ (from -73€ to +127€). The standard error reduced quite a bit relative to the amount of bet and house edge. The standard error is reduced by the square root of the number of games played - in this case by a factor of 10.

Later still there were 10,000 games played for a total bet of 100,000€. The expected casino result is 2,700€ ±  1,000€ (+1,700€ to 3,700€). And the casino result is in this range with 68% certainty.

In this example you can see that that when the number of games is low the casino is quite possibly taking a loss. But with more games played the win of the casino is almost guaranteed. The following graphics presents this change as the number of games increases. The blue line represent the interval of the casino result that can be expected in 68% of cases after 1, 100 and 10,000 games played. 

But what about higher volatility bet like the straight number? For 1 game of 10€ bet the expected result is 0.27€ ± 58.4€, that is -58.13€ to  58,67€. For 100 games the expected result is 27€ ± 584€, that is -557€ to 611€. After 10,000 games per 10€ the expected result is 2,700€ ± 5,840€ (-3,140€ to 8,540€). The casino might be winning quite some more but it might also be loosing quite some.

In next graphic you can see comparison between red-black bet (blue line) and straight number bet (green line). Both lines represent the interval of the casino result that can be expected in 68% of cases.

Do note that the numbers were a bit rounded in this example and the mathematics a bit simplified.

Conclusion

To summarize, you should request volatility information for each game you receive! Use that information to know what to expect from a certain game and also to know when a game seems suspicious.

What is your opinion on this topic? Do you use the volatility information? Tell me what you think in the comments below.