Slot Volatility Slot Volatility. The word volatile as applied to a slot machine basically refers to the amount of risk inherent to a specific game. It is used to describe how often and how much you can expect to win during your playing sessions. Some games can present long dry spells with occasional big wins. Mean / Median /Mode/ Variance /Standard Deviation are all very basic but very important concept of statistics used in data science. Almost all the machine learning algorithm uses these concepts in.
Standard Deviation The Standard deviation slots strategy is perhaps the most advanced of all slots playing tactics. It involves using a mathematical equation to determine on what spins the machine is most likely to yield a winning slots.
In our everyday lives, the notion of “volatility” is associated with changeability and impermanence. Whether it is applied to people’s emotions, stock market performance, political situations or the weather, being “volatile” implies a certain fickleness that seems random and capable of leading to explosive outcomes. In casino gambling, the same attributes apply.
Identifying Volatile Games
When we say a casino game is highly volatile, we mean it pays out big now and then but also causes lots of losses, making it less than reliable as a source of steady winnings. A good example is Keno with its potentially massive rewards and frequent streaks of worthless cards. Slot machines are typically very volatile, too.
On the other hand, games with a low degree of volatility are seen as more dependable, producing a rather steady dispersion of expected wins and anticipated losses. Pai Gow Poker and Baccarat come quickly to mind as table games of this sort. Roulette, Blackjack and Craps also feature limited volatility, depending on the bets that are made.
Players should be very aware of just how volatile the games they choose to play can be. Questions to ask include: How much should I expect to win (or lose) if I wager a certain amount? How likely are the outcomes of this game to fluctuate from that expectation? How confident can I be in the actual win (or loss) matching up to my predictions?
Fortunately, beyond the obvious financial swings that accompany each deal, spin or roll, there is a mathematical foundation to every game found in a casino. With a highly precise degree of predictability, it is possible to use statistical theory to calculate just exactly how volatile a game might be and use that information to one’s playing advantage.
A Matter of Standard Deviation
In gaming, the ups and downs likely to be encountered during play are characterized by a function called “Standard Deviation.” The symbol for Standard Deviation is “σ” (the lowercase Greek letter sigma). It gives us a way to know the probability of outcomes deviating from expectations, particularly in the short term. In other words, σ is how we quantify “the luck factor” in a casino game.
For any game, Standard Deviation can be determined by calculation. It is “the square root of the arithmetic mean of the squares of the deviation of each of the class frequencies from the arithmetic mean of the frequency distribution.” Expressed as an equation,
where N = the number of values evaluated, x = each value in N, μ = the mean of the values and Σ is the sum of values from the first value (i = 1) to the last value (N).
Although the math may look a bit imposing, the Standard Deviation for the most common casino games has already been worked out by gaming analysts for ready access by anyone. The following table is a simplification of the calculations expressed as ranges, taking into account varying rules and types of bets possible, and listed in order of lowest σ to highest.
Keep in mind that higher potential payouts usually mean a higher σ and thus greater volatility. Also a true picture of volatility requires comparing σ to the House Edge for the game in question. If two games have the same House Edge, the one with the higher σ will be the more volatile of the two. Similarly, if two games have the same σ, the one with the higher House Edge will be the more volatile. For a more detailed analysis of the application of Standard Deviation to casino games and bankroll management, please see the section on “Variance” provided elsewhere on this site.
What is Standard Deviation?
Standard deviation is a number that describes how spread out the values are.
A low standard deviation means that most of the numbers are close to the mean (average) value.
A high standard deviation means that the values are spread out over a wider range.
Example: This time we have registered the speed of 7 cars:
The standard deviation is:
0.9
Meaning that most of the values are within the range of 0.9 from the mean value, which is 86.4.
Let us do the same with a selection of numbers with a wider range:
The standard deviation is:
37.85
Meaning that most of the values are within the range of 37.85 from the mean value, which is 77.4.
As you can see, a higher standard deviation indicates that the values are spread out over a wider range.
The NumPy module has a method to calculate the standard deviation:
Example
Use the NumPy std() method to find the standard deviation:
speed = [86,87,88,86,87,85,86]
x = numpy.std(speed)
print(x)
Example
speed = [32,111,138,28,59,77,97]
x = numpy.std(speed)
print(x)
Variance
Variance is another number that indicates how spread out the values are.
In fact, if you take the square root of the variance, you get the standard deviation!
Or the other way around, if you multiply the standard deviation by itself, you get the variance!
To calculate the variance you have to do as follows:
1. Find the mean:
2. For each value: find the difference from the mean:
32 - 77.4 = -45.4
111 - 77.4 = 33.6
138 - 77.4 = 60.6
28 - 77.4 = -49.4
59 - 77.4 = -18.4
77 - 77.4 = - 0.4
97 - 77.4 = 19.6
3. For each difference: find the square value:
(-45.4)2 = 2061.16 (33.6)2 = 1128.96 (60.6)2 = 3672.36 (-49.4)2 = 2440.36(-18.4)2 = 338.56(- 0.4)2 = 0.16 (19.6)2 = 384.16
4. The variance is the average number of these squared differences:
(2061.16+1128.96+3672.36+2440.36+338.56+0.16+384.16) / 7 = 1432.2
Luckily, NumPy has a method to calculate the variance:
Standard Deviation Slot Machine Jackpots
Example
Use the NumPy var() method to find the variance:
How To Find Standard Deviation
speed = [32,111,138,28,59,77,97]
x = numpy.var(speed)
print(x)
Standard Deviation
As we have learned, the formula to find the standard deviation is the square root of the variance:
Or, as in the example from before, use the NumPy to calculate the standard deviation:
Example
Use the NumPy std() method to find the standard deviation:
speed = [32,111,138,28,59,77,97]
x = numpy.std(speed)
print(x)
Determine Standard Deviation
Try it Yourself »Symbols
Standard Deviation is often represented by the symbol Sigma: σ
Variance is often represented by the symbol Sigma Square: σ2
Chapter Summary
The Standard Deviation and Variance are terms that are often used in Machine Learning, so it is important to understand how to get them, and the concept behind them.