Learn to calculate the odds in Keno

This video aims to address the following inquiries:

• What are the rules of keno?
• What are the chances of winning?
• What is the payout percentage for this particular wager?

Hello, I'm Mike, and today you will master how to compute the odds in keno Keno is an incredibly straightforward game. In brief, players select between 2 to 10 numbers from a selection of 1 to 80. Once the player completes their selection, the game randomly chooses 20 numbers from the same range.

The player is paid according to…

…the count of balls that correspond with the numbers selected by the player. For instance, if I choose five numbers and only two match, I won't win anything. To secure a win with five numbers, at least three need to correspond.

So in that instance, I matched three numbers: 17, 25, and 56. I ended up winning $3 from a $1 wager. When I mention winning, that reflects what I received back. In the game of Keno, all payouts are on a 'for one' basis , which means that even if you win, the original amount you wagered is not returned. Essentially, winning merely means you get your original stake back, akin to a push.

Click “See Pay”

This will present the complete payout chart based on how many numbers you chose. For example, if you selected 10 numbers and matched 5, your payout would be 5. Matching 6 yields 24, and matching 7 gives you 146, and so forth.

This game, by the way:

can be found atvideopoker.com My friends graciously permitted me to use their game for the purposes of this video. Let's dive into the math now.

Before we delve into Keno's math intricacies,

I want to introduce a couple of concepts that are essential for understanding what comes next. One of these is the factorial function, which represents the product of all integers from one up to the number you apply the factorial to. For example, five factorial equals one multiplied by two multiplied by three multiplied by four multiplied by five, resulting in 120.

What is the practical use of this?

This simply indicates the number of ways to arrange n items. To illustrate, the possible arrangements of the numbers 1 through 5 total 120.

Now, let’s discuss the combinations function.

This represents the number of ways to select Y items from a total of X items. For instance, at El Pollo Loco, they have eight different side dishes, and you're likely allowed to select three of them.

How many different ways could you choose three out of eight options?

This is expressed as 'three choose eight', calculated using the formula X factorial divided by Y factorial and then divided by (X - Y) factorial, where X stands for the total items and Y represents how many you're selecting.

For our El Pollo Loco example, where there are eight side dishes and you can choose three, the total combinations equal eight factorial divided by (eight minus three) factorial, which is five factorial, divided by three factorial, giving us 56, if I'm not mistaken.

Let's calculate the odds for selecting five numbers:

If the player correctly identifies all five, their payout will be 838. The possible combinations for that scenario amount to 20 choose 5, totaling 15,504. To achieve four correct picks, which awards 13, is calculated as the number of ways to choose 4 winning numbers from the 20, or 20 choose 4, multiplied by the single method to choose the incorrect number, resulting in 290,700.

The minimum win occurs when three out of five are correct, thus the combinations for picking three winning numbers from the pool of 20 are calculated as 20 choose 3, multiplied by the combinations of selecting two from the 60 non-winning numbers, equating to 2,017,800.

Now…

However, instead of explicitly calculating the number of losing combinations, let's just find the total combinations available, taking into account both wins and losses. This is simply the number of methods to select 5 numbers from the 80 available, which equals 24,040,016.

Next, we multiply the payouts by the total combinations to obtain results.

The combined returns, or the expected payout for the player if one were to cycle through all possible scenarios, work out as follows: 838 multiplied by 15,504 equals 12,992,352. Similarly, 13 multiplied by 290,700 results in 3,779,100. In addition, 3 multiplied by 2,017,800 equals 6,053,400.

Summing up all these return totals provides us with 22,824,852. This implies that if the player participates in this game 24,040,016 times at a $1 wager each time, their expected return would be $22,824,852. To find the return percentage, we simply divide that figure—22 million—by the 24 million total, resulting in 94.95%.

Another way of expressing that is…

The player can anticipate recouping nearly 95% of their total wagers, while 5.05% is retained by the casino. It's important to note that this paytable is exceptionally generous, representing the maximum potential. Generally, paytables tend to offer lower returns, highlighting the necessity of finding a lucrative paytable.

Finally

Now, let's examine Keno odds using Excel. The total combinations for the player to achieve correct selections pick 10 out of 10 represent the potential combinations for the player to select 10 numbers from the 20 that the game generates, which totals 184,756.

The count of correct guesses when the player matches 9 out of 10 corresponds to 20 choose 9 multiplied by 60, the one incorrect selection. A general formula for determining accurate predictions can be articulated as 20 choose the number of accurate picks multiplied by 60 choose the number of incorrect picks, represented as follows:

We can easily copy and extend this calculation. Let’s try to replicate it upwards as well to ensure accuracy. Yes, it appears correct.

I won’t be calculating the number of losing combinations; instead, I will focus on the overall total combinations, which represent the number of methods to select 10 numbers from 80. The potential return is calculated by multiplying the total combinations by the payouts.

Let’s extend that downwards and compute the grand total.

If the player were to partake in this 1,646,492,110,120 times, their expected average return would be $1,534,456,875,040. To express that in percentage terms, it equates to 93.2%. Essentially, for every dollar wagered, a player can expect to receive 93.2% back, with the remaining 6.8% going to the casino.

I might remind you, again…

…it’s worth noting that not every paytable is as favorable as this one. In fact, this represents the most advantageous scenario. Many times, that figure may lower to 23 or even less. The payouts for 146 are often lower as well, though the major prizes tend to remain consistent. Once more, it cannot be stressed enough the benefit of looking for superior paytables.

In conclusion, I hope you can indulge my request to share information about my website here . It hosts a wealth of resources regarding Keno, featuring this specific game where you can choose between 1 to 15 numbers. You can opt to select your numbers manually or utilize a quick pick feature. Additionally, there's an option for autoplay.

Besides this, we have a bunch of keno calculators . Let’s take a look at the standard Keno version. I will refer back to the pick 10 payout structure I mentioned earlier. As you may recall, correctly guessing 10 numbers results in a payout of 10,000. Nine gets you 45,000, eight brings 1,000, seven pays 146, six returns 24, and five nets you 5. After clicking calculate, you will see the full breakdown: probabilities for each potential win, frequencies, and variations. Here we can also see the expected payout.

The bottom line…

...and here's that same figure of 91.2%. I trust you can spot that minor number I previously explained how to calculate. My discussion does not stop at regular Keno—I'm also covering Power Keno, Super Keno, Cleopatra Keno, Caveman Keno, Caveman Keno Plus, Extra Draw Keno, and Triple Power Keno.

I provide comprehensive resources regarding the returns for every potential game and paytable you might come across while in Las Vegas, Keno surveys, insights on who offers the best games in this city, along with numerous internal links related to Keno. I frequent this topic because, candidly, the math involved is quite straightforward.

Well, I believe this video has sufficiently covered the topic. Thank you for tuning in. Until next time!

Written by: Michael Shackleford