11.04.2015

It is played at casinos all over the world, but it is also offered by national lottery companies along with other lottery games.
Explore Keno from the probability point of view.How To Play KenoKeno is a lottery game where there are 20 winning numbers drawn out of the total 80 numbers, while players can choose to catch 1 to 20 numbers by marking spots on a Keno ticket. In case of the traditional way the bubble is filled with 80 balls and mixed by an air blower.
The players are encouraged to wager by so called Keno runners.Some casinos and lottery companies limit the choice of numbers to be hit to 10 to 15 numbers. The highest win is then paid out when a player manages to hit those 10 to 15 numbers out of the 20 drawn. Then it depends on, of course, how many numbers a player attempts and manages to catch or hit. These hypothetical odds would have to be given for the event of hitting 20 numbers out of 20. Some casinos offer quite a large payouts or at least they return money if you fail to hit any number. However it varies from casino to casino, therefore it is always useful to familiarize with the pay table.The following two tables show the probabilities and the corresponding true odds for any-spot Keno ticket, that is for all combinations of spots (1 to 20) and hits (0 to 20).

Thus they are universal for any Keno game regardless of the maximum number of spots allowed. Additionally casinos or lottery operators may quote different payout ratios for the same wagers. Potential winnings are stipulated as multiples of the bet amount on the pay tables that have to be placed on a visible place or published online.Various payouts present various house edges. It is typically limited to 10, 12 or 15 numbers (spots), but it can also be 20 numbers right away.
Let us put the most typical 10-Spot Keno variation under the microscope and follow some concrete calculations.This web page is a follow-up to the general Keno rules. We will also use some model or possible pay table, which is the last element to enable us calculate the house edge (based on this model pay table). As the pay tables vary from casino to casino, so does the house edge.A Model PaytableLet us start with the pay table. Table 1 shows the payout ratios (the multiples) for all combinations of spots and successful hits. The calculations of odds and probabilities below are 100% valid for any ten spot Keno game.

First of all, as always, the total of probabilities in a column must equal one (or 100% if you like). We already know that probability can be defined as the number of positive possibilities (the nominator) divided the total number of possibilities (the denominator).It is easier to determine all possibilities (combinations) a€“ they are the same for all-spot Keno games. We may use the Excel function =COMBIN(80,20) and get the result of 3,535,316,142,212,180,000 combinations (the denominator).
To calculate the number of all winning possibilities is a bit harder as we have to catch 10 numbers out of 10, but there are 20 winning numbers drawn out of 80. That is the only fair way to assess it and that is actually how the house edge is being calculated. Thus if you played 10 spot Keno with this pay table (Table 1), then, in the long run, you would likely lose about 50 cents per each dollar wagered in the game.It is needed to highlight, however, that the expected value is related to the long-term period and that it does not mean that you could not be lucky enough to win the top prize with your first Keno ticket.

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