Keno Odds |
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Keno Odds, Mathematics and Statistics
First of all, it is important to note that Keno is much more difficult to win than it appears to the average player. This is because most of the players do not have a realistic conception of how probabilities work. In the game, for instance, there are 80 numbers on a card and 20 of those 80 are randomly selected for each drawing. Drawings are completed independently of one another, thus their outcomes are wholly random and unrelated to what has happened previously. Therefore, in a good Keno game, no numbers are favored and everything is random. Players, however, tend to fall prey to the gambler's fallacy of logic that allows them to think that drawings are interdependent of one another, or influenced in some outward manner. This is, of course, not true, and any such anomalies are only due to the random walk of the game and the chance route of the probabilities. It would, next, be apropos to discuss the mathematics that are behind the game. The math starts out very simply but quickly becomes much more difficult to follow. The most basic proposition in the game can be found when the player selects one number on their game card. The result of such a selection is a 1 in 4, or 25%, chance that the player's number will be selected. This is because there are 80 numbers and 20 are chosen, thus, 20/80 equals 1/4, or 25%. Now, it would seem, then, that any further number selections would have equal odds. For instance, outwardly it would appear that if a player selected 2 numbers then their odds would be 1 in 4 multiplied by 1 in 4, or 1 in 16. This estimate, however, while close, is not entirely accurate. Why? The answer is that when a player selects more than one number then the numbers become influenced by one another and how many have already come up previously. Therefore, a player's actual odds of hitting both of the 2 numbers they've selected is 1 in 15.6316, or 6.01%. The odds quickly escalate, too. For a 10-number card the odds of hitting all 10 numbers is 1 in 8,911,700, or 0.00000011221%. Finally, it would be interesting to discuss the odds differential that makes Keno a profitable game for casinos. Players are generally allowed to choose from 1 to 15 numbers per drawing. The odds, though, of hitting all 15 numbers that one has selected are almost statistically insignificant. Even 10 numbers, as mentioned above, are extraordinarily difficult to hit. Despite this, though, the odds given to the player are usually but a fraction of what they should be. For instance, the odds of hitting a 7-number card for all 7 numbers is 1 in 40,978. Therefore, the odds given to the player should be somewhere in that neighborhood, with consideration given to the fact that they have the possibility, in most games, of getting a return on their money by hitting as few as 3 numbers. However, in many Keno games, the players are given odds like $2,000 to 1 for hitting all 7 numbers. Obviously, this doesn't even approach the true chances of doing so, and that is precisely why Keno is such a profitable game for the casinos and is considered to be such a bad bet for gamblers that only amateurs will play. Speaking of odds brings up mathematical thoughts. There is a very interesting site at Winning with Numbers that covers bingo, lotteries and keno. It has sections discussing the odds of each as well as additional information about each game. Definitely worth the time to check it out if the mathematical side of games interests you. The Keno Odds section is an even more in depth discussion than I have here. Gambling - The Gambling.co.uk
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