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29th January 2007

For those of you who like to play a little Keno I've done a few calculations to help you pick which game you would like to play. This is based on our local Queensland Jupiters Keno, but many Keno games throughout the world use similar numbers and payment schemes.

The Keno here is based on 80 numbers. A player makes a selection of numbers and hopes to match some or all of them with 20 numbers drawn by the Keno computer.

It is up to a player how many numbers they choose, and the rewards paid correlate to the probability of matching those numbers. eg. You choose 3 numbers from 80, the computer chooses 20 and you match all 3 - you get $44.00 return for a $1.00 bet. You would have returned $1.00 if 2 of your 3 numbers matched, and you would lose if 1 or 0 numbers matched.

The Three Number Game

I've heard people say that they like to play 3 number games because if they win they get $44.00 back, and it feels like they have quite a few wins. If they match 2 numbers they get their money back. This is exactly what the Casino wants you to think.

When you consistently play the three number game, only the Casino stands a chance of getting rich.

The odds

All games offered by the Casino (from 1 number to 40 number picks) offer roughly the same odds over time. See below for the probable return you will get for each dollar you play on various Keno games...

1 number: $0.75
3 numbers: $0.75
7 numbers: $0.82 (assuming 7 from 7 has a $12000 jackpot prize)
10 numbers: $0.762 (assuming the jackpot is at $2,000,000)
15 number: $0.748
40 numbers: $0.746

This means that over time, you can expect to lose. If you're playing a 3 number or 1 number game because you think the returns are better, think again. If you think that there just has to be more chance of getting 20 out of 40 than there is getting 10 out of 10, again the answer is no. In actual fact the probability of getting 10 from 10 is 1 in every 8,911,711 games, whilst the probability of getting 20 from 40 is one in every 25,646,754 games. Getting 10 from 10 pays a Jackpot prize which is often around $2,000,000 dollars whilst 20 from 40 only pays $250,000. The reason the overall probabilities are so similar is due to the combinations of smaller prizes for getting less matches than the numbers selected.

Life Changing Wins

So looking at the above I ask, if you are going to play the Keno at all, isn't it more sensible to play the game that has the best chance of giving you a life changing win? What one person considers life changing may not necessarily be life changing for another, but look at the following analysis and make up your own mind.

Continued below...

Analysis based on playing 1000 games for $1.00 per game

Play 1 Number

Average** money returned: $750.00
Expected*** Money Returned $750.00
Biggest possible single game win: $3.00
Estimated chance of winning the maximum within your 1000 games: 250 times
Estimated chance of winning the maximum in a single game: 0.25 times (1 in 4 games)

Play 3 Numbers

Average** money returned $750.00
Expected*** Money Returned $750.00
Biggest possible single game win $44.00
Estimated chance of winning the maximum within your 1000 games: 14 times
Estimated chance of winning the maximum in a single game: 0.014 (1 in 71 games)

Play 7 Numbers

Average** money returned $821.00
Expected*** Money Returned $567.00
Biggest possible single game win $12,000 (depends on jackpot)
Estimated chance of winning the maximum within your 1000 games: 0.024 (1 in 41)
Estimated chance of winning the maximum in a single game: 0.000024 (1 in 41667 games)

Play 10 Numbers

Average** money returned $762.00
Expected*** Money Returned $415.00
Biggest possible single game win $2,000,000 (depends on jackpot)
Estimated chance of winning the maximum within your 1000 games: 0.0001122 (1 in 8,911)
Estimated chance of winning the maximum in a single game: 0.0000001122 (1 in 8,912,655 games)

Play 15 Numbers

Average** money returned $748.00
Expected*** Money Returned $654.00
Biggest possible single game win $250,000
Estimated chance of winning the maximum within your 1000 games: 0.00000000233 (1 in 428,000,000)
Estimated chance of winning the maximum in a single game: 0.00000000000233 (1 in 428,000,000,000 games)

Play 40 Numbers

Average** money returned $746.00
Expected*** Money Returned $464.00
Biggest possible single game win $250,000
Estimated chance of winning the maximum within your 1000 games: 0.000039 (1 in 25,647)
Estimated chance of winning the maximum in a single game: 0.000000039 (1 in 25,647,000)

** Average Money Returned is based on the overall probability %. It assumes that a person playing the number of games required to win the 1st prize will win the first prize once and each successive prize the exact probable number of times (this itself is highly improbable).

*** Expected Money Returned takes account only of the winning combinations with a probability of 1 or more in 1000 games.

If you are going to play the Keno, you should at least know what you are playing for, and your chances of getting it. Hopefully the above will help to clarify this. Now, for those who didn't work out that the 10 spot game is the best life changing option, drop me a line, I think I have a deed to the Sydney Harbour Bridge somewhere I can let you have for cheap.

Re-betting winnings

Another point to consider is that most people re-bet their winnings if the winnings are of lower value than the amount originally played. This can be explained by simple psychology: nobody wants to be a loser and accepting less than your original bet is accepting a loss, so if you win less than your original bet you feel as though you should keep trying for "the big win".

With this in mind, a person playing any system is more likely to walk away with nothing than with a win, but the person playing a minor system such as a sytem 3 is more likely to have some days where they walk away with a win larger than their original bet. However, playing system 3 over a long period will never result in any substantial wins and the cumulative total of the wins that you keep will almost certainly be much less than the total amount of money lost. It's just that you will remember the wins more than the losses.

So if you like to put a few dollars on Keno with the hope that you might walk away with a few dollars more, but the knowledge that the odds are strongly in the casino's favour - play the minor systems.

If you want the best chance at winning a substantial amount, again knowing that the odds are strongly against you - play the system 10.

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