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When I was in high school there was a story about a man who won millions of dollars playing keno.

The amount of money and the location appear to be true based upon this wikipedia article:

In 1994, Ranogajec reportedly won a $7.5 million Keno jackpot at the leisure and entertainment complex North Ryde RSL Club, of New South Wales, after reportedly betting "significantly more than $7.5 million" to win it but coming out ahead on account of the additional, smaller prizes awarded along the way to the jackpot.

My question is, with a reasonable knowledge of statistics and enough money (say $10 million) is it possible to win the KENO jackpot?

The version of KENO I am referring to is the on on this site: http://playkeno.com.au and I cannot confirm how many numbers he matched to get the jackpot (so was did it match smaller numbers with a larger investment or visa-versa).

As commented below, What I'm trying to get across is that this wasn't just some guy off the street, he is a highly seasoned gambler and maybe one of the best in the world. He played for a long period of time with large amounts of cash wagered. He seemed to expect that he was going to win. If you read his wiki article you will see he always tries to stack the odds in his favor. So why Keno, if it's just any old game? This is not just a question of maths or just saying if gambling you will always lose. He obviously didn't think so.

Sklivvz
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going
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    It's an anecdote. Anecdotes should be regarded more like opinions or even as part of a marketing strategy. MLM/Pyramid schemes often rely on anecdotes similar to the myth you outlined (which reminded me of this) as a sales tactic. When it comes to gambling, the odds are typically in the favour of the dealer/casino, despite the appearance contrary to that. – Randolf Richardson Jun 06 '11 at 04:38
  • @Randolf - I've removed the anecdote. – going Jun 06 '11 at 04:49
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    @xiahouzi79: The anecdote was actually okay -- I was just commenting on that part of it (I wasn't expecting you to remove it). In fact, I think you wrote it all very well and that the anecdote provided some interesting background for the question. – Randolf Richardson Jun 06 '11 at 04:53
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    @Randolf - It's a tough crowd here. I personally prefer a bit of background info than just reading the claim. But I seem to get in trouble with most of my question. – going Jun 06 '11 at 05:03
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    @xiaohouzi79: Don't buckle in to peer pressure (and please don't view this as an attempt by me to pressure you to not buckle in to peer pressure, heheh), even among skeptics! Being skeptical is a learning process that is much more difficult than being an optimist or a pessimist because true objectivity can be very hard on one's ego -- new facts can arise that cause us to change our perspective (we have to leave a previously established comfort zone and adapt). It's clearly the right thing to do, but it may also be the harder choice (as it seems most things in life are that are "right"). – Randolf Richardson Jun 06 '11 at 05:12
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    There is no claim in this anecdote that this *will* happen when you do this. Only that it once happened. And such is the nature of lotteries. Yes, it's possible to win, by having the luck of getting the right number. Can you bet in a specific way to make the chance of this happening 1 or larger? No. – Lennart Regebro Jun 06 '11 at 09:49
  • @xiaohouzi79: Of course. And those mathematics are there to make sure the lottery gets more money in than out. You would have to be pretty crazy or bad at maths to make it otherwise. :-) If you want mathematical proofs of this, math.SE is the right place. – Lennart Regebro Jun 06 '11 at 09:52
  • The wikipedia article on KENO says that the expected return is 62 cents for every dollar invested. This is much lower than 99.56 cents per dollar invested in Video Poker (some variants). There used to be a variant of Video Poker (Deuces Wild, I believe) that had higher than 1 dollar expected return, but, obviously, the game is no longer available in casinos. – Alexandru Jun 06 '11 at 10:31
  • @Alexandru - What I'm trying to get across is that this wasn't just some guy of the street, he is a highly seasoned gambler and maybe one of the best in the world. He played for a long period of time with large amounts of cash wagered. He seemed to expect that he was going to win. If you read his wiki article you will see he always tries to stack the odds in his favor. So why Keno, if it's just any old game? – going Jun 06 '11 at 10:34
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    Long-term play invokes the Law of Large Numbers, which means that results tend towards the expected. In any gambling against the house, the house will win in the long run. Gambling is a game of chance for the individual, but statistically a sure thing for the house. – David Thornley Jun 07 '11 at 02:19
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    In April 1994, Daniel Corriveau managed to win $600,000 CAD playing the Casino de Montréal keno. He was able to pick 19 of the 20 winning numbers three times in a row. Turns out the keno numbers were picked by a Random Number Generator which was reset every morning with the same seed number. Oops. – ghoppe Jun 08 '11 at 09:02

1 Answers1

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Ah, good old Zeljko Ranogajec. He has so secretive and has so many rumours of his super-human abilities flying about, he's like the Keyser Söze of the gambling world!

Keno has a growing jackpot, where a portion of the losses from previous players accumulate.

The expected return (in the statistical sense of "expected") of a ticket depends on the size of the jackpot. Generally, the expected return is negative. If the jackpot is exceptionally large, which occurs rarely, it could actually turn out to have a positive expected return.

In such rare cases, it may make sense to purchase a large number of tickets. It would take millions of dollars to bring the expected variance in the return down to a manageable level, but Ranogajec (allegedly!) spends that sort of money on bets regularly.

I have heard other (plausible but unsubstantiable) rumours that Ranogajec gets substantial discounts from TABCorp in return for his business. (Casino Online claims it accounts for 6-8% of TABCorp's revenues.) [I heard discounts as high as 7%, this newspaper article suggests 4%.] This should be factored in when trying to work out the estimated return.

Gambling is an area where skepticism is particularly called for, and problem gambling is a real problem. Please consider your own situation carefully before placing a bet.

Addendum:

I just snuck a look at the original anecdote that was deleted from the question, and that was not inline with this answer. It suggested long-term play for a smaller amounts. It also suggested that Keno organisation asked him not to continue. I find both of these claims unlikely.

Keno has, long-term, a negative expected outcome, and only becomes positive occasionally when jackpots are particularly high. After the jackpot has been won, the professional player will stop playing voluntarily, as the return has become negative again.

The casino (i.e. TABCorp in this case) knows they have a positive expected return, and would therefore always encourage further play (even when the jackpot is high, as that money is always set aside, and not considered profit. They aren't "risking" it in the normal sense.) They have no motivation in turning down a winner from betting again. (This is not necessarily the case in all situations - including blackjack, and smaller bookies declining to accept large bets.)

Addendum 2:

A recent Australian Financial Review piece suggests that Ranogajec's syndicate won at least four Keno jackpots (out of North Hobart in Tasmania, not North Ryde in NSW). The article leans heavily on hearsay, but suggests that, indeed, they bet when the Keno jackpot was high, and that they had negotiated a considerable reduction in the agent's commission.

Oddthinking
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    Here is another case where a lottery may, when the jackpot is large enough, have a positive expected outcome: http://articles.boston.com/2011-07-31/news/29836200_1_lottery-tickets-claim-prizes-massachusetts-state-lottery – Oddthinking Aug 02 '11 at 07:27