[RD (OP)]

The Bulgarian authorities have ordered an investigation after the same six numbers were drawn in two consecutive rounds of the national lottery.

The numbers - 4, 15, 23, 24, 35 and 42 - were chosen by a machine live on television on 6 and 10 September.

An official of the Bulgarian lottery said manipulation was impossible.

A mathematician said the chance of the same six numbers coming up twice in a row was one in four million.

http://news.bbc.co.uk/1/hi/8259801.stm

 "one in four million" ?

If the numbers are 1 - 50, then the odds of any particular six number balls are 13,983,816 ,
 (this ignores the sequence in which they were drawn).

So every time six balls are drawn, (whether or not they are the same as last weeks draw),
 is a 1:13,983,816 event , i.e. 1 in ~14 million, not 1 in 4 million.  

[The fact that the same numbers were drawn the week before does not make the odds that same numbers will be drawn the next week more or less likely: it's 14 million to one on each occasion].

[Geezer]

The 1 in 14 million number is for 1 - 49. For 1 - 50 the odds are slightly worse; 1 in 15,890,700.
Even if it's 1 - 45, the odds are still 1 in 8,145,060, so I don't know how he could figure 1 in 4 million. Maybe they don't use the typical pingpong ball system.

For those that want to play along at home, for numbers 1 - 49, the odds against any particular combination are:

49/6 x 48/5 x 47/4 x 46/3 x 45/2 x 44/1 = 13,983,816

[Bored chemist]

Perhaps the mathematician knew the odds of the machine being tampered with were about 1 in 4 million.

[Geezer]

It may be reassuring that the same numbers came up twice in a row. There is no reason why that should not happen.

Related thought: If instead of picking six numbers between 1 and 49, players were asked to select any number between 1 and 13,983,816, would anybody play the lottery?

[RD (OP)]

The 1 in 14 million number is for 1 - 49. For 1 - 50 the odds are slightly worse; 1 in 15,890,700.

My mistake it's 1-49, not 1-50. I have a good excuse for this error: I don't play the lottery.
To paraphrase Dr Johnson : national lotteries are a tax on stupidity.

Maybe the "4 million" is a typo in the BBC article: forgot the "1" (14 million).

[I wish they left off the "1" from my annual BBC licence fee   [] ]

[Geezer]

Now, if we could improve our odds a bit using the premonition techniques being described at the moment on another thread, we'd be off to the races. Even a marginal improvement would give us a big win on the Roulette wheels (until they kicked us out of the Casino!)

[RD (OP)]

Sod premonition, use science ...

Professional gamblers are rushing to buy £1,000 devices that they believe will enable them to win millions of pounds in casinos when the gambling industry is deregulated next year.

Hundreds of the roulette-cheating machines - which consist of a small digital time recorder, a concealed computer and a hidden earpiece - were tested at a government laboratory in 2004 after a gang suspected of using them won £1.3m at the Ritz casino in London.

After the research, which was never made public but has been seen by the Guardian, the government's gambling watchdog admitted to industry insiders that the technology can offer punters an edge when playing roulette in a casino, and the advantage can be "considerable".

The government's national weights and measures laboratory investigated the technique. It is thought the cheats first identify a "biased" wheel, where the ball appears to commonly drop in roughly the same zone. They also look for signs on the wheel of a "manageable scatter", which means that when the ball strikes a certain number, it will usually fall into a neighbouring pocket. The unpublished report concluded: "On a wheel with a definite bias and a manageable scatter, a prediction device of this nature, when operated by a 'skilled' roulette player, could obtain an advantage when used in a casino."

Mark Howe, who sells the devices for £1,000 from a workshop in Sheffield, claims his software will also work on level wheels. Surrounded by the soldering irons and laser sensors he uses to make his devices, he gave the Guardian an apparently successful demonstration of the software he said earned him a substantial sum before he was banned from British casinos in the 1990s.

http://www.guardian.co.uk/uk/2006/sep/16/gambling.mainsection

[Geezer]

I think the casinos in Nevada go to great lengths to eliminate bias, or at least, long term bias. They switch the wheels between tables etc. They probably keep a record of every spin so they can detect any quantifiable bias. Come to think of it, if they are not doing that, we should file a patent on such a process. Might be worth more in the long run.

[RD (OP)]

Given the type of businessmen who run casinos,
 anyone caught using a computer in one will have to use their winnings to pay for an extended stay in hospital.

[Geezer]

Agreed. That is why it would be better to provide the businessmen with technology that helps them protect their investment. It's not so different from selling anti-virus software.