Help me Win A Case of Beer Of My Stupid Friend

Hi,I am new here and not great at Maths and apologise if this question has been answered before.

I am trying to prove my aquaintance is wrong with his supposed fool proof system. It is based on a two number Bingo game(20 numbers drawn between 1-80 paying $12 for the two correct numbers),where you mark off numbers in consecutive games until only two numbers are left that have not been drawn yet. These two numbers become your numbers. You then wait til the 15th game(unless one of the numbers has been drawn where you start again ie wait another 15 games)to start betting. For every non winning bet you increase the stake.

Now my friend claims that because the win pays 12-1,the numbers haven't come out as a pair yet and the fact you wait 15 games before betting you are giving yourself a huge advantage and the law of averages dictate that you must win sooner rather than later(definately within 29 spins with a profit of $55 if it occurs on spin 15 ie $5 outlay for $60 return up to $300 profit on spin 29 ie bet of $75 with total outlay of $600 for return of $900). Now my argument is that,despite the discipline and patience he is showing, he has fallen for the Gamblers Fallacy and he is just as likely to win if he picked two random numbers on the first draw rather than waiting for the two last numbers to be revealed. The fact you wait 15 games does not change the probability of the last two numbers coming out,the odds do not change for an outcome from the first draw to the 100th draw.

Can you please tell me who is right?

Thank you in advance and any advice or explanations would be greatly appreciated,as I like beer.

Quote: Speedymetric

the law of averages

Tain't no such thing. So without bothering to untangle the details of your friend's system or whatever it is, I would say you get the beer.

Enjoy your beer.

The bingo balls do not know if they have or have not been drawn previously. They are just as likely to appear as not appear.

Ask your friend to consider how his system would work if in the time leading up to the start of your tracking period, the two numbers had appeared together in every single game since the hall opened 20 years ago. It was just your luck that you just happened to start tracking when the balls, needing to adhere to the "Law of Averages", decided not to appear. Not only that, they will not appear together for another 20 years, since the LOA dictates that everything even out.

Crazy, if it worked that way, but it doesn't. While there will be streaks one way, or the other, the number of appearances of the two numbers together will approach the expected "average" over many, many trials. In the short run, there is nothing to say that it couldn't be a bankroll breaking period of trials before you see those particular numbers together.

Past results cannot influence future outcomes.

End of story.

Quote: Speedymetric

Thank you in advance and any advice or explanations would be greatly appreciated,as I like beer.

You're right about the Gambler's Fallacy but it's not clear how that translates into winning the beer. What exactly do you need to do to convince *him* that you're right?

Hi, you are right MathExtremist I will have to do a lot of cutting and pasting and a bibliography for my friend to study and work out his errors.

Would anyone be able to tell me what the probability of the two numbers being in the 20 drawn is as his claim that it payed 12-1 was also a selling point. Surely this is way under the odds of what it should pay according to probability.

I'll help you drink the beer.