The Big Bass Jackpot
The Start of the Slippery Slope
01 September 2013
When I asked my kids what they'd enjoyed most on our holiday to stay with relatives in the USA, my heart sank when the first thing that they mentioned was their visit to an old fashioned seaside arcade.  We could have gone to Blackpool for that.
There was one arcade game in particular that caught their imagination: the Big Bass Wheel.  It's a big spinning drum with a pointer.  In the version we saw, for the price of 25c you get to pull a lever, and when the wheel stops, you collect the number of tickets being pointed to - tickets are seductively pumped out of the machine in a long stream.
Here is a picture of one of the wheels: http://www.bhmvending.com/Amusements/Baytek/baytek_Big_Bass_Wheel.png
The drum is sixteen sided (a hexadecagon?).  On fifteen of the faces are scores of between 10 and 50 tickets, but on one face is the magic 1000.  And as luck would have it, on her first spin my ten year old hit the jackpot.
She didn't appreciate how lucky she was.  Although 1000 appears in large print, if you look closely, the 1000 ticket section on that panel is only a narrow line.  Either side of it, you score only 4 tickets.  So even if the pointer ends up at the 1000 panel, there is only about a 1/10 chance that you would get 1000 tickets, with a 9/10 chance of getting 4 tickets.  So overall, my daughter had a 1/16 x 1/10 = 1/160 chance of the jackpot.
And what did these 1000 tickets win?  You get to visit the prize desk, where all sorts of goodies are on offer, each priced in tickets.  The star prize is a mini gumball machine which pumps out gumballs (retail price around $3 I believe), so she gleefully got one of those, and with her remaining tickets she bagged a range of other sweetie goodies, the total value of all her prizes coming to about $5.  So it works out that the value of a ticket is about 0.5 cents.
If we say the average number of tickets won on Big Bass (except for the 1000 panel) is about 30, then according to my crude back of envelope calculation, the expected return of a spin on Big Bass is 1000x(1/160) + 30x(159/160), or about 35 tickets.  So if you put in 25c, you expect to get back 35 x 0.5, or about 17c worth of goods in return.  Well, it's a better return than the lottery, I suppose.
Statisticians often ridicule the lottery as being nothing more than a way to waste 50p, but of course this ignores the fact that the act of playing offers people entertainment in the form of anticipation, which is arguably worth at least 50p.  The same is true of Big Bass.  The appeal of the spinning drum, the sight of tickets being fed out (even ten tickets look good) and then feeding those tickets back into another machine to get a voucher - these are all exciting things for wide-eyed children.
The problem comes with the addiction and warped sense of value.  After she won, my daughter was now the envy of her siblings and cousins, who all wanted to go back the next day to win THEIR OWN gumball machine.  Never have gumball machines been such an aspirational item. We did go back the next day, and nobody won anything of note.  That second visit was probably $10 well spent, since they discovered the anticlimax of failure. The Lottery mantra is "It could be you", and for my daughter on day one, it WAS her.  But after tasting outrageous success (or luck) so early in her gambling career, I fear it's going to take a while for the gloss to wear off.