Pavlov used food to do it with dogs. Skinner used bells to do it with pigeons.
Casinos use multi-line slot machines to do it with gamblers, which may or may
not be the same as using bells to do it with pigeons. "It," in all three
cases, being reinforcement for behavioral training and eliciting of desired responses.
What if you started playing a machine and hardly got any hits maybe you averaged
one every five spins or less. You'd leave. Maybe go to another machine, a different
casino, an activity other than gambling. More, say this happened on a few casino
visits running. You might just skip your next planned jaunt to the jackpot joint.
This isn't talking wins, although they'd be nice. It's talking hits. Getting
at least something back in a fair fraction of rounds motivates players to keep
betting and feeds their fantasies about this shaping up as their lucky day.
The quandary for casinos is, how to set up a slot machine with a hit rate that
provides good reinforcement, yet also offers engaging payouts and still holds
the money needed to cover the mortgage. The traditional problem is that these
factors represent trade-offs. For instance, if hit rate gets to 50 percent,
you'd only get your money back on each try and the casino would just break even.
To offer big jackpots and decent intermediate returns at some established house
advantage, the bosses have to lower the hit rate below 50 percent. You can see
the dilemma.
This is the genius of the multi-line machines now swallowing the slot scene.
They can offer hit rates well over 50 percent, while retaining attractive prize
structures and keeping a lot of the solid citizens' hard-earned moolah at the
end of the month.
To get an idea of how this is done, picture a highly simplified machine with
two win-or-lose lines. More complex devices would work the same way. For a $1
bet, each line of the hypothetical machine has a 40 percent chance of hitting
and returning $2.25 ($1.25 win and get the $1 back), offset by a 60 percent
chance of losing. The house has a steep 10 percent edge, giving a payback of
only 90 percent. For enquiring minds who want to know, this is found as 40 percent
of $1.25 minus 60 percent of $1.00.
The accompanying table shows what can happen if both lines are statistically
equivalent and you bet $1 on each. Entries in the "probability" columns
are the chance of the combined event; these are the products of the probabilities
of the two separately so, for example, win-lose is 40 percent times 60 percent,
0.4 x 0.6 = 0.24, or 24 percent. The theoretical net per hundred spins is the
probability times the profit or loss multiplied by 100.
Effect on hit rate and casino edge of playing two lines together
|
result
|
probability of result
|
win or loss betting $1 per line
|
theoretical net for 100 spins
|
|
win-win
|
16%
|
+$2.50
|
+$40
|
|
win-lose
|
24%
|
+$0.25
|
+$ 6
|
|
lose-win
|
24%
|
+$0.25
|
+$ 6
|
|
lose-lose
|
36%
|
-$2.00
|
-$72
|
Sum the first three rows of the "probability" column and to get the
overall hit rate on this machine as 64 percent. Up from 40 percent on one line.
What about edge? It was 10 percent on each line by itself. Bet $200 in all and
the casino chalks up $20. On two lines together, at $1 apiece, the handle on
100 spins would be $200. The "theoretical net" column shows you pick
up a total of $52 and drop $72. The loss is still $20 on a $200 handle, 10 percent.
So the casino has made the game tantalizing and gives you reinforcement, but
hasn't sacrificed its take on the action.
Pretend you play across the board on a 10-line machine with a 90 percent return.
Further, imagine that to show an imposing list of possible returns, each line
has a paltry 20 percent hit rate. The chance you'll be told you've won and get
something back on a spin, even if you actually lose by missing on nine lines
and only recovering your bet on the 10th, is 9,999,998,976 out of 10 billion.
So reinforcement acts two ways. It keeps you playing and encourages you to bet
on more lines. Unless, of course, you've heeded this hoary hortation of the
Helicon, Sumner A Ingmark:
Since appearances can fool you,
Don't let smoke and mirrors rule you.
