There is a theory in physics that goes for every action
there is an equal and opposite reaction.
In gambling, there is a similar theory.
For every table game there will eventually be a sidebet. And, for every sidebet there will be a
Progressive version of the sidebet. The
math behind Progressives is probably the least understood math of any type of
gambling. It really isn't that hard once
it is explained properly, but I've worked with a lot of inventors on a lot of
Progressives, and it is fairly obvious to me that few people, even in the
industry, understand how a Progressive works mathematically.
Generally speaking there are 3 components of a sidebet -
the fixed pays, the seed and the contribution rate. Normally when we calculate the payback of a
sidebet, we simply multiply the fixed pays by the frequency of each winning
hand and sum up these values. For a
Progressive, we have to alter one step slightly and add one. For the jackpot event, we use the seed amount
as the equivalent of the fixed pay for that event. Each time it is hit, the casino is on the
hook to put that money back on the meter, so it is similar to a fixed pay in
that regard. We then need to add the
contribution rate - which is the amount of each dollar wagered that goes on the
meter - to the total payback calculated.
I'll save more details for another day, as this is not the point of
today's column. What is the point is to
discuss how a Progressive differs from other wagers.
While the top pay for most sidebets are pretty large, the
amount they contribute to the overall payback is usually pretty small. If you pay 1000 for a 1 in a million even,
the contribution rate is a meager 0.1%.
In video poker the Royal Flush contributes only 2% to the payback of the
game. If we were to look at most table
game sidebets, we'd probably find that most top pays contribute about 1-2% (or
less) to the overall payback. But, when
we switch to a Progressive, we find that the top pay frequently contributes
15-20% to the payback when we take into account both the seed and contribution
rate. What does this mean for the
Player?
As I said, the Royal Flush accounts for 2% of the payback
of video poker. What this usually means
is that until you hit one, you're only playing at about 97.5% which can be a
bit rough. When you hit one - and if you
are a regular player, you WILL hit one, you bring the theoretical payback back
to 99.5%. Hit the Royal more frequently
than 'normal' and you're likely up money as you will be above 100%. With Progressives, it doesn't quite work the
same way. That top hand is either more
rare or you'll be playing a game that deals much more slowly than video poker,
meaning that there are no guarantees that you will EVER hit it. So, even if the sidebet were paying 99.5%
like video poker, ONE PLAYER is going to wind up winning 15-20% of that payback
and everyone else will be playing at 77.5% - 82.5%.
When you consider the fact that many sidebets have
paybacks far lower than 99.5%, you realize that the picture for those that
don't hit the jackpot is even more bleak.
So, why do people play Progressives?
There are two main reasons. One
is a bit emotional and the other a bit more practical.
First, Players have always been willing to accept low
paybacks for a chance to win a life-changing amount of money. The Lotto has made a lot of money for a lot
of states. Most states payout only 70%
on their lotteries. This is lower than
the legal minimum of any casino game here in Nevada. But, for the chance, however slim, of winning
millions of dollars, Players are willing to throw a few dollars in for the hope
of getting struck by lightning.
The second reason deals with the way Progressives work
and makes far more mathematical sense.
To the casinos, the payback of a game is the long-term payback, which is
calculated as I described earlier.
You'll note that what I described completely ignores the specific value
on the meter at any point in time. This
money is merely an accumulation of the contribution rate over time. It really doesn't matter to them
(mathematically), if a jackpot that is supposed to hit about once a year,
doesn't get hit for 3 years. However, to
the Player, the payback of ANY wager is dependent upon the specific payouts for
each winning hand at the point in which you make the wager. It doesn't really matter if the contribution
rate is 10% of 20%. If a Jackpot which
is supposed to average $250,000, goes all the way up to $600,000 then the
payback at that point in time is WELL above the theoretical payback.
It is possible that at a particular point in time that
the payback of a wager could be over 100%.
At this point, it makes sense to play the game mathematically. The problem is, however, that it will be one
person that will benefit from this occurrence and it may not be you. Then again, it might!
