I recently gave a lecture that was an introduction to gaming math. It was not meant to be in-depth, but was targeted to casino personnel who don’t necessarily focus on table games.
I walked through five basic areas of gaming math – side bets, progressive side bets, simple games, blackjack games and poker games. Over the years, I think I’ve found the area that confuses most people, even those in the industry, is progressive side bet math.
Years ago, progressive math was relatively easy. Casinos were a bit nervous about the large payouts when the jackpot was hit and some of the first table game progressives were essentially banked by the owners of the side bet game.
Because of this, the money for the side bet had to be accounted for completely.
So, a $1 wager would be made and 75 cents would be added to the meter. If any winning hand for the side bet was paid out, it would be subtracted from the meter.
Eventually, the jackpot would be hit and the meter would be re-set to some value. In this case, the payback of the side bet is equal to the 75% put on the meter plus the value of the seed (the amount of the seed times the probability the jackpot hits.
Since the seed usually doesn’t add much to the overall payback (1-2% at most), the payback of these progressive side bets was just a bit over the total contribution rate.
One of the issues of this type of progressive accounting was that the jackpot could be eaten away if a large number of small winning hands were hit – more than would be considered average. On the positive side, the payback would always be the same. It didn’t matter if there was a larger than normal number of small wins – the payback was the payback every time the jackpot was hit.
The modern progressive doesn’t work this way. Casinos began to realize they were giving up serious cash cows. Progressives tend to have relatively low paybacks and although it might be painful to occasionally fork over hundreds of thousands of dollars, this is money the player put in in the first place.
The higher the jackpot, the more profit the casinos made along the way. Now that all the money belongs to the casino there is no need to keep the monies so separate. The process of subtracting every winning hand from the meter is a slow and cumbersome process, so the casinos eliminated it.
Now, a much lower percentage of each wager goes to the meter. This might be 8-25% (give or take). The meter will appear to grow more slowly, but the only time it will be reduced is either when the jackpot is hit or a secondary payout (10% of jackpot) is hit. This change is for the most part immaterial to the player.
The actual jackpot size will no longer vary based on how many of the lower hands are hit and will only be based on how often the primary or secondary jackpots are hit. In the grand scheme, this makes little difference to the casino as well now that they own both the base game and the progressive side bet.
The calculation of the payback changes slightly but only in our methodology, not in the final value. For hands that do not come off the meter, we calculate the payback the same as we do for a non-progressive side bet. We multiply the frequency of each winning hand by the payout of that hand and sum up the values.
We add to this number the percent of each wager being added to the meter and then add the impact of the seed (which is unchanged from our earlier example). The casino can work backwards to get the new contribution rate. So, if the fixed pays add up to 63%, the casino simply uses a contribution rate of 12% (adding 12 cents of every dollar wagered to the meter).
The net result is a side bet with exactly the same payback as the one described earlier. Only now, if some of the fixed pays show up more than normal over a short period of time, the casino’s true advantage will be a bit less and the jackpot size will be unaffected.
Most of you reading this, however, do not work for the casinos. The unique thing about progressives is there are really two paybacks. The one described here is the casino’s theoretical payback and it does not change over time.
While the player should be somewhat concerned with this, he should be more concerned with the specific payback at any point in time. To the player, what matters is how much is the jackpot right now and what is the payback as a result of this jackpot. I’ll cover this next week, along with an example to completely illustrate the relationship between the casino payback and the player payback.
Elliot Frome is a second generation gaming analyst and author. His math credits include Ultimate Texas Hold’em, Mississippi Stud, House Money and many other games. His website is www.gambatria.com. Contact Elliot at [email protected].