This past week, I got asked by a friend about what I do for the gaming industry. I told him I do the math for new casino games. I explained how I work out the strategy for games and determine all the key math numbers.
That invariably leads to “what numbers?” Well, it starts with payback, but there are many other key statistics that impact a game. In this case that answer led to “what do you mean by payback?”
Payback is the single most important measure of a game for casinos. If that isn’t in the right spot, the rest of the game doesn’t matter. For table games, it tends to vary between about 98% and 99.5%. But what does this number actually mean?
The payback is the percent of the total amount wagered the player can expect to have returned to him. The amount of money the player has brought to the table has no impact on this number. Some people erroneously believe a 98% payback means: if I show up with $100, I can expect to keep $98 of it.
This is certainly not the case. It does not matter if I show up at a blackjack table with $20, $100 or $1,000.
Let’s say I play 40 hands at $10 per hand. This would mean I wager $400. Blackjack has a 99.5% payback, and 99.5% of $400 is $398. So, a 99.5% payback for blackjack means that of every $400 I wager I can expect to get back $398 and lose $2. But, this calculation is not completely accurate for blackjack. It should be 99.5% of the total wager, not the total initial wager.
In blackjack, we need to account for double downs and splits. When this is accounted for, we find the amount wagered is really about 1.13 units per base wager. So, in reality, a $10 table means an average total wager of $11.30.
With 40 hands at $11.30, that is actually a total of $452 wagered. With a 99.5% payback, that means the actual amount lost is expected to be $2.26 over 40 hands. In the case of blackjack, the difference between the initial and total wager is not that big.
In the case of a game like Three Card Poker, the total wager is about 1.67 units of the ante. So, a $10 table really means a $16.67 average wager, and a 98% payback means an expected loss of 2% of $16.67 or 33 cents per hand vs. 20 cents if we had only calculated this on the ante.
If we consider Ultimate Texas Hold’em we see that the spread goes up much further. What might be called a $10 table actually requires two initial $10 wagers (the Ante and the Blind). The average Play wager is about 2.2 times the Ante. So, our total wager is actually 4.2 times the stated table minimum. Thus a $10 table will have an average of $42 wagered per hand. Ultimate plays (with near perfect strategy) at about 99.5%, so the expected loss per hand is just 0.5% of $42 or 21 cents.
There are two other very important aspects of payback we need to keep in mind. First of all, it is the long-term theoretical payback of the game. If you play blackjack for an hour, playing 40 hands, you will not likely lose exactly $2.26. You might lose more, you might lose less. Over time, the more hands you play, the more likely your total loss will come close to the 0.5% of your total wager.
The second important fact about all published payback is it assumes using either perfect strategy or something very close (depending on how the payback was calculated). In the short run, some other strategy might provide better results. But over the long haul, there is a reason why perfect strategy is called perfect strategy. It will provide the highest payback over time.
Any deviation from this strategy can only cause the payback to go down and you can expect your average loss to go up as a result.