If there is one frequent casino practice with which I strongly disagree, it is the “Maximum Aggregate Payout,” which basically allows the casino to accept bets without being obligated to pay out in accordance with the paytable of the game in question when a large payout is achieved. Consider the possibility if there was a Video Poker machine with the typical graded payouts to the Royal depending on coins staked, such as 250-500-750-1000-4000, but with the proviso that the “maximum payment of this machine is $300” was shown on the machine. On the surface, this is the same idea as a Maximum Aggregate Payout; for example, the Video Poker paytable says that you would get 4000 quarters ($1000) on a wager of five credits ($1.25), but this is obviously not the case since $300 is equal to 1200 coins.
Another way in which this (hopefully non-existent) Video Poker game is similar to Maximum Aggregate Payouts is that if the paytable of the Video Poker game is otherwise perfectly graduated on lesser paying hands, then the Optimal bet is anywhere between 1-4 credits and the player receives a worse return by betting the maximum amount of credits. For the simple reason that 1200 credits would graduate exactly with the rest of the game on a wager of 4.8 credits, anything other would result in the player effectively handing the house a Loss Rebate (i.e., a loss).
When it comes to carnival games, I’ve observed that maximum aggregate payouts are often used, and on occasion, I’ve even seen them used on roulette. Although it is a widespread misunderstanding that the Maximum Aggregate Payout would only have a negative effect on high rollers, this is not always the case. Unfortunately, this is not always the case. Progressives, on the other hand, are primarily player-banked and should not be included in any calculation of the Maximum Aggregate Payout.
The game of Let It Ride will be used as an example for this case study. In this game, players are given three starting cards and must decide whether they want to leave all three wagers on the table or take one back in order to win. Having made this choice, the fourth card is shown, and the player is given the opportunity to choose whether to leave any leftover wagers on the table or to withdraw one unit of money. This is definitely not the first game for which a Maximum Aggregate Payout has been established, but for the sake of illustration, it is perhaps the most straightforward in terms of mathematics.
We’ll be using the Standard Paytable from WizardofOdds for our calculations.
The most current Let It Ride game I’ve seen has a Min-Max wager range of $5-$50 with a maximum aggregate payout of $25,000, according to the information I’ve gathered.
Assuming that a player is going to be paid in full, the Optimal Strategy for Let It Ride would have us let ride any Three Royal Flush cards that we get at the beginning of the game. For example, we would let Jc-Ac-Kc to ride mostly because we had a good probability of striking the Royal.
When playing Let it Ride, hitting a Royal Flush is mathematically the same as receiving a dealt Royal Flush, which is 1/649739 percent or 0.000153907 percent of the time. In other words, it’s an improbable occurrence that will never happen. Still, it provides 0.004617 percent of the return to the game, resulting in a House Edge of 3.5057 percent, even if that is the case. The Royal Flush pays 1000 to 1, which would result in a payout of $150,000 less than the stated odds with a $50 wager each location, but unfortunately, that is when the Royal Flush pays 1000 to 1. In the event that no side bet is placed and no other players play and hit winning cards, this $150 bettor would only get $25,000, which is just one-sixth of the amount he should have received. As a result, the return of the Royal is just one-sixth of what it should be.The return of the Royal Flush is effectively reduced to.0007695 or 0.07695 percent, which effectively increases the House Edge by 0.38475 percent, resulting in an Effective House Edge of 3.89045 percent.