Do the math: A larger house edge is better for the bottom line, study finds
It is a well-established mantra that, when it comes to casinos, the house always wins, at least in the long run. That’s because casinos entertain a small house “edge” – not enough to scare players, but enough to make sure the house is finally progressing. Some players think that they can avoid this by jumping from slot machine to slot machine, for example, hoping to hit one at the right time to win a big payout.
There is a belief among casino operators that skilled players can actually feel changes in how much and how often a particular machine pays – that is, they can discern subtle differences in the house edge between machines. But mathematics says otherwise, according to a recent article in the International Journal of Contemporary Hospitality Management.
Slot machines are known to be the source of most of a casino’s revenue. It’s about manipulating the payback percentage: the percentage of the “coin in” a player gets back when he finishes the game.
Lucas worked in Lake Tahoe as a gaming operations and financial analyst directly a-college for about 34 years, so he has a long-standing interest in the types of challenges the industry is facing. For 20 years he has been researching at the UNLV. “Most of the research I’ve been tracking has come from the issues we faced in the industry,” he said. “We’ve never had time to solve them because the economy’s decision-making horizon is so short, and you do not have the chance to do that longer-term academic thinking.”
The Price Is Right
The house edge for gaming machines typically falls between 5% and 10%, with most machines providing a payback percentage in the range of 90% to 97%. (If it’s 90%, the casino’s take – and the player’s loss – is 10% of the coin, for example.) But how can casino operators determine the best house edge for their final score within that range? “It’s really a price problem because it’s a unique product,” Lucas said. “For real slots, the price is not marked anywhere.”
Conventional wisdom among casino operators is that, although there is no explicitly marked price, the law of demand occurs. They think that normal players can feel intuitively when a game they play comes at a higher “price” – that is, a house edge is too big – and therefore, when this house edge is too big, players become their business into another casino with a more generous approach.
“It’s basically how you react to a price shock,” Lucas said. For example, if Whole Foods doubles the price of your favorite brand of almond milk, you can switch to a cheaper brand. This is the law of demand, which states that if you increase the price of a product, you should expect demand to fall. The big question now for slot machines is, “How much more will this demand drop?”
“We could see a drop in the coin in, but if it’s less than the product of the coin in the higher par game, sometimes the par, then we do not care,” Lucas said.
Many past studies have relied on simulations or brought volunteers into the lab to play slots. Lucas considers field studies to be a much better indicator, citing two major benefits. “Number one, you label the games differently because you have the ability to lose your own money,” he said. “Plus, when people go to a casino and play games, they do not play the games the way they do in a lab, and the benefit of the field study is that you watch the behavior as it does in the setting you understand would like.”
For example, in a simulation, virtual players do not respond to how a human being would react if, for example, they lose six or seven times in a row. And a typical lab setup will ask subjects to play a game for 500 spins with a constant bet. In a real scenario, that just does not happen. Players will not play a slot machine for exactly 500 spins without varying their stakes. They are suitable for mixing the inserts and changing machines if they do not achieve the desired result.
This leads according to Lucas to significant deviations in the distribution of results. “You jump games, so identifying the true population parameter that’s the same is even more difficult,” he said. “They have uneven sample sizes – they do not have constant bets.” For example, if a study contains a 3% match and a 9% match, there is a wide range of score variations in both, with a large overlap between them. “You get that tiny faint signal that beeps in a sea of variance.” That’s before considering such cognitive biases such as the player’s fallacy and hot-hand fallacy.
For their own study, Lucas and Spilde tracked the daily performance of two identical slot machines (pairs of “Tokyo Rose” or “Dragon’s Fortune X”) in similar positions on the casino floor for nine months. Each machine in a pair was set to a different level (the percentage of the total coin that the machines hold over time), between 7.98% and 14.93%. They measured the daily coin as well as its theoretical gain (“T-win”), determined by multiplying the coin-in and the par to obtain the expected value of a machine. According to Lucas, such a comparison would show whether players really move from higher par to lower par games over time.
Unfortunately, mathematics does not support conventional wisdom. The differences between the high and low par games were stable throughout the nine-month period and the high-par games recorded significantly higher sales. But this conventional wisdom is so strong and enduring that Lucas struggled to make operators listen when his research challenged their preferred operating paradigms.
“We’re taking so much industrial flak because nobody wants to challenge this mental model,” he said. But the cake grows and everyone gets a smaller piece, so they have to become a little more technical. “At some point, I think that the power of research will overtake resistance because there is so much pressure on them to do that Optimize revenue. “
Lucas recently completed a similar study in Mexico, where two slot machines were placed side by side. “It was a 15% game and one was a 4% game, eleven percentage points apart – almost a 300% price increase,” he said. Still, he found that it was the same amount of game and the same amount of win, on both games over a period of 180 days. The players did not change to the machine with the smaller house edge. “This place does not even have a hotel, so all players are frequent players, which was argued as the population that would have the best chance of determining the price,” he said.
The message to the casino operators is clear: they should stop annoying themselves so much about losing customers by opting for higher-par machines that are better in the long run for a casino’s bottom line. “Many believe that lower pars will attract more revenue by appealing to customer value (ie lower ‘prices’), but our work suggests otherwise,” Lucas said. “Our results are probably due to the players’ inability to recognize Par, of course, but the most helpful thing to know is that the higher pars perform better when it comes to optimizing sales.”