Everyone knows that casinos have a gambling edge or advantage over their patrons. On table games, this parameter is traditionally expressed as a percentage of the amount. On machines, this information is usually stated more benignly as the percentage returned to players. Edge and return are complementary – 2 percent edge is 98 percent return, 5 percent edge is 95 percent return, and so on. Both figures indicate what the casino earns from the action when averaged over many bets.
Most often, edge is built into the games through payoffs being somewhat less than the odds players overcome to win. Occasionally, the edge is achieved wholly or partly by means of a “vigorish” paid directly by players either when the wager is made or wins. Regardless of how implemented, the effect of edge is largely undetected on a round-by-round basis. Winners take the payoffs and losers sacrifice what’s put up for grabs. Players notice the accompanying gross swings in their fortunes, but are generally unaware that they’re short-changed on their triumphs.
As one illustration, craps buffs who win $5.00 Place bets on nines and fives happily rack $7.00 earnings, oblivious to receiving only 7-to-5 (2.8-to-2) after besting 3-to-2 odds. Buy bets on fours or 10s at craps show how this works with a vigorish paid up-front. Odds of 2-to-1 are surmounted to win, and $40 is indeed paid for a $20 bet. But, the house charges $1 to book a $20 Buy bet. So players begin by dropping $21 on the layout. Winners gladly pick up the $40 payoff and recover their $20. But the $1 vigorish isn’t returned. So the $60 they have at the end is only $39 ahead of the $21 with which they began. The payoff is accordingly $39-to-$21 (1.86-to-1).
The greater the edge, the less of the money wagered over the long term that solid citizens carry home. Conventional wisdom is that higher edge lowers players’ prospects. It should stand to reason that gamblers would gravitate if not flock toward low-edge games.
They don’t For one thing, the effect of edge doesn’t become evident until the number of resolved bets increases to the range where actual frequencies of outcomes start to approach the rates implied by the probabilities. Casinos earn their profits because they reach this level by agglomerating the action of all their patrons. Particular players rarely get anywhere close. A second factor is that, in the statistically short term of a particular round, session, or even series of casino visits, the effect of edge is swamped by swings in fortune occasioned by individual wins and losses. Third, choosing a game based on edge is not as straightforward as it might appear.
Consider a choice between two propositions having the same payoffs but different edge. Bets on 12-spot columns at single- and double-zero roulette offer an example. They each pay 2-to-1. Edge is 2.70 percent on the first and 5.26 percent on the second. This disparity arises because probabilities of winning aren’t the same; they’re 32.4 and 31.6 percent, respectively. Who’s gonna notice the 0.8 percent divergence? More importantly, when a casino has both single- and double-zero tables, minimum bets on the former are too high for many players.
Complications grow when the amounts of money involved change along with the probabilities. Blackjack presents several such situations. The house has a small edge when this game is taken as a whole. But some individual hands – once dealt – favor players to varying degrees. Picture an ace-two versus a six-up. A bettor is in the catbird seat either hitting or doubling. For $10 wagered at the start of the round, over the long term, hitting is projected to gain an average of $1.62 and doubling $1.86 cents. The player has an edge over the house either way – more so when doubling. But the chance of winning $10 by hitting exceeds that of picking up $20 by doubling – and conversely, losing $20 by doubling is more likely than dropping $10 by hitting. In such a situation, edge may not be the player’s strongest motivation.
On the slots, edge isn’t even a selection factor. Payoffs for winning combinations are displayed right on the machines. The probabilities associated with the returns are confidential, however, and can’t be deduced from first principles or observation over reasonable numbers of spins. As a result, slot players don’t and can’t know the edge on any particular machine. Even having proprietary information about a game may not help. Devices that are nominally the same game and look identical may have disparate sets of probabilities and therefore different values of edge. Data about one machine or averages for multiple devices therefore don’t necessarily pertain to a unit someone might select. Choosing is consequently picking a pig in a poke.
Anyway, who’s gonna tell the slot buffs who happen to win life-changing jackpots that they were foolish to play the machines on which they scored, when other devices had much better statistical player return percentages? As that tactful troubadour, Sumner A Ingmark, told it:
For giving advice, it’s far too late.