The four horsemen of the gambling apocalypse

In oral and written discussions of the respective merits of casino gaming options, one perennial topic is which games are “best.” Such discussions usually focus on the percentage advantage, or “edge,” with low edge games generally considered better for the player and higher edge games better for the casino. If edge were the sole criterion, why would players patronize high edge games (some with a house advantage of over 20%), and why would casinos offer low edge games (some, with proper play, offering edges of a fraction of a per cent)?  The answer is complex, and much of the explanation lies in history and consumer preference, not math.  But, stripping away those non-mathematical factors, is edge the sole determinant of the value of a game?  If not, what other factors are relevant?  I suggest there are four factors that gamblers should, and good casinos do, take into account in evaluating a game.  In addition to house edge, these are bet size, speed and, especially for the player, volatility.  Let’s discuss each:

House edge – the basic premise of the gambling business is that the house enjoys a mathematical advantage on each game.  House edge refers to the long-range percentage of every dollar gambled that the house, on average, retains.  For example, a slot machine with a 10% house edge will, over the long run, retain 10 cents out of every dollar run through it by players, returning 90 cents to the players.  In the short run, especially from an individual player’s point of view, the machine might return a lot more or a lot less than 90%, but that should be the average return to the casino in the long run.

The next two factors bring to mind the old TV commercial for a discount house offering extremely low prices. “How do we do it?” asks a guy in a loud checkered coat.  The answer:  “Volume!!”
Bet size and speed determine the amount of money a player must expose to a given house edge in a given period of time. A player betting the minimum at a $100 blackjack table will expose ten times more money per hour to the house edge than a $10 player, yielding ten times more profit to the house. That’s why lower limit tables usually have rules that are less favorable to the player than high limit tables. Slot machines, especially those at lower denominations, combine high edge and high speed, ensuring house profits even from penny players. If you are a low level horse bettor or keno player, these slow games will expose little of your bankroll to a high house edge, and could be less dangerous than faster, lower-edge games like slots.

Volatility refers to the ups and downs of a game. One going for big gains on long shot propositions faces high volatility, and needs a much larger bankroll, than one playing games in which the player experiences many low denomination wins. Many players switching from blackjack to video poker, particularly the bonus or loose deuces varieties, has learned this the hard way. Volatility is not as big a concern for the house as for the player, unless a baccarat whale gets really lucky.

Many “sophisticated” gamblers look down on those who play high house edge games. But the dollar keno player may be exposing his bankroll to a lot less potential harm than the blackjack or video poker player. To each his own.


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