SumGames - Craps (and how it compares to investing)


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     There are plenty of web sites that explain craps (links below). The purpose of this summary is to explore the odds of the game, the strategies that offer the highest expected returns, and offer some comparisons between craps and investing. If you choose to play craps you should expect to lose money, not make money, although this information (including the links) may help you lose less money and play craps for a longer period of time. The right reason to play craps is for entertainment, not profit (unless you are the house). Craps is a game of luck since your success beyond the house advantage or vigorish is dependent on the dice (which are presumed for this discussion to be fair). Yet you can improve your odds by making bets with the lowest expected loss and avoiding bets with the highest expected loss. There are no professional craps players because their are no aspects of the game that allow players to take advantage of other suboptimal players (like in Poker).

     One of the unique aspects of Craps is that it offers the opportunity to make bets where the house has no advantage. Pass Odds and Don't Pass Odds (as well as Come Odds and Don't Come Odds) bets are payed based on the true odds or probabilities of their occurring and the house has no advantage on those bets. The catch is that to make the odds bets you first have to make a Pass Line, Don't Pass, Come, or Don't Come bet. Once a point is made you can make odds bets. And in most cases you can bet multiples of your original pass/don't pass come/don't come bets.

     Odds bets are the best bet in the casino, so it's somewhat ironic that they aren't even on the table. You have to ask the dealers at the casino what multiple of odds you can play. Pass line odds bets are placed behind the pass line after a point is established, while to make don't pass odds, come odds and don't come odds you will generally have to communicate your intention with the dealer who will place the bet in the appropriate location on the table for you. The house has an advantage on the line bets, but not on the odds, so the greater the multiple on the odds, the lower the house's advantage on the combination. The house advantage is roughly 1.4% with pass line bets. With 1 X odds it's about .85%, with 2 X odds its roughly .61%. And some casinos apparently will let you go up to 100 X odds which brings the house advantage down to roughly .02%

     The highest expected return strategy is to make these pass line and come bets with full odds. But the house tends to make plenty of money because most gamblers don't just stick to those bets. They place other bets that have larger house percentage advantages. For instance Place bets (on 4-6, 8-10) have higher house advantages of about 2-3% and buy bets on the same numbers have over a 4% advantage. Hard way bets have even higher house advantages and proposition bets tend to have even worse odds. Field bet house advantages can vary depending on whether certain numbers pay 2 or 3 to one.

     The bottom line is relatively straight forward. To maximize your entertainment value and minimize the house advantage, a craps player should make pass line (or don't pass) and come bets (or don't come bets) and take the maximum allowable odds when a point is made. If you want to bet with the roller you play pass/come, if you want to bet against the roller (and likely others at the table, which may not make you any friends) you play don't pass/don't come.

     When a player rolls for a long time without a seven out, gamblers playing pass/come with full odds can make a ton of money, have a great time, and that scenario is often the source of load celebrations often heard at a crap table.

     To play craps effectively, information you need includes a basic understanding of the 11 possible combinations you can get from rolling a pair of dice (2-12). Then you need to understand the probabilities of each of those rolls. For instance the odds of rolling 7 are always 1/6 since no matter what you roll on one die, you have a one in six change of adding up to 7 with the second die. Rolling two ones for a total of 2 is a 1/36 chance (likewise two sixes for 12).

     A general rule for Craps bets is the larger the area used on the actual table, the worse the odds you get on it. As discussed above, the best odds come on "odds" bets which aren't even on the table. But "Field" bets take up a large portion of the table and tend to have very large house advantages. Plus some casinos have "Big 6" and "Big 8" on their tables, which pay if a roller throws that number before a seven out. They pay even money 1-1 if you win. But you can make a 6 or 8 bet with better odds (7-6) by making a place bet with the dealer. In other words, only people that don't know craps (or are drunk or stupid) would logically make a Big 6 or Big 8 bet. Similarly, in the investment business you'll often find the highest cost investments are the most advertised and the lowest cost and highest expected return investments are not advertised at all.

     Investor's that like to follow market momentum or direction, as in buying during bull markets and selling during bear markets arguably would likely play craps in a similar way - betting with the rollers when on a hot streak. Those that use options to try to make large gains for large price moves or increasing volatility are somewhat like craps players that like to make proposition bets (like hard way bets) that will pay off big if the happen, but the odds are against them. And they are also similar in that both proposition bets and options have high costs/vigorish, thus the more and longer you use the strategies, the worse you are likely to perform.

     Another similarity between investing and craps is how some firms give away index funds (like the casino giving true odds bets) to get you to invest with the firm, because most investors/players will also buy higher cost/vigorish products that the house makes more money on.



Gary Karz, CFA
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