The Intelligent Gamblergambler™
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The Intelligent GamblerGambler™ © 1995 ConJelCo, All Rights Reserved Number 4, November 1995 ing craps for a zillion years and is still a play for the rest of your life. Second, you PUBLISHER’S CORNER lifetime winner; how does that jibe with have to decide how you want to model Chuck Weinstock “the long run” theory? each session. Since you don’t play the Welcome to the fourth issue of the Intel- There are actually two ways to look at same way (length of time, starting bank- ligent Gambler. In this issue we have the this question. The first is “how long will roll, possibly even number of bets) every usual articles on poker, blackjack, and it take until I’m guaranteed to lose (for session, what you’d ideally like to do is craps, and a few surprises as well. We’re some initial bankroll/playing system)”; set up the simulation so that it models especially pleased to have an excerpt to this question there really is no answer. this behavior. This is difficult, however, from Jeffrey Compton’s new book on There is actually no guarantee that you so it’s probably good enough to pick an slot clubs, just published by Anthony will lose (or win!) for a given number of “average” behavior and just use that as Curtis’ Huntington Press. rolls, be that 10 rolls, 1,000 rolls, or representative for every session. As our mailing list grows, printing and 1,000,000 rolls. The only thing that can Once you have these parameters, you can mailing the Intelligent Gambler is be “guaranteed” is that the longer you then crank up your simulator and start becoming more costly. We’re exploring play, the more likely you are to wind up recording the number of “lifetime win- ways of dealing with this problem a overall loser. This also suggests the ners” and “lifetime losers” there are after including turning the Intelligent Gam- answer to those individuals who say that particular number of sessions. You bler into a magazine aimed at the “well, you can’t win in the long run, but can also record the information needed thoughtful gambler and containing you can in the short run!” There is no to calculate the house p.c. (net loss and longer, more in-depth, articles. It would way to guarantee that you’ll win in the bet handles for each trial), and do statis- be sold on a subscription basis. short run any more than you can guaran- tical confidence checks on these num- We haven’t made any decisions on this, tee you’ll win in the long run; however, bers to ensure accuracy of winner/loser so if you have any thoughts on this or on it’s more likely that you’ll wind up a net numbers. ways we can make the Intelligent Gam- winner “in the short run” than it is in the So what might be interesting is to look at bler better, please let us hear from you by long run (although it’s even more likely various player “lifetimes”. I’ve per- mail, fax, or telephone. you’ll wind up a net loser in the short run formed simulations for session lengths (a than wind up a net winner short run); session is one “session” of play at a craps We invite you to visit ConJelCo on the we’ll look at this in more detail shortly. World Wide Web where we maintain the table; from the time you buy in to the premiere gambling site full of all sorts of The second way to look at it is “how time you color up and leave) of 20, 50, information for the intelligent gambler. many rolls will it take until I’ve got x% 100, 300, and 500 sessions. For example, Look for us at http://www.conjelco.com. confidence that my expected loss is the 20 session case might represent If you don’t know how to get on the Web, within plus or minus $y of what’s math- someone who whet to LV once a year for give us a call and we’ll try to point you in ematically predicted”. The answer to this 10 years (playing craps twice each year), the right direction. ♠ question is, in my opinion, only interest- and then got hit by a bus and didn’t play ing to stats geeks or simulator geeks, anymore. The 500 session case might since answering it will give an indication represent someone who estimates they’ll The Long Run for when a simulation’s results are statis- go to LV for twice a year for 25 years, Ken Elliott tically valid. So let’s discuss the first, and play 10 craps sessions on each visit In many books, articles, and other media more interesting, question some more. (2 * 25 * 10 = 500). you’ll see claims about house advantage, Let’s say that you want to figure out the In the simulations, our player estimates or statements that craps can’t be beaten, likelihood of your winding up a net win- that they’ll play pass/2 comes for $5 etc. All of these are claims are made for ner or net loser in craps from the time each, full double odds, odds off on the large numbers of rolls, typically called you start playing to the time your oxygen “the long run”, as in “If you play craps tank runs out while you’re in the middle The Intelligent Gambler is published on an you’ll lose in the long run” or “the house irregular basis by ConJelCo as a free service to of that once-in-a-lifetime hand and you our customers. ConJelCo, 132 Radcliff Drive, advantage of a straight pass line bet is keel over just as you seven out. We’re Pittsburgh, PA, 15237. 1.41% in the long run.” But what exactly going to try to find the answer via (sur- Phone: 412-492-9210, 800-492-9210. Fax: 412-492-9031. is “the long run”? I’m sure someone out prise) simulation. To begin, estimate the Internet: [email protected] there has an Uncle Ferd who’s been play- number of craps sessions you’re likely to Web: http://www.conjelco.com. ♠ Intelligent Gambler 1 come-out. Starting bankroll will be to die after only 20 sessions of craps, the team of Holmes, Kissinger, and Pav- $200, and they’ll play until they win you’ll have likely to only wagered about lov at a slot machine and you will get the $100, bust out, or have played for 4 hours $19,500, losing an average of about $130 idea.) (400 rolls). It’s important to note that the (with a standard deviation of about Tangible benefits following numbers are only valid for this $650). particular strategy; in general, the more On a final note, Bernie Luger has mathe- Getting the most out of the tangible ben- action you have (especially if you regu- matically calculated the number of rolls efits requires information and some larly play the props, bet the inside and that it would take to be 99% sure of being entry-level mathematical analysis (i.e., a outside numbers, etc.) the more likely it a lifetime loser just betting the pass line, little arithmetic). Not only do you have to is you’ll wind up a lifetime loser no odds: about 91,000. This means after compare casino to casino, you must be (although some people will argue that if about 91,000 rolls (if you figure 100 rolls able to compare the value of one benefit you play conservatively the more likely per hour, that’s about 910 hours; at 4 to another. (Should I redeem my points it is that you’ll die of boredom at the hours per session, that’s about 230 ses- for cash, a meal comp, or a T-shirt?) craps table). sions; if you go to Vegas four times a Cash—Though more than 50% of the Although I only ran each for 10,000 tri- year and play four sessions per time, slot clubs award cash rebates, there are als (this is like the medical studies where that’s about 14 years of play!) 99 out of major differences in the bottom-line they take data on 10,000 people; so we every 100 people will have less money amounts. For example, for $100 coin-in, have 10,000 craps players we’re keeping than they started with. However (even the Cal Club at the California rebates track of), the confidence limits for the more amazing) it’s likely that 1 out of 10¢, the Golden Nugget’s 24 Karat Club simulations in most cases were consis- every 100 people is a winner, and those rebates 67¢, and the Celebrity Club at the tent when taken as a percentage of the are the people you’ll never convince that Desert Inn gives back $1. All for the simulated net loss (this is for you statisti- craps is negative expectation game! same $100 in action. cal purists out there. What I mean is that Ken Elliott is the author of our CrapSim On the surface, it seems that your choice if the result final bankroll is, say, $2,000, Professional craps simulator, and is simple: if you want the highest cash the confidence limits may be plus or CrapSim Interactive craps game. ♠ rebate, just compare the percentages and minus $10, which is 0.5% of $2,000. If choose the DI.