Lucas's Strategy Guide to Gambling
So, my family took a trip back in May with a couple of our friends to Atlantic City, New Jersey. While there, I decided to try my hand at some low-stakes gambling (AKA "penny slots and video poker"). As the kind of person that likes to analyze things more or less to death, I did a lot of thinking during and after the trip. And here, my friends, are the results: Lucas's Strategy Guide to Gambling.
Gambling strategy occurs at three levels: (1) Managing Bankroll, (2) Game Selection, (3) Strategy in Game
Now, here I'm going to assume that you're a gambler like I am. Which is to say "not a regular gambler". If you're someone who lives in Vegas and visits the casino for an hour every day or week and so on, then the Law of Large Numbers is going to win, and there's basically nothing you can do about it.
For those of us who are "occasional" or "maybe only one time ever" gamblers, there's a lot we can do to improve our odds. At heart, gambling is about statistics. And the statistics are clear. On average, the casino will win. And will win at a very predictable rate. On average.
But, no particular session is average. You can never walk away from a craps table saying "Well, that was an average roll." Literally EVERY roll is either better or worse than average for the bettors. The average comes about because there is such a large quantity of rolls that happen. If we gamble a lot, then our average is probably going to match the casino's average - it's just losing instead of gaining. But, if you just roll once or a few times, you're likely to have a result that's farther from average.
Caveats aside, let's hop in.
(1) Managing Bankroll.
There are lots of betting systems out there. They are almost all garbage. Fundamentally, you can't change the casino's average edge. BUT, what you can do is play with the distribution AROUND that average.
Here's an example for how:
Let's assume a fair game - a simple coin flip. On each flip, you bet some money. If you win, you double your money. If you lose, you lose.
On average, you're probably going to walk away with as much as you started with if you just keep flipping the coin forever. But, this isn't realistic for a big reason: EVENTUALLY YOU RUN OUT OF MONEY. Given a sufficiently large number of flips, the odds of hitting a very good (or very bad) run at SOME point is very high. A very good run doesn't force you to stop. A very bad run DOES force you to stop. So, for managing bankroll, the trick is to build in your stops on both the low end (that is, have a maximum acceptable loss), and ALSO on the high end (that is, have an acceptable gain that makes you leave the table, too).
With this system in place, you can manipulate your odds of winning by changing the relative size of your loss limit and win limit.
We know that, on average, you're going to break even. Mathematically, we can sum that up in this equation: Average gain - average loss = 0. Rearranging, this means that average gain = average loss. But, your average gain is really just the odds of winning multiplied by the amount you win each time (and similarly for gains). So, odds of winning * individual win = odds of losing * individual loss.
By the world of math, odds of winning + odds of losing = 1. (That is, you're either going to win or you're going to lose.) Doing some algebra, we get this result:
Odds of winning = individual loss / (individual win + individual loss)
Now, with a fair game like a single coin toss, the individual wins and individual losses are equal, so you get "odds of winning = 50%"
But, with a SESSION of gambling, the same rule still holds - but you can CHOOSE what the individual session win or session loss would be. Here's how: You say to yourself: "I'm either going to walk away when I've lost $100 or when I've gained $10 compared to where I started". This rule tells you when to walk away from the table. And, in this case, the odds of a winning session are about 90%. Why? because it's MUCH more likely you'll hit the "I won $10!" threshold before you hit the "I lost $100!" threshold. In effect: the win streak needed to win $10 is fairly short, so your odds of hitting it before you hit the LONG losing streak needed to lose $100 is quite good.
Lesson here: if you're willing to lose a LOT more than you're asking to gain, your odds of ending up a winner are much higher. The flip side is also true: If you're not willing to lose much, but want to win a lot, you'll almost certainly end up losing.
Now, some of you may be saying "But, Lucas, the casino DOESN'T play fair! There's an edge for every game!" This is true. But, it makes FAR less difference than you might think. The adjustment for the casino's edge isn't that hard to make, and it makes almost no difference, it ends up.
An example: if you make conservative bets on craps the casino edge is about 1%. So, if you do the "$10 win limit, $100 loss limit" strategy described above, you have a 90.83% chance of having a winning session. If you were doing the coin flip bet with the same limits, you'd have a 90.91% chance of a winning session. If you switch to a REALLY bad game like Keno, there's a 25% house edge. That cuts the odds of a winning session to 88.24%. So, the difference between a fair coin-flip game and Keno is about 2.6%. Not a huge difference.
What does make a difference? Trying to win big. If you try to win big, you'll almost CERTAINLY walk away empty handed, even if you play a fair game.
Suppose you say "I'm either going to lose $100, or gain $1000". In that case, your odds of a winning session for the coin flip game is 9.1%. For conservative craps bets, 9%. For Keno, 7%.
I saw this at work in Atlantic City. The first night I was there, I hit the Casino floor with $5, and played some penny slots. I decided that if I was EVER ahead AT ALL, I'd leave. So, I basically said "I'm either going to lose $5, or gain 1 penny." With that ratio, even a tight slot machine that gives the house a 15% edge (which is about right for penny slots), I had a 99.4% chance of walking home a winner. And, I won that night. I came back to the hotel room with $5.23. The last night we were there, I had $10 or so to play with (from my gambling budget for the day plus what my wife had left over from her foray in the afternoon). My wife said to either lose it all, or to come back with $300. With that ratio, playing penny slots I had a 2.75% chance of coming home a winner. And, sure enough, I lost it all.
You might be thinking: "But, if everyone used this strategy right, we'd do like you did the first day, and the casino would make no money." This isn't quite true. Most people would walk away winners, yes. But, the losers would lose a LOT compared to the winners. (If each loser loses $5 while each winner wins a penny, the ratio of winners to losers can be 500 to 1, and the casino breaks even!) So, psychologically, you have to be ready for that. Your odds of winning are good - but the loss, if it happens, will be large.
The key: The ratio between your win goal and your loss limit determines your odds of a winning session.
There are also different betting strategies that tell you when to increase or decrease your bets. These are mostly worthless, so I'll ignore them. (Okay, on exception: the Martingale strategy - which increases bets after a loss - is not a bad strategy if your goal is to have a large probability of a small win or a small probability of a large loss. However, this strategy drastically decreases the time you'll spend in the casino before you hit one of your goals. Since the casino is often an "experience" in itself, increasing your time there is probably worth using a different betting strategy.)
(2) Game Selection
One site I've found marvelous on issues of gambling strategy is the Wizard of Odds (www.wizardofodds.com). His mastery of the relevant statistics and analysis of casino games is second to none as far as I can tell. I highly recommend his site if you want to get into the nitty gritty of decreasing the house edge. I'm just going to summarize some of the more popular games here.
First, compared to your win goal/loss limit ratio, house edge makes VERY little difference in your odds of a winning session. However, it CAN make a difference in how quickly you approach the losing session. So, here we go...
There is a set of games where the house edge is about 1%. Those are: craps (if you stick to conservative bets), baccarat (a totally incomprehensible game that is, none the less, easy to gamble on), blackjack (using reasonably good strategy), and video poker (again, with good strategy).
The big downside with these games is that many of them are "table" games - which often require a relatively large minimum bet. The casino we stayed at had table game minimums of $10. (And some tables were more than that.) So, losing will happen more quickly than at, say, basic penny slots, which only takes 1-5 cents to play.
The exception to this is video poker. Video poker is a great game. If you include "comps" (that is benefits that casinos provide their players), the house edge for video poker can actually vanish. But, as a "perhaps only once in my lifetime" gambler, I didn't register for the comp program at the casino. I wasn't planning to lose enough money to make it worthwhile for the casino to give me anything free. But, even with comps, the house edge on video poker is very small, and it can cost as little as 25 cents a play. Not bad! I actually spent enough time playing video poker that I got bored of it, and wanted to do something a bit flashier.
Slightly worse than this set of games is Roulette. Roulette is a weird game in that there is almost zero strategy involved. The house edge for nearly every bet is right around 5%. The reason: every bet pays fairly - if we forget the zero and double zero. So, the house edge is really just the odds of hitting either a zero or double zero, which is 2/38 - right around 5%. The bets on zero and double zero are the exception - and they provide the house with a larger edge. Roulette, as a table game, has the same problem as craps, blackjack, and baccarat: high minimum bets.
Worse than roulette are slots. How bad slots are, though, is something that's hard to say. The casino can program slots to be as loose or as tight as they want to. But, statistics from Las Vegas suggests that the house edge is between 5 and 15% for most slot machines. There appear to be two regularities here: the edge is smaller for more expensive machines (so dollar slots provide a smaller edge than penny slots), and the edge is typically smaller for older, less flashy machines. I played a lot of penny slots on old-style machines, and also on some Mr Cashman machines, which were a bit flashier. There was at least some point on these machines when I was ahead. Now, if you want to "understand" slot machines, I have a recommendation for you. Don't bother. The old style slot machines are very simple. Anyone, at a glance, can confirm the win and why it happened. The new machines are totally incomprehensible. They, somehow, manage to construct 20 different (many jagged) lines out of 25 symbols. Confirming HOW you won is often very difficult. And, in the end, utterly irrelevant, as there is no strategy. (I suspect that playing more lines decreases the house edge, but I'm not positive on that.)
One of the worst games in a casino - in terms of the house edge - is Keno. The house edge is 25% or higher, depending on how many numbers you try to match.
All to say: if you have lots of money and want to be social, play craps, baccarat, or blackjack. If you don't have lots of money and don't want to be social, play video poker. If you don't have lots of money and want to be social, hang out at the craps table and pretend to be friends with someone. (Craps, apparently, is a game where it is considered acceptable to just watch while a friend plays.) If you have lots of money and don't want to be social, play video poker, but bet $1.25 per game to get the better payoff tables, or dollar slots.
If you have lots of money and want to pick numbers at random, do it at the roulette table instead of playing Keno.
(3) Strategy in Game
In some games there is basically no strategy. Roulette, Slots, and Baccarat all have more-or-less fixed payouts, regardless what you do in-game. The edge on almost every single bet in Roulette is right around 5%. Doesn't matter whether you bet on All Red or whether you bet on #32. In some games, there is minimal strategy. In craps, there is some strategy in which bets to make and which to avoid, and whether to lay/take odds or not. (Answer: bet Pass or Don't Pass, and always take/lay odds to minimize the house edge.) But, in some games, there is continuous strategy - especially in the various forms of poker - Blackjack and Video Poker in particular. Much of the time, the more in-game strategy there is, the less of an edge the house has. Video Poker and Blackjack are two of the fairest games in a casino - as long as you play well. In effect, the casino finds it worthwhile to give a handful of clients a fair game because most clients won't play these games well.
You can obviously use this to your advantage. If you're planning to play one of these games, read about strategy ahead of time. The key: look for someone who is statistically oriented (Wizard of Odds, folks). They do the math about what the best move is in each case. Wizard of Odds - again! - has a few systems for Blackjack. The "Optimal" system is a bit complicated - but he has some "simple" strategies that are almost as good, and keep the house edge very low. Similarly with video poker. There are optimal strategies (and free online trainers to help you improve your game!) - and there are simple strategies that work pretty well. Look them up.
But, really, the reality is that there are two types of people: one type likes the strategy. The other doesn't. If you do, then certainly play Blackjack and video poker, and try to get really good at the strategy. If you don't like it, then play one of the less strategic games with a low house edge (baccarat, craps), and avoid stupid bets.
In the end, of course, gambling is a leisure activity. And, in the long run, the house will win if you decide to make it any kind of regular hobby. That’s what “the edge” means. Over a large number of bets, that’s the percentage that the casino will end up with on average. If you make a large number of bets, then that’s the percentage that the casino will end up with FROM YOU on average.
The best strategy, then, is to ask a simple question - the same question you ask about any leisure activity - “How can I have the most fun using the least amount of money?” This is a very subjective question. Should you always wait until a movie comes to Netflix to see it “for free”? Maybe YOU should. But this isn’t true for everyone. Sometimes the extra expense is “worth it”. And that’s a judgment that only you can make.
So, is gambling “worth it”? Well, it depends. What are your other options? What will they cost? In my experience, gambling was fun, and not terribly expensive. At the same time, video games certainly provide more “bang-for-the-buck” for me. (Though that may be because I refuse to buy any game that isn’t selling at a sharp discount… And I don’t mind playing games LONG after they’re released.) At the same time, I don’t regret having done it, though I doubt I’ll ever do it again.