This weekend I watched a casual craps table (at a Vegas-themed birthday party).

The number of different bets that can be placed are legion, and it took me a while to get a basic understanding of what was happening.

It seems, though, that there are fixed odds for any potential roll, and that once the point is established, there is one and only one bet that will give the best return, and that any other bet is throwing money away.

Is there actually strategy to craps, or are any deviances from the optimal bet just silly humans not understanding how math and probability work?

Are you equating highest return with the best bet? Many players don’t and for good reason: there is a lot of money to be made on rolls where the point is not made. If I simply bet the Pass Line, my bet is at risk with every roll, and I can only win when the point is made. But I can make side bets that pay off on every roll, thereby increasing my opportunities to win. You could bet on double sixes hoping for a 36:1 payout, but it doesn’t happen very often, so I wouldn’t consider that the best bet just because it has the highest odds.

Sure. Maybe I was unclear about my question (which would not be surprising). There must be some equation that points to a particular bet having the best ROI over infinite rolls of the dice. Isn’t that always the best bet?

You can certainly use probability to calculate the true chances of winning any particular bet, and thus the return on your bet given a fixed schedule of house odds.

I’m not sure how the odds are set at “a casual craps table”, but if they’re based on Vegas, then the odds are stacked in the house’s favor, it would probably be a case of finding the “least bad” return on investment, ie the one that would cost you the least in the long run. But the only way to win is not to play, and how much fun is that?

(Well, the best way to win is to be the house, but then you have to convince other people to come bet at your table…)

At its essence, it is just a simple matter of probability. And if you can afford to play for several thousand rolls, so that the laws of probability outweigh the random chance of a single roll (or a dozen, or a hundred), then you could create a ‘best’ strategy for playing the game. But if you’re only at the table for a few hours, or you want to have ‘fun’, then it might be worthwhile to risk a bit on some of the lower-probability outcomes.

Of course, in the very long term, the only way to win in a casino is to own it.

Yes, there are optimal bets in craps. Free odds bets pay out at true odds (0% house edge). In order to place free odds bets, you must first make a Pass/Don’t Pass or Come/Don’t Come bet, which carry a 1.4(ish)% house edge. All the other bets pay out even worse.

The poorer bets exist because betting pass, laying down a free odds bet, and watching the shooter roll, roll, roll until pass/don’t pass is resolved is boring. A number of the other bets resolve immediately upon the next roll of the dice.

I heard that the “Don’t” lines allow you to remove your bet the point is established. So is there any advantage to playing the Don’t line and removing your bet for the points which are less likely to pay off?

No, as the shooter is more likely to roll a 7 before the point number, which means your don’t pass/come bet wins, than to roll the point number before a 7.

The “best” bet, in terms of percentage, is usually to bet Don’t Pass and then as much as you can on “odds”. I say “usually” because if you are lucky enough to find a table with something called “5% buy commission on wins only” and the commission on a $25 buy bet is rounded down to $1 (in effect, making it a 4% commission), then buying the 4 or 10 is slightly better (in effect, you are betting $25 against the house’s $29 that a 4 (or 10, if that’s the number you bought) will be rolled before a 7).

If we’re just looking at rate of return, then the optimal bet is “don’t”. This gives a 100% rate of return, while everything else at the table is less than that. Obviously, this is not the tactic used by absolutely anyone at the table.

If you are saying, as the computer determined in “War Games,” that the optimum strategy is to not play, you are obviously correct. If you are saying that Don’t Pass and Don’t Come bets are the best of all the even money bets you would also be correct. While almost all experienced crap players insist that taking or laying the odds is the best possible strategy, if you win you will win a lot more though if you lose you will run out of money a lot more quickly, the player has no advantage when making those bets.

All things considered, including an honest game and shooter, yes - Craps is strictly a game of the odds. However, it’s a percentage game and you have to carefully analyze not just the dice odds, but the betting odds. Most authorities advise staying completely away from some of the corner bets, which are loaded in favor of the house.

Of course, as a PC game, the whole thing is loaded in favor of the house. In the long run, you can only lose to the house rake.

My first year of stats grad school, a homework problem was to determine the probability that a shooter in craps wins. It was tedious as fuck.

The probability on the first roll of lose (2, 3, or 12) or win (7 or 11) was easy enough. For the others (4, 5, 6, 8, 9, or 10), I had to calculate each one separately. The probability of winning for each of those scenarios becomes an infinite series, which is fairly easy to figure out. But doing it for each one was a pain in the ass.

If I recall correctly, the probability of winning was slightly greater than 0.5.

I learned to play craps in Reno in the 60’s. After midnight they would lower the minimum bet to 25 cents. And all the regulars would show up. A ten dollar buy in would give you hours of fun! I quit when the buy in was lost, or if I made $30 (3 times the buy in).

A few observances.

Always take care of the dealers. They want you to win. And they will watch your money. Place bets for them. Some people would toss chips on the table and say, “#12 for the boys”. One time a dealer said, “Thank you. But we would rather be on the pass line with you”.

When the dice have a good run, and the table is full of people shouting, it is a hoot! When someone walks up and places a Don’t Pass bet. It is not well received by the players.

I don’t know what the table minimum is today. Anyone know? I suspect it is out of my reach. Which is too bad. It can be a very fun game.

Depends on where, of course, but on the Vegas Strip, expect $5 minimums at Excalibur and other lower-end places, $10 in most other places. Possibly some $3 minimums on the couple remaining really old and smokey places, but you’re more likely to have to move off-strip to find them.

There is a way to calculate the chance of winning if your first roll is, say, a 4, without need of an infinite series.
If you roll a 4, then the only numbers that matter from that point forward are a 4, which wins, and a 7, which loses. Of the nine possible “ending” rolls, three are winners and six are losers, so the probability of winning is 1/3.

In fact, the chance of winning is slightly less than 50%. You can bet to lose (“don’t pass”), and the chance of winning would be more than 50% had there not been a rule saying that if the first roll is a 12 (or a 2 in some places, like Reno and Lake Tahoe), the bet is a push instead of a win.

That’s because Dark Side players are generally assholes.

You want the best return? Go to the bank. If you’re at the table, just bet the Pass Line, take maximum odds, buy your favorite numbers and press when you feel lucky. In the long run you’ll probably go broke, but then, in the long run you’ll also be dead, so don’t sweat it, just have fun! Place a bet for the dealers every now and then, keep your hands clear of the table and always tip the cocktail waitress.

I liked to hang in there while the dice makes a turn around the table. Remembering what each person did with the dice, and bet accordingly the next time around.

If a lady is shooting the dice, increase the bet.

Not very scientific, but it works for me. Well, at least it is fun.

The dealers might want you to win, but it doesn’t much matter, since there’s nothing they can do to alter your odds. Get on their good side if that’s more fun for you, but don’t expect it to get you anything beyond fun.