Again, you’re reading my intention completely wrong. I am not suggesting that the odds bet is an *additional * bet that helps you extend your time, it is an *alternative * bet that helps extend your time. For instance:
I go to Vegas with $500, with the intention of betting in $15 increments. Which of the following strategies is going to maximize my enjoyment (assume my enjoyment is derived from the process of gambling - not actually winning): betting $15 on the pass line, or betting $5 on the pass line and $10 behind it?
True, but the casinos know about blackjack team methods, so when they see a “gorilla” lurching from table to table, betting large sums and winning consistently, they can consclude it might at least be worthwhile to start shuffling more often.
Well Bricker said he would go cash in, i.e. NOT lurch from table to table. Unless of course he’s an idiot. Also, an intelligent crew would probably want to have more than one routine.
OK, first I want to clear up a misconception. The odds do not favor the house on any game. The odds of the house winning or losing any given bet are equal over the long haul. But the house pays winning bets at a rate slightly lower than the chances of that bet winning. For example, on a craps table, the chances of aces or twelve hitting are one in thirty-six, but the house pays the bet at thirty one for one (actually thirty to one, because the bet is usually left up for the next roll). This is called the house percentage (pc for short).
Odds are the only bet in the casino that the house does not take a pc on. By taking the maximum odds the house will allow on a pass line or come bet, you can reduce the house pc to a fraction of a percentage point- if the house allows five times odds, this can shave the house pc to scant hundredths of a percentage point. So, no, you won’t reduce your chances of winning, but you can greatly reduce your rate of loss.
Of course the downside to this is that since craps is such a fast-paced game, if the dice are cold, you can blow your entire wad in a matter of minutes…
so an ideal strategy to while away time and have a higher chance of winning in a casino is to play with minimum bets till it’s time to leave, then dump your entire disposable budget on a single bet?
Those obsessives are actually a pretty large chunk of a casino’s take; according to some studies, Ontario casinos are very reliant on gambling addicts, making perhas as much as 25% of their revenue from them. The continued profitability of Ontario casinos is heavily dependent on the business strategy of destroying people’s lives.
I would imagine it’s much the same everywhere else. Vegas, I would think, may actually be the least depedent on problem gamblers, but that’s just a guess.
muttrox:
That’s true only if
A) You’re measuring the utility of gambling by the expected probability of doubling your money, and
B) Your only acceptable end states are either doubling your money (or double and a half if you hit a blackjack) or losing it all.
But of course most gamblers do not measure their utility accordingly. Speaking as a blackjack player, much of my enjoyment stems from spending time playing the game, getting free drinks, and interacting with other gamblers, when they aren’t dinks. Also, I don’t play towards an inevitable result; I usually play by time, and rarely double my money or lose it all. It’s entertainment, not a math exercise.
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A/B) Not true, it also holds if you want to quadruple your money. Or go up 50% – in any case, the best bet is to bet as much as you can, not rinky dink your way around and give the casino more chances for their house edge to take effect. (Minimize the action, in other words.)
I agree with you about the goal though. It’s a sub-thread wending through this thread. What is it you’re trying to accomplish? Time? Enjoyment? Money? Expected money? Minimized loss of money? For example, when I first went to a casino with my fellow stats geeks, we had justifications to play any game:
Blackjack: Best pure odds in the casino
Roulette: Easiest to minimize your expected loss (since virtually all roulette bets are equal).
Craps: Most enjoyment time for your dollar (since many “hands” last for a lot of rolls). Also very social.
Slots: Well, it ain’t a table game so we didn’t like it, but it beats even craps for making $10 stretch out for a long time.
I think that’s part of the confusion here about craps and odds. One way examines it from a percentage of money played standpoint, which leads to saying you should always take odds. Another is to look at the bet in the context of your overall moneyroll, and it gets iffier then.
But if you want to measure entertainment value, you are no longer in GQ territory. If you want entertainment value for your dollar, maybe it’s cheaper to flip coins with a stripper, or bet on who will be kicked off of My Fat Obnoxious Boss. For this to have any kind of factual answer, you must assume the player is trying to maximize money or something very close to that kind of measure. On SDMB, it’s not entertainment, it’s a math exercise.
All this does is limit your variance from hand to hand until you actually lay down the big bet. Your best strategy over the long run (assuming you are doing more than betting once), is to play with a strategy that maximizes your odds in a casino game with a low house edge, in this order: poker, blackjack, craps.
Playing min bets until it’s time to leave doesn’t do anything (except expose your bankroll more often), unless you’re counting cards and playing blackjack. You’re better off placing one huge bet. Some of my math friends have stated that the best strategy for this method is to take your entire bankroll and place it on one bet, and then, win or lose, don’t bet again for the rest of the trip. If you’re going to one-time bet, I think craps edges out blackjack (by like .2 percent, more if you up the odds you place to more than double). Also, if you’re going to one-time bet, remove poker and replace it with single 0 roulette to round out the top 3.
I think it’s best to leave poker out of this discussion entirely. After all, if you happen to be Phil Hellmuth or Howard Lederer, playing poker is a fantastic bet. The relationship of your skill to luck is entirely different in poker, I don’t think it can be fairly lumped in with casino table games.
I always thought the craps don’t come/pass bet was the best in the casino, but it turn out that basic strategy blackjack gives the house an average edge of only .5%, while in craps it’s something like 1.4%. Howver, if you play odds, that brings it down to something like .8%, double odds .6% and if your casino will let you lay down triple or more your line bet on odds, then the house edge will be less than blackjack.
I admit I am not a statistician or even remotely good at math but this does not seem correct.
A particular hand in Blackjack is not 100% independant of the hands that went before it. This is not Roulette where the same numbers are on the wheel each and every spin and the ball dropping is purely random. In Blackjack cards leave the shoe and are out of play and a player may use a variety of strategies (good or bad) that can affect the outcome. A player could hit with 20 showing on his cards and probably lose or stand and probably win that hand.
Point is Blackjack is not a purely random exercise like Roulette so I do not see that it can lend itself to easy statistical analysis such as this.
Oh, in that case, you are best served staying off the line altogether. Place that $15 on 5 or 9 instead. At this point, I would like to point out this quirk that many odds fans have trouble accepting:
$5 Pass w/ $10 odds on 5 or 9 costs $15 and pays $20
$15 Place on 5 or 9 casts $15 and pays $21
So where does that extra dollar come from? The naked line bets have less than half the house advantage compared to the Place bets (other than 6/8), so the extra dollar clearly does not come from the house advantage differential. And yet, when you combine the free odds with the superior line bet, you still don’t get the nice payout of the much weaker Place bet. What’s going on?
Whether you already know the answer, or are figuring it out now, pondering this question should eventually lead you to the realization that odds bets really are superfluous bets that do nothing but increase variance.
However, if you are still not convinced, then why is it that you don’t play odds on the darkside? Odds on the lightside utilize the exact same principle as the darkside. Plus, the darkside has a slightly better expected value than the lightside. Yet most players never even bother to calculate what the double odds actually are for the Don’t, much less play them.
Why? Is it because the large chip layout to cover it increases your variance so blatantly that most gamblers instinctively realize that it will burn through their money too quickly? (That’s a trick question; the darkside odds increase your variance by the exact same amount as the lightside. The appearance of increased variance is quite blatant on the darkside, however.) I say that is exactly the reason. The lightside odds have the exact same effect, only it is slightly less exaggerated. This small difference is enough to push people from the “best bet on the table” attitude when considering the Pass into “way too much variance to be a smart bet” attitude when considering the Don’t. I find that interesting.
Don’t get me wrong, I love playing darkside odds when I play odds, but I prefer it at 3-4-5 tables.
I digress. The Place bet answer wasn’t my top recommendation to the question I quoted here. I would make a $5 Don’t Pass bet, followed by (instead of $10 lightside odds) two $5 Don’t Come bets. Far more action than the single bet with double odds, adding to the fun quotient, plus it has several advantages:
Can’t lose them all in one roll, but you can win them all on a 7.
Much easier for the dealers to handle, as only one denomination of chips is required.
You don’t get sucked into that uber-irritating lightside rollercoaster, where you root against 6s and 8s because of the paltry 6:5 payout odds, and find yourself starting to root for 4s and 10s, which are annoyingly difficult to actually win.
All in all, I would never recommend a single pass line with max odds bet to anybody except a complete novice at the game. (The reason being that I can’t explain the whole game to somebody, and I could never be taken to task for recommended what is widely considered to be the “smartest” bet.)
Actually, betting the don’t is only about a hair better than betting the pass line.
I agree about only betting the pass line with odds, though. Standing around waiting for your solitary bet to win on a hot roll can be frustrating. From a dealer’s standpoint, I would have to say pass line with full odds and two come bets with full odds would give you the maximum action with the minimum outlay. Place bets actually have as somewhat higher house pc than come bets with odds taken, plus when seven out rolls, all of your place bets lose, so, say you bet $27 across, and the next roll, seven out rolls, you’ve lost that money, plus your line bet and odds, if you took them.
OTOH, if you’re using the two come bets method, if you get a point and a seven out the next roll, your come bet still wins, which lessens your overall loss. If a hot roll fires up, then feeding in come bets so that you have two numbers besides the point means you will be winning on repeating numbers but also reducing your loss when the seven our rolls. Also, if the dice are choppy, you’re not blowing your wad by loading up all the numbers with come bets. I’ve seen this happen a million times- some guy keeps feeding in come bets until he has all the numbers covered at full odds, then seven out and he’s lost a signivicant portion of his bankroll on a hand that only lasted 6-7 rolls.
If you multiply all 36 possible rolls by 55, you can come up with the precise odds of all permutations:
Pass = 976 / 1980 = 49.29% chance to win; 28 / 1980 = 1.41% house advantage
Dont = 949 / 1925 = 49.30% chance to win; 27 / 1925 = 1.40% house advantage
Excellent post. I agree with virtually everything you said, except the “maximum action with minimum outlay” part. I would suggest three $10 points with no odds is superior to three $5 points with double odds. I suggest $10 because $15 is a bit pricey for each bet, requiring $45 simply to get established. Notice that the double odds requires that $45 as well…
Here’s a question for those who believe that odds are a good bet. Assume a $500 session at a $5 table. (This seems crazy; I would recommend $300 sessions at a $5 table, but that’s just my decade of periodic analysis talking. Since $500 was mentioned upthread let’s go with that.)
The casinos in this area all allow 3-4-5 odds. Would you still take maximum odds at every opportunity? (3-4-5 odds means 3x odds are allowed on 4 & 10, 4x odds allowed on 5 & 9, and 5x odds on 6 & 8.) If not, why not?
Now let’s say you are going to O’Shea’s in LV. They allow 100x odds. Let’s assume you play at a $1 minimum table that allows $100 odds behind it. With your $500, is it still the “smartest play” to take maximum odds? I’m assuming it is, because all the arguments that favor 2x odds favor 100x for the same reasons, and much more strongly at that. But if you realize that it isn’t, what justification do you have? If odds are the best, you should always avail yourself of them, no?
Here’s the thing. The comeout roll is often overlooked by players who dismiss it as the occasional bump in the road before they get to their real bets, which are odds. But the comeout is resolved immediately on a 2,3,7,11, and 12. There are 12 ways you can roll those numbers. Since there are only 36 possible rolls, you get 12 of 36 points resolve immediately. That reduces to 1 in 3. So fully one third of all Pass Line bets are resolved without odds ever being allowed. (The Don’t has slight variation.) That’s a huge percentage of points.
Now look at the line bets in respect to the comeout. The Pass Line wins you 8 out of 12 points, or 2 in 3. The Don’t wins you 3 out of 11 points. So on the comeout, you want as much money as possible on the Pass Line and as little as possible on the Don’t.
Now look at the established points, which happen the other 24 out of 36 trials. Using my technique of multiplying all rolls by 55 to keep the math in integers, you get 1320 possible points. Skip the remainder of this paragraph if you want to just trust me on the math. 4/10, 5/9, and 6/8 have a 3:4:5 relationship to each other. (Which explains the 3-4-5 odds, btw.) So of the 1320 points, 330 are 4/10, 440 are 5/9, and 550 are 6/8. You win a third of the 4/10s, which is 110, two fifths of the 5/9s, which is 176, and five elevenths of the 6/8s, which is 250. That’s 110+176+250=536 winners out of 1320 possibilities. 536 / 1320 = 40.6%.
For the Pass Line only, you have 66.7% chance to win on the comeout, and a 40.6% to win an established point. Odds players are maximizing the money at risk in a 40.6% proposition while minimizing the money at risk in the 66.7% proposition. To me, that’s silly. The odds do pay better than 1:1, but you’re not playing craps to earn a living. You’re playing to have fun. You have fun by winning bets.
It is not smarter to increase your number of losses, especially considering that the payouts aren’t even as good as the crappy Place Bet payouts. The whole reason that the double odds bet is “better” than a Place Bet – despite a worse payout – is because of the huge advantage of the comeout roll. Those who do not play odds at all are putting much more money in the player-friendly scenario of the comeout roll, which I contend is the smarter play.
I did not understand this until I compared the actual numbers, which are in this post but not next to each other, as it is a rather unusual comparison. Of the 976 ways to win the Pass Line, 440 are won on the comeout, while 536 are won on established points. When you divide the 440 comeout wins by the 976 possible wins, you come to the frankly counter-intuitive realization that 45.1% of all Pass Line winners are won on the comeout roll. Before you read this post, I bet you assumed (as I did) that the comeout probably only contributed about 20%-30% of all Pass Line winners, if you even wondered about it at all.
So that’s why most people believe odds are a great bet; they don’t realize that for the most part, the Pass Line bet is really won on the comeout, and established points aren’t much more than window dressing tacked onto the real bet. The casino knows this all too well. Why do you think they allow you a “free odds” wager in the first place?
One final attempt: Free Odds in craps serve the same purpose as a free odds wager in blackjack that allowed you to triple your bet if the dealer showed a face card. Would you always triple your bet when the dealer showed a face card, even if the extra money paid double (or whatever)?
Actually, before I read this post, I had about five and a half years of experience dealing the game, and though I hadn’t done the math, I knew that pretty close to half of all pass line wins happen on the come out roll.
Also, the casino I’m currently working in (Oh, Mr. F, when oh when does the new spa open?) usually has a $3 minimum with 5X odds. Three dollar games are actually pretty easy to find downtown, as are 5X odds (I think anything more than 5X is for lunatics with way too much money on their hands, but I digress).
The advantage of come bets is that if your bet wins, it is returned to you (or, if you have a new one out there, it is paid “off and on”). If you still have one sitting out there when seven out rolls, it gets paid.
Also, it’s been my exprience that maybe a third of craps players actually bet the come. They generally tend to bet place bets. Nothing wrong with place bets, really, but I’ve seen this incredibly stupid strategy where people start pressing as soon as they hit, which means on a short roll, they’ve lost their original bet and not collected any of their potential winnings.
If you’re going to make place bets, I would say bet the inside numbers (4,5,6,8,9), and start pressing after you’ve won back your initial outlay, then press them one unit every second time they hit. That way, you’re collecting a good portion of your winnings, and using house money to increase your bets beyond the original outlay.
I’m enjoying your excellent posts. I’m confused by your discussion of the comeout rolls though. What’s the difference? Since the two strategies are identical on the comeout roll, why even bother discussing what happens there.
(Every poster seems to have differing version about what the two strategies actually, adding to the confusion.)