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# Craps Pass Line With Odds Bet - Casino AdvantagePrev TopicNext Topic

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• Sugar Land
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August 28, 2019
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For those with an interest in Craps, a dice game that is available in just about any casino with table games, I have worked out a simple formula for % casino advantage for the Pass Line bet (which is probably one of the most common bet in Craps) coupled with a side "odds" bet. Briefly, the initial Pass Line bet has a casino advantage of  about 1.414%, but in most casinos an additional (side) "odds" bet (after the Pass Line bet) can be made, and the "odds" bet is paid at true odds (no additional casino advantage). The amount of the optional, additional "odds" bet can range anywhere from 1x the Pass Line bet to 100x or more. For example, if the Pass Line bet is \$10, then a 100x odds bet would be \$1000, so a total of \$1010 would at risk in this case. The greater the % of your overall stake made in the "odds" bet, the lower the overall casino advantage.

Here is the formula for the overall casino advantage with the Pass Line Bet + (n)x additional "odds" bet. Here, "n" is a variable that can be zero or any positive integer. Zero means no "odds" bet is made, just the Pass Line. (Again, the "odds" bet is optional.) n=1 is single odds, n=2 is double odds, and so on.

Let's take a few examples:

 n % Casino Advantage 0 1.414 1 0.848 2 0.606 5 0.326 10 0.184 50 0.041 100 0.021

As you can see, if you are at a \$10 table, and your bankroll is so large that you can risk \$1010 at a time, you can get the casino advantage down to a razor thin 0.021% with a Pass Line + 100x Odds bet.

• United States
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March 28, 2019
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Interesting analysis. I didn't know the additional side bets in craps had true odds and no house edge. Is this universal, or does it vary by establishment?

I'm not a casino gambler but someone tried to explain craps to me a long time ago. Afraid I couldn't make heads nor tails of it.

• Sugar Land
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Yes, the "odds" bet, sometimes called "free odds", is universally paid according to the true probabilities, without house advantage. However, before making this bet, you must make the Pass Line bet first, and that has a 1.414% house advantage. The casinos vary in how much you can bet on the "odds" as a multiplier of the original Pass Line bet. For example, a casino that offers 10x Odds on a \$10 Pass Line bet will let you bet up to \$100 on the "odds" bet.

As an example of how "odds" or "free odds" function, consider the basics of the Pass Line first. Two six-sided dice are rolled, and the total is summed. A result of 2, 3, or 12 means you immediately lose your Pass Line bet. A result of 7 or 11 means you win, and you are paid at even money, so for a \$10 bet, for example, you will be returned your \$10 bet + \$10 winnings. Any other result is called a "point". The way the "point" works is that the dice are continued to be rolled in succession until either the "point" is rolled or a 7. If the "point" occurs, you win and are paid at even money. If a 7 occurs before the "point", then the House wins, and the bet is lost.

Enter "odds"/"free odds". As mentioned, this bet can only be made when the Pass Line bet is made first. Also, crucially, it is only possible when a "point" is established. Let's say, for example, the "point" is 4, and the House allows 10x odds on a \$10 pass line bet. You can then make a (side/additional) \$100 "odds" bet over and above the original \$10 Pass Line. If, after additional rolls, 4 occurs before a 7, then you win both the original Pass Line bet as well as the "odds" bet. Because 7 is twice as likely to occur as 4, you are paid at 2 to 1 on a winning "odds" bet, proportional to the true probability. (If 7 occurs first, you lose both the Pass Line bet and the "Odds" bet.) In my example, assuming 4 is rolled before a 7, the \$100 (10x) "odds" bet would result in \$200 winnings, and that is in addition to the even-money win of \$10 on the original \$10 Pass Line. The total winnings would be \$210 on \$110 at risk.

• United States
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Thanks Orange71, you make much more sense than the guy who tried to explain to me before -- granted he was a degenerate gambler and not one for mathematical precision.

What I remember is 7/11 = automatic win, 2/3/12 = automatic loss, 4/5/6/8/9/10 = keep rolling till you either get your number or bust at 7, and also you have to hit the back wall. I worked out the probability of winning the pass line bet is 244/495, same as 7/495 = 140/99% house edge. Now it totally makes sense to put more of your money on the side bets that are edge-free.

It's kind of incredible that with such a razor thin house edge a casino can still rake in the big bucks from craps. They just have to process a massive volume of bets.

• Sugar Land
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I believe the majority of people playing this game (would it be ungracious to call them chumps?) make one or more of the many other possible bets that have a much greater casino advantage (some even >10%). They might as well be playing the lottery I presume that's why the casinos continue to offer the game. A "whale" (big-money gambler) coming up to a table betting \$10,000 at a time on a Pass Line then taking 100x odds bets (\$1M) would be a risky proposition for a casino.

In case you're interested, there is another type of bet called Don't Pass that is nearly the opposite of the Pass Line. 2/3/12 rolls are even-money winners (though in some casinos the 12 is a "push", meaning the player merely has his bet returned with no winnings). 7/11 are losers. All the other numbers are points. In the Don't Pass case if a 7 is rolled before the "point" the player wins, else if the point occurs first, the player loses. The subsequent odds/free-odds bets (when a point is established) is termed as a "lay" bet in this case. The player bets that 7 will occur before the point. If it does, then the lay-odds bet is paid at true probability. For example, a \$12 Don't Pass bet with 100x lay odds (\$1200) means that, if the point is a 6, and a 7 occurs before 6 after the point is established, the lay odds winning would be \$1000 (5/6 of \$1200, representing the odds of rolling a 6 vs. 7). The player would also win \$12 Don't Pass bet at even money (\$12 won).

The Don't Pass and Lay-Odds bets are slightly lower House advantage than Pass Line with Odds. So a player who really wants to squeeze out every cent would place Don't Pass with Odds. It's the best possible bet you can make in Craps statistically. You can work out the probabilities yourself, or, if you want, I can post them.

• Sugar Land
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Correction: on Don't Pass, a result of 12 must be a "Push", meaning the bet is returned to the player and settled. This is necessary to keep the overall House advantage. The House advantage on Don't Pass is 1.364% (or 3/220 to be precise). In the Pass Line case it's 1.414% (or 7/495 to be precise).

• Sugar Land
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The equivalent % House advantage per unit bet for Don't Pass with Odds is (45/11)[1/(2n+3)]. n is the Odds multiplier (1x, 2x, 5x, 10x, etc.) Here is the summary:

• Kentucky
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February 14, 2006
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Quote: Originally posted by Orange71 on Sep 7, 2022

Correction: on Don't Pass, a result of 12 must be a "Push", meaning the bet is returned to the player and settled. This is necessary to keep the overall House advantage. The House advantage on Don't Pass is 1.364% (or 3/220 to be precise). In the Pass Line case it's 1.414% (or 7/495 to be precise).

On Northern Nevada crap tables "2" is barred and a push on "Don't" bets.

Nice explanation of the game, odds and house advantage!

"When will we ever learn?"

• Sugar Land
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Stack47, thanks. I wasn't aware of this variation in northern Nevada. Whether 2 or 12 is barred, of course, the result is exactly the same odds.

• LAS VEGAS
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Hey Orange, thought you would find this nformative and interesting on the craps green felt jungle, Las Vegas where the dice never stops rolling

Page 1 (jpg)   Barstow’s Controversial Theories on Craps

Casino games of so-called "independent trials" such as craps, baccarat and single-zero roulette, can be beaten long range, as well as short range. This statement is predicated not only on personal experience and observation, but also on one highly unorthodox theory. I believe that, notwithstanding a small
minus expectancy -- the house edge -- there are certain times when true probability actually favors the bettor. I'll try to explain.
Mathematicians and physicists agree that as the number of trials increases, and substantial percentage deviation from the norm must tend to decrease. When dealing with a 50-50 proposition such as heads/tails or pass/don't pass, they agree there is a 90% probability that the variation will not equal of exceed the square root of the number of trials. This means, for example, that in 16 trials there is less than a 10% chance of one side winning as few as four times, while the other wins 12 times.
Thus, when very wide percentage variations from norm occur, as the often do in a small number of trials, the equalizing process is likely to be close at hand, and at least one new factor has begun to tip the scales of probability. If at the start of a new series we've seen 6 or 7 repeats of anything, we've already reached or surpassed the normal variation quota for 100 trials.
Why shouldn't the trend change? Of course there's no law that says it must change, but I contend that we're no longer dealing with strictly even chances. I contend that is we now bet on the weak side using a 3-bet, or 4-bet Martingale series, the probabilities in our favor will generally be strong enough too fully off-set a small mathematical disadvantage of say, one to three percent.

pg 2 (jpg)

Suppose we've seen 5 successive passes at our table or at 5 different tables; it really doesn't matter which. The odds were 31 to 1 against the sequence - and any conventionally trained professor will tell you that there is still 1 chance in 32 that the next 5 decisions you see will also be passes.
If you question that, the explanation you'll get sounds plausible enough: "The dice don't know what they have just finished doing; they don't have memories - so if there was a 50% chance one way or the other to begin with, that percentage cannot vary as long as the dice are thrown randomly."
You protest that one sees 5 passes or 5 misses quite often, but runs of 8 or 10, hardly ever. Again the explanation seems plausible: "Odds against 10 repeats of a specific even chance are better than 1000 to 1."
You ask whether there might not be factors other than arithmetic alone that cause dice or tossed coins to behave as they do; for example, cycles, the theories action and reaction, or permutations and combinations. You observe that there are different numbers of spots on each side of the dice, different shooters throwing them, etc. Mightn't one or more of these factors influence the outcome of those so-called independent trials? "Actually," you ask, "is there really any such thing as a completely independent trial?"
When your questions are scornfully dismissed, you remind your instructor that Emile Borel, one of the more prominent founders and exponents of the modern theory

Eddessa_Knight with Lucky LIGHT

Nota Bene:

The odds will deceive you >>>>>

• Sugar Land
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Astounding streaks happen in any game of chance. In fact, given enough trials (this is the key point), they are inevitable.

Casinos go to great lengths to ensure there are no physical factors that result in bias deviating from theoretical odds. The dice used in Craps are very tightly engineered not to have a bias, and they're changed out periodically. Notwithstanding, streaks inevitably still occur. There is nothing abnormal or mystical there, it's perfectly consistent with random fluctuation and the Law of Large Numbers (i.e. large number of plays). The thought that betting along with a trend on a game of pure chance leads to an advantage is a fallacy. Dice really don't have "memories", unless there is a physical defect, and as already mentioned, painstaking measures are taken to ensure they do not. For example, does a player have an advantage by playing the Pass Line if the shooter has rolled 7 for 20 times in a row? No, not at all. The chance that the shooter rolls another 7 is no different than the chance the very first time he rolled.  The trend may continue or abruptly stop on the next roll, and the probability of either is clear.

In purely random games like craps or lottery with fixed odds on every play, there are no systems that will increase player odds, notwithstanding streaks. This is not necessarily so for games where previous plays impact current and future results. In Blackjack, for example, card counting is a well-known method to gain advantage by betting more or less on the next play depending on the cards remaining in the deck. This advantage is very real and well-grounded in mathematics. The casinos are fully aware of this, as the method has been around for decades, and they take measures to thwart card counting, e.g. multiple decks, frequent re-shuffles, asking card counters (who they can usually readily identify) to leave.  Another example is table poker. A player is playing against other players, with the casino taking a commission to host the game. The player's return is limited only by the relative skill of other players, the stakes bet, and the House's commission.

• LAS VEGAS
United States
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November 22, 2006
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Knowing how to figure the odds will not make a wining player;

need to have something extra on your play

Caution the odds will deceive you

• Sugar Land
United States
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August 28, 2019
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Correct, in games of chance where current and future play is independent of past play, knowing how to figure the odds will not make a winning player. (Examples are lotteries, craps and baccarat.) Neither will software or "systems" which purport some sort of advantage over randomness. Mathematics are just facts, neither favoring nor disfavoring anyone. There is not, and cannot be, anything extra in my play, your play or anyone else's play. In games of chance where past play changes either probabilities of hitting prizes or the prize levels themselves (returns), that's a different story. Knowing the probabilities and returns helps. These are games of skill, e.g. Blackjack or Poker. Example: why would casinos try to shut down card counting in Blackjack if it's futile? They do it because it has the possibility of giving a skilled player an advantage over them, and they cannot and will not tolerate that.

Odds (probabilities) don't deceive, they're just facts.

• LAS VEGAS
United States
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November 22, 2006
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Thank tou for your considered opinion "0"

Odds don't change but probabilities can and facts can have a point of view

For your fun consideration, it's been my experience with all speculator action,  that there are special times, when experts in their fields up for, a rather out of the box  i.e. extraordinary or abnormal play action that works brilliantly. There is possibly a download into the majestic pituitary or pineal gland that this is the  moment  to deviate from the textbook with this winning improbable solution

A hint, only for out of the conventional box solution seekers:

'Deus Ex MachinaT heoria'

-

Bona Fortuna

Vivat & Bonum Noctis

Nas  Par

• LAS VEGAS
United States
Member #47,728
November 22, 2006
8,277 Posts
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From the horse's mouth, first have to be smart to be LUCKY!

~

From venerable Ancient Chinese house of wisdom: if one could choose between having a good life VS having a Lucky life -  a LUCKY life is most prerable  :-)

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