Chance Of Winning Craps

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• Chances Of Winning Craps At Casino
• Chance Of Winning Craps
• Best Chance Of Winning Craps

So, if the number you bet on is rolled before a 7 you win and you are paid as follows: 4 or 10 placed – 9:5 odds, 5 or 9 placed – 7:5 odds, 6 or 8 placed – 7:6 odds. As you can see the best for you is to place a bet on 6 or 8, because these bets have the best odds and also they have a good chance of hitting. A CASINO GAME OF PURE CHANCE. Craps is an exciting game with lots of action. Here is a summary of your winning probabilities in craps: YOUR INITIAL TOTAL. Home › Game Odds & Strategies › Craps. The Odds is like a side bet in craps made after a. A 'wrong' bettor and is usually winning when. The first roll a new shooter makes. Another way of thinking about the craps game is thinking that since there is a 1 in 6 chance that a 7 will be rolled, there is a 5 in 6 chance that a 7 will not be rolled. So betting on a point number in this case or betting for the shooter to not roll a 7 is a great bet as 5 out of 6 rolls will not be a lucky seven.

pass line win probability = 244/495
(244/495)^3 = 0.119771609 exactly 3
you want 3 or more
formula for the sum of a geometric series is a/1-r
where a is the first term
r = the ratio
a = (244/495)^3
r = 244/495
so (244/495)^3 / (1-(244/495) = 0.236202973
But now you want this to end. Multiply the above result by 1-(244/495)
0.119771609
((244/495)^3 / (1-(244/495)) * (1-(244/495))
added my table

at least in a row then lose	Prob	1 in
2	0.242979288	4.1
3	0.119771609	8.3
4	0.059038934	16.9
5	0.02910202	34.4
6	0.014345238	69.7
7	0.007071188	141.4
8	0.003485596	286.9
9	0.001718152	582.0
10	0.000846928	1,180.7
11	0.000417475	2,395.4
12	0.000205786	4,859.4
13	0.000101438	9,858.3
14	5.00017E-05	19,999.3
15	2.46473E-05	40,572.4
16	1.21494E-05	82,308.7
17	5.98878E-06	166,978.8
18	2.95205E-06	338,748.0
19	1.45515E-06	687,214.1
20	7.17286E-07	1,394,143.4

pass line win probability = 244/495
(244/495)^3 = 0.119771609 exactly 3

Mustangsally: Maybe I'm missing something, but I get different results from what you show. Suppose (for simplicity) that it was a coin flip with p=0.5 instead of 244/495. To get at least one win in a row would be P=0.5. To get at least two in a row is P=0.5^2, etc. To get the answer for exactly n in a row, you need to multiply the 'at least' by the probability of losing on the n+1 try.
For the pass line problem, I think the 0.119771609 figure is for 3 or more, not for exactly 3.
Isn't that correct, or what did I miss?

For the pass line problem, I think the 0.119771609 figure is for 3 or more, not for exactly 3.
Isn't that correct, or what did I miss?

rudeboyoi and Sally both arrived at the same value.
Sally did it differently by starting with 3 pass line wins in a row in 3 trials.
The OP asked a unique question.
Most ask the probability of winning 3 pass line bets in a row. And for 3 trials it is simply p^3
OP wanted to add the probability of 3 *or more* and *followed by a loss*.
Sally's math shows 3 in a row in 3 trials and the OPs Q arrives at the same value. It should.
IF the OP had asked what is the probability of winning 3 pass line bets in a row then losing, we would have p^3 * q or 0.06073
Let us see if OP is happy and replies.
added
average number of trials to see a run of 3 or more pass line wins: 16.466
4 or more: 33.404
5 or more: 67.765
6 or more: 137.475
Multiple streaks of pass line winners.
15 trials about 30 minutes of play at 100 rolls per hour
30 trials about 1 hour of play
Example: 30 pass line trials
about a 90% chance of at least 3 pass line wins in a row at least one time
about a 58% chance of at least 3 pass line wins in a row at least two times
about a 23% chance of at least 3 pass line wins in a row at least three times
here is the losing streaks (miss) for the pass line per N trials

added
average number of trials to see a run of 3 or more pass line wins: 16.466
4 or more: 33.404
5 or more: 67.765
6 or more: 137.475

You guys are great. Thanks for the detailed responses.
How did you calculate the average number of trials to see a run of 3, 4, 5, 6 or more pass line wins?
How do you define a trial? Would each shooter be a new trial? Or does a new trial begin after any losing pass line bet, in which case a single shooter could have multiple trials that end and start over with a losing pass line bet from throwing 2, 3, or 12 on a come out roll?
If a bettor were to power press the pass line bet with a $100 wager:

at least in a row then lose	Prob	1 in	Bet	Win	Lose
1	0.492929293	2.0	$100.00	$100.00	$100.00
2	0.242979288	4.1	$200.00	$300.00	$100.00
3	0.119771609	8.3	$400.00	$700.00	$100.00
4	0.059038934	16.9	$800.00	$1,500.00	$100.00
5	0.02910202	34.4	$1,600.00	$3,100.00	$100.00
6	0.014345238	69.7	$3,200.00	$6,300.00	$100.00

Does this mean that on average you would be betting about $1600 to win $700 on a press of 3 pass line wins for a net loss of $900?
$3,300 to win $1,500 on 4 pass line wins losing $1,800?
$6,700 to win $3,100 on 5 pass line wins losing $3,600?
$13,700 to win $6,300 on 6 pass line wins losing $7,400?
What's the best way to interpret this expected value for power pressing a pass line bet?

Chance Of Winning Blackjack Hand

Beginning gamblers often shy away from the craps table because the game looks complicated. It’s actually easy to play craps because the math keeps everyone honest. A rule of thumb to live by in any casino game is “the more they pay the less likely you are to win the bet”. Hence, there is no shame and a lot of wisdom in playing a conservative craps strategy. Here is a look at 12 secrets every craps player should learn to improve their game.

1. Why are Casino Dice Special?

Casinos use transparent dice because they hide no flaws. Opaque dice can be manufactured to varying standards and can hide balancing flaws. Unbalanced dice do not roll randomly.

And casinos replace their dice often. Casino dice have machine-tooled straight edges. These edges eventually wear down, accumulating imperfections. Imperfections add bias to rolls.

Casino dice are larger and straighter than board gaming dice because players must throw the dice so far on a craps table. The felt top and lining help the dice bounce more randomly than a smooth table top does.

So while you may be practicing your die throws at home, you’re not going to get the same action as at a casino, especially if you never replace your practice dice.

2. How the 5-Count System Works

Since 1994 craps players have debated whether the Captain’s 5-Count system is legit. This system tells you when to bet on a shooter other than yourself. Here are the 5 counts:

• Any point on the Come Out roll roll.
• Any good roll after the 1^st Count roll.
• Any good roll after the 2^nd Count roll.
• Any good roll after the 3^rd Count roll.
• The first point rolled after the 4^th Count roll.

You begin placing low bets on the shooter after he hits his 5^th Count roll. If he never gets there then you never bet on that shooter. Never bet big on another shooter.

The 5-Count method reduces the number and size of bets you place on other shooters, thus reducing your overall risk. The downside of using the 5-Count method is that you watch more than play, but betting on a drunk guy to throw dice the way you want is a pretty risky bet.

3. You Can Stop the Game for a Dispute

Sometimes the dice roll funny, or maybe you’re not sure you were paid correctly. Before the dice are thrown again, if you are certain something is wrong, you can stop the game. You can ask the dealers to recount or reconsider or, if you disagree with their decisions, ask to speak to the pit boss. This is an option of last resort when you are sure you are right. Casinos want to keep the table in play and will work to resolve disputes quickly but they’ll also ask troublesome or argumentative players to leave.

Stopping play is a mix of courtesy, privilege, and right. It’s not a gambling strategy, at least not a winning one.

4. The More Bets You Place the Worse Your Chances of Winning

This is true in any table game, but some craps players love to place multiple bets. You’re taking on more risk, not spreading the risk, when you place several bets at the same time.

5. Know the Die Roll Probabilities

In a completely random game the chances of any given number on either die being rolled is 1 in 6. The chance of rolling any combination of numbers on the dice is 1 in 36. This “1 in 36” number can mislead you. There are only 11 possible values (2 through 12) that you can roll.

“7” is the most frequent die roll combination. There are 6 ways to roll a “7”. Some writers say there are three ways to roll a “7”: 1 and 6, 2 and 5, or 3 and 4. However, the math has to account for each die separately; hence, the probability of rolling a “7” in craps is 1 in 6.

In declining order of probability, the possible combinations in craps are:

• 7 (1 in 6)
• 6 or 8 (5 in 36)
• 5 or 9 (4 in 36)
• 4 or 10 (3 in 36)
• 3 or 11 (2 in 36)
• 2 or 12 (1 in 36)

6. The “Pass” Bet is More Likely to Pay on Come Out than the “Don’t Pass” Bet

Both Pass and Don’t Pass pay even money so you can bet either way. Still, when you look at the probability table above, the shooter has 8 chances in 36 of rolling 7 or 11 on the Come Out roll and 3 chances in 36 of rolling a 2 or 3. If you are just hoping to win on the Come Out roll, go with the “Pass” bet.

7. The 6 and 8 Points Pay the Most over Time

The 6:5 odds for the 6 and 8 points are the worst and the 2:1 odds for the 4 and 10 points are the best. But the probabilities are best for the 6 and 8 and worst for the 4 and 10.

The premium on a 6:5 payoff for 6 or 8 is 20% over your bet. The premium on a 3:2 payoff for a 5 or 9 is 50% of your bet. The premium on a 2:1 payoff for a 4 or 10 is 100% of your bet. In a perfect distribution of 36 die rolls your expected total premiums are:

• 5 * 20% = 100% (betting on 6 or 8)
• 4 * 50% = 200% (betting on 5 or 9)
• 3 * 100% = 300% (betting on 4 or 10)

Although the 300% ROI for 4/10 looks great there is a slight edge for 6/8 bettors. Because you are losing all those other bets, you lose the least amount of money with the 6/8 points. Note also that multiplying (bets + premiums) by expected wins across the board results in a 600% return. The distribution with the fewest losses is the way to bet.

8. The More Complicated Your Strategy the More Risk You Take

The more you have to think about where your money goes, the odds and probabilities, and when you can bet, the more likely you will make a mistake. High risk strategies pay off less often than low risk strategies. Most experts agree that the long, slow game works best in craps, especially for non-expert players. Keep your money on the Pass Line until you’re way ahead.

9. Avoid Hedge Bets

Ignore dealer calls for “any craps” bets. Your expected return declines your risk grows when you hedge bets. “Any craps” betting is a bet on a bet. This just adds conditions to your Pass Line bet. The strategic way to gamble is to minimize risk while maximizing potential return on bet. The house will drain your bankroll any way it can and hedge bets are a favored gimmick.

10. Use the Tower of Hanoi Method to Manage Your Betting

The Tower of Hanoi is a math puzzle about moving stacks of disks among three pegs. You can never place a disk on a smaller disk. The Tower of Hanoi rule assumes you are willing to lose everything in your bankroll. To conserve your money and manage risk, begin by making minimum bets. Increase your bets only when your bankroll is above its starting value.

Many craps players only risk 5% of their stakes on any bet. The 5% method works well enough but you’ll eventually run into the table minimum. The Tower of Hanoi method starts with the minimum bet as a floor, not 5%. As long as your bankroll is growing you can increase your bets toward the table maximum.

Chances Of Winning Craps At Casino

11. Never Return to Your Starting Stake

Let’s say your betting strategies have paid off enough that you have doubled your money. Once you reach that goal you should set a new floor. Walk away from the table if your stake drops to 150% of your original bankroll. This way you walk away a winner.

But there is another reason to do this. If you play any game too long you become tired, especially if you have been drinking. Your decision-making suffers when you are tired. Take “winner’s breaks” as often as possible so that you can give your brain a chance to rest.

12. The House Edge is not Determined by the Odds

Chance Of Winning Craps

Some gamblers assume the house loses more money on the basis of the odds on a given bet. It doesn’t work that way. The game is designed to pay about the same over time on any basic bet but to dilute your return with extra bets. In other words, the house edge is determined by the math behind the game. The odds are just what they are willing to pay you to maintain that edge over time.

Conclusion

Craps is a fine game for any gambler who enjoys taking risks, but you do need to understand the game. Fortunately, craps is designed for players of all experience levels. You don’t have to play all the different types of bets. And isn’t it interesting that the best strategies favor beginner-level bets anyway?

Best Chance Of Winning Craps

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