- Craps Small Tall All Odds
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- All Tall Craps Bet
- Casino Craps Bets And Payouts
Can someone please explain me the calculation formula for 'Small', Tall' and 'All' win probability calculations?
Small bet wins if the shooter rolls a 2, 3, 4, 5, and 6 before rolling a seven - The probability as presented in the site are 0.026354
Tall bet wins if the shooter rolls an 8, 9, 10, 11, and 12 before rolling a seven - The probability as presented in the site are 0.026354
All bet wins if the shooter rolls a 2, 3, 4, 5, 6, 8, 9, 10, 11, and 12 before rolling a seven - The probability as presented in the site are 0.005258
Although the site presents the probability ,I'm interesting in the detailed calculation.
Thanks,
Dryfus
Hi,
Although the site presents the probability ,I'm interesting in the detailed calculation.
try here
Feature or bonus bets such as the Fire Bet offer a 1,000 to 1 payout, and the Small and Tall bets offer 35 to 1, while the All offers 175 to 1. These feature or bonus bets give craps players the chance of hitting a jackpot the way a slot player might hit triple-7s or a video poker player might hit quad aces or a royal flush. The Small, Tall, and All Bets: Fairly new to the craps table, but they're quickly making their way onto the layouts in casinos across the country. And with good reason. And with good reason. The 'Free Odds' Bet in Craps: We explain the Free Odds bet in detail in our other articles about the Pass Line and Don't Pass bets.
http://wizardofvegas.com/forum/gambling/craps/17175-new-all-high-all-low-casino-craps-prop-bet/2/#post332587
There are many methods that work.
Some more challenging than others depending on your math skill level
I did not yet add the all small/all tall matrix/recursion solution (I have them completed)
There are 1022 possible states the ALL can be in plus 3 more for 0, fail and success
we just fill in the transition probabilities and sum the products (a little more involved actually)
only 30 states for small/tall plus 3 more for 0, fail and success
we could hit just 1# 10C1 = 10 so there are 10#s that can be the first #
now, having the 1st we want a second and there are
10C2 = 45 possible combinations (where order does not matter)
like so and we can calculate the probabilities of moving from each of the first 10 states to these 45 states
and so on. lots of math
10C3 = 120 possible 3# combos
10C4 = 210
10C5 = 252
10C6 = 210
10C7 = 120
10C8 = 45
10C9 = 10
Hey looks like Pascal's Triangle
Maybe if get some time, it is Friday,
I can clean up my Excel workbooks and link to them online
Once you see how it it done, it is quite easy IMO, just a bunch bunch of calculations that a computer can do lickety–split
Sally
I also forgot to mention we can just list all the permutations of the winning sequences (small/tall for example)
5! = 120 of them
then calculate the probabilities for each and add them up
another snap shot in Excel for small/tall
examples
23456 = 120/1,247,400
23465 =120/1,134,000
the denominator is what changes for each different sequence
because from the starting 21 ways the bet could be resolved (win or loss)
it gets smaller with each number hit
do you see why?
Okay...
the All requires 10! calculations (3,628,800) using this method (oh, actually not as 2,3,4,5,6,8,9,10,11,12 and 12,3,4,5,6,8,9,10,11,2 have the same probabilities. I have to look closer into this too) and I just did (fri afternoon)
3,628,800 /2^5 = 113,400 unique permutations (32 ways for each) and I have a unique permutation generator for the free program R
sure Excel could do this too
this method should be avoided unless you just let a computer do it for you, as I did.
can not even imagine doing this by hand
here is the snapshot and the probability is the same as all the other methods that have been used
calculus, inclusion-exclusion (R and Excel), Matrix Algebra, recursion and summing permutation probabilities
WOW!
the sequences used 0 for 2 and 12
1 for 3 and 11 and so on
I guess I can explain every method if you have a request for a favorite one, except the calculus one
I just can't do everything
but watch out for what I do accomplish
Sally
Wow! never imagine to get such good explanation, thanks!
BTW, I've ran simulation in R and got nice approximations for these probabilities:
Code:
Here are the simulation results of 100,000 Iterations:
Small bet Win | Tall bet Win | All bet Win | |
---|---|---|---|
Frequency | 2,615 | 2,606 | 503 |
Probability | 0.02615 | 0.02606 | 0.00503 |
![How to win at craps every time How to win at craps every time](https://media.architecturaldigest.com/photos/593efea59f4b48583154a6a8/master/pass/chloe-warner-kitchen-02.jpg)
Dryfus
Again, thank you very much for your answer,
Dryfus
and thank you
it was fun and I got a chance to finish my bonus craps projects too :)
I got this running your sim one time (about 50 seconds time)
The fastest way IMO to solve these type of questions (if you do or do not understand the math behind the bet)
is to use the code I linked to
in R for any subset
it is done before you know it
Sally
P({2,3} before {7}) = P({2} before {3,7}) * P({3} before {7}) + P({3} before {2,7}) * P{{2} before {7})
When the set you want has just one number, the probability of rolling it before the set of other numbers is the number of ways to make the one number divided by the number of ways to make that number plus the others. So, for example, P({2} before {3,7}) = 1 / (2 + 6) = 1 /8.
The exact probabilities produced by the program are P(small) = P(tall) = 20049/760760 and P(all) = 126538525259/24067258815600
Administrator
4 thoughts on ' Small, Tall, Nothing at All: New-To-Us Craps Side Bets ' Chigu September 4, 2018 at 9:04 am. I wish they had the small/all/tall bet in my casino. On back to back throws I had a roll of 19 and then 29. I hit all small with the 19 rolls, and hit the ALL with the 29 rolls. Would have been an even better night!! 'Pass Line' Bets. The most basic craps bet is the Pass Line bet. When you place a Pass Line bet, you're betting with the dice. In other words, you're betting that the either a 7 or an 11 will be the first number rolled (called the 'come out' roll). If this happens, you double your money right away. Craps (version 2) - Part 3 of 5: Video for the new Craps tutorials, Sucker Bets. AUG 7 Vegas 2066: Fiction about a reclusive individual fifty years in the future and how the game of craps opens him up to the possibilities in the, 'Real world' JUL 29 Craps (version 2) - Part 2 of 5: Part 2 Video for the new Craps tutorials; View All. Here to ask advice about the maths behind the make 'em all craps side bet. For those who don't know, the bet is a wager that a shooter will roll every number 2-6 and 8-12 before rolling a 7. I have seen the wizard's answers to the house edge on his site and it lines up with the brute force calculations I have seen simulated previously. Beginner craps players, if you can remember only one bet, make it the pass line bet. This is the starting bet for all craps games and has one of the lowest house edges at 1.41% and highest odds of landing (251 to 244 to be exact). This is one of the best bets craps players can make, with payout odds of 1 to 1.
With its origins going back over 500 years, craps is a popular dice game in North America. Based on a game called hazard that is referenced in books dating back to the 14th century, craps was brought to New Orleans in the early 1800s. The game found a foothold with fieldhands and deckhands of the time, allowing its popularity to spread up the Mississippi River.
The word 'craps' is actually a mispronunciation of the word 'crabs', which were the numbers 2 and 3 in the game hazard (which were the numbers that were automatic losers).
The Basics of Craps
At its core, craps is a dice shooting game. The goal is to match or avoid certain numbers. Boiled down to the essentials, the rules of the game are:
- In the first roll of the dice, if you shoot a 7 or 11, you automatically win.
- In the first roll of the dice, if you shoot a 2, 3 or 12, you automatically lose.
- If you roll a 4, 5, 6, 8, 9, or 10, you roll again, this number becomes the 'point'.
- You will then keep rolling and each time the point is hit, you win. The game continues until the player retires or a 7 is rolled ending the game
The hard part of the game is understanding the table and the betting. But if you understand the essentials, the betting becomes easier to understand.
The 5 Smartest Craps Bets
The Pass Line
The most common and popular bet at the craps table is the pass line bet. This bet the bet that backs the shooter. A bet of this type means that you are betting on the shooter to roll a 7 or 11. If he does so, you win instantly.
If he rolls a 2, 3, or 12, you automatically lose.
If he rolls anything else, he must roll again and this number becomes the point. Each time he rolls the point, you win. If he rolls a 7, you lose.
Most of the bets on a craps table will be pass line bets. There are a few reasons for this. First, it is an easy bet to understand. Second, there are chances for multiple wins without having to bet over and over again. Third, it is an even bet. And fourth, the house edge is only 1.41% which is not only one of the lowest on the table, it is one of the lowest in the whole casino.
The Don't Pass Line
Another smart bet in craps is the don't pass line. In this bet, you are betting against the shooter. In this scenario, you are betting that the shooter rolls a 2, 3, or 12 for an automatic win. If he rolls a 7 or 11, you lose.
Much like the pass line, if he rolls a 4, 5, 6, 8, 9 or 10, he rolls again to try and hit point. If he hits point, you lose, if he rolls a 7, you win.
The house edge on this bet differs slightly from the pass line and is 1.36%.
There is a pitfall to this bet. Because craps is a communal game, you are betting with other people on the results of the roll. This can cause issues with people around you if you are continually betting don't pass line and they are betting pass line and you win. It might be a bit intimidating and can even cause friction with other bettors. So if you do choose this bet and are doing so regularly, you might want to limit your celebrations as it may draw the ire of your fellow gamblers.
Odds Bets
If you bet the pass line, don't pass line, a come bet or a don't come bet (which I will cover later) you can place an odds bet. Because of the way the bet is placed, it makes it a pretty integral part of the game.
A good way to think of an odds bet is like raising in a card game. An odds bet is simply adding a wager to the bet you made when the shooter started (assuming he didn't crap out with a 2, 3, or 12.
Each casino has different rules about odds bets. Some will only let you match the original bet. Some will let you bet several times more than the original, so you'll need to know the casino's rules before entering into this type of bet.
On an odds bet, you'll win the even-money payout on the original bet. For example, Lets's say the point is 10. If you bet $100 on the pass line, you'll win $100 each time he hits point before he rolls a 7. In this case, you win 2 to 1 odds on the odds bet. Therefore if you added $200 to the bet, you'll win another $400.
An odds bet is one of the only neutral house advantage bets in the casino with a house edge of exactly 0%.
The odds vary based on the point and whether you are betting pass line or don't pass line. The odds for pass line bets are:
- Point of 4 or 10 – 2 to 1 odds
- Point of 5 or 9 – 3 to 2 odds
- Point of 6 or 8 – 6 to 5 odds
For don't pass lines, they are the opposite:
- Point of 4 or 10 – 1 to 2 odds
- Point of 5 or 9 – 2 to 3 odds
- Point of 6 or 8 – 5 to 6 odds
One of the wonderful things about odds bets is that you can decide on each roll whether you want to continue. So you can do it for one roll, skip a roll and start again while the same shooter is playing the same point.
Odds bets are a real money maker for players when played correctly especially considering that there is zero house edge.
Betting on 6 or 8
While 7 is theoretically the most common roll in craps, the second most common roll is a 6 or an 8. And the great thing about craps is you can bet on the shooter rolling it.
With a house edge of only 1.5% and the odds of rolling a 6 or 8 being 13.89% (second only to the probability of a 7 which is 16.67%), you can make a decent amount of money betting the 6 or 8
After the shooter makes the point, you can simply tell the dealer how much you want to bet on either 6 or 8 or both. (If you bet on both, you've just doubled the probability of winning.)
A bet on a 6 and/or 8 pays 7 to 6.
You can bet on other point numbers but the probability of landing on these are lower and the house edge increases. On 4 0r 10, the probability is only 8.33% and the house edge is 6.7%. On a 5 or 9, the probability is 11.11% and the house edge is 4%, so the 6 and/or 8 is the best bet.
Come Bet
The come bet is playing an on-demand pass line bet, the same way a place bet work. At any point after the come out roll, you can place a come bet which essentially creates your own personal pass line bet.
In a come bet, after the shooter has rolled the come out roll and established a point number – any point number – you can then place a come bet. Then, on the next roll, you're playing out your own pass line bet separate from everyone else at the table.
So, if the next roll is a 7 or 11, you win even money on your come bet. But, if the next roll is a 2, 3, or 12, your bet is lost to the house. And any other number (4, 5, 6, 8, 9, or 10) will establish the new point number going forward, but one that only you care about.
With this bet, you are really playing 2 games at once. Which can make it a bit harder to keep track of, but the house edge is the same as a pass line bet at 1.41%
The 5 Dumbest Craps Bets
To me, dumb bets are long shots where the odds are not in your favor. Is it possible to win? Yes. Is it likely that you'll win? Not very. Craps have a few bets that are long shots just like they have bets that are really good to make.
Betting on 4 or 10
One of the worst bets to make is on the 4 or 10 (especially individually). I discussed earlier that the odds of rolling a 4 or 10 are the least like point rolls in the game with a probability of 8.33% on either. But placing a bet on these also have a house edge of 6.7% making it one of the tougher bets, not only in craps but of most bets you can place in table games in the casino. A win on this bet does pay 9 to 5, but you can make better bets that will yield you a better return with less risk.
Betting on 5 or 9
Another dumb bet in craps would be betting on the 5 or 9. The probability of a roll of a 5 or 9 is 11.11%, which is higher than the 4 or 10, but not enough to make it a good bet. Also, the house edge is 4%, which is still more than twice that of a 6 or 8 bet. The payout on this bet is 7 to 5.
Field Bet
A field bet is when you place a bet on the shooter rolling a 2, 3, 4, 9, 10, 11, or 12.
I like to think of this bet similar to endcaps at a grocery or department store. The items they display on the endcap may be on sale, but if you look in the right section, there are much better deals elsewhere. Much like an endcap, this bet looks attractive because it has a wide field of possible results, but they have some of the lowest probabilities of actually being rolled. In the chart below, you can see the probability of each total:
- 2 – 2.78%
- 3 – 5.56%
- 4 – 8.33%
- 5 – 11.11%
- 6 – 13.89%
- 7 – 16.67%
- 8 – 13.89%
- 9 – 11.11%
- 10 – 8.33%
- 11 – 5.56%
- 12 – 2.78%
The house edge on this bet is 2.78%. The payout on this bet is 3 to 1 on a roll of 12, 2 to 1 on a roll of 2 and even money on all others.
Betting on 2 or 12
We can see from the chart that a 2 or 12 (also known as 'snake eyes' or a 'boxcar', respectively has only a 2.78% probability. So this is a sucker bet. It will pay 30 to 1 if you win. The house edge on this is 13.89%. Just remember, the higher the payout, the lower the chances of it happening.
Betting on 3 or 11
While the odds of hitting these numbers versus a 2 or 12 is double, it is still highly unlikely and that makes if also a dumb bet. This bet has a house edge of 11.11% and pays out 15 to 1.
Conclusion
For the new or casual gambler, safe is always the way to go. Betting online bets are going to be the best chance of winning.
The great part about this game is that you don't have to shoot, you can bet on the abilities of others, so if you find someone that is 'hot', you can keep betting on him and keep winning.
But if you do shoot, remember the pitfalls of the 7 on the point. And don't be afraid to invest in yourself by betting odds or come bets.
I recommend that you try to learn a bit before going to the casino by checking out some videos on YouTube or another video site. This way you'll be prepped when you get there and you can focus on having fun and winning.
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Also, the reason I stopped trying to make a sheet like that, is I thought maybe I could find a formula to solve the whole thing?
someone did, but it is not like a+b-c = pit uses the inclusion/exclusion principle.
BruceZ(?) did this some time ago
and wrote some R code for it.
Anyway, if i can do that,
can I not do a formula for odds of a 5 and a 9 before a seven?
I don't honestly even know if its possible just seems like to me that it should be!
https://forumserver.twoplustwo.com/25/probability/craps-probability-1208676/
here is the code I have
returns this
> p # prob of not rolling a subset of numbers before a single number
[1] 0.7714286
> 1-p # prob of rolling a subset of numbers before a single number
[1] 0.2285714
> a=1/(1-p) # 1 in
> a
[1] 4.375
> a-1
[1] 3.375
> Odds.to.1 = 1/(1-p) - 1
> Odds.to.1
[1] 3.375
>
Sally
Craps Small Tall All Odds
I did this in Excel using a transition matrix.this is way faster and easier once you know what is up
and one can run this R code online it you do not want R on your machine
Craps Make Em All Bets
http://aleph.sagemath.org/(select R 1st)
[1] 0.7714286
[1] 0.2285714
[1] 4.375
Printable Craps Payout Chart
[1] 3.375
Printable Instructions On How To Play Craps
[1] 3.375Craps Make Em All Betting
here is for Allhope this can help out
All Tall Craps Bet
Hi BruceZ!
I have yet to win that All bet!