September 15, 2003
A really crappy blog entry.
Posted by Matt and Jess in
Gaming
In addition to silly things Matt and I come up with to think about (how do they get soda bottles filled so close to the top without the foam overflowing? When exactly is the carbonation added? Ok, so that one was mine…(do you see what I have to put up with on long car rides? Keep reading, it only gets better), we think about math questions.
In fact, there’s nothing better than a terrible, horrible, KEEP YOU UP AT NIGHT brain buster of a question (if it keeps me up at night, I think I would rather it be something good then terrible. She makes it sound like heartburn). Well, this one is probably quite easy for some people. Though however difficult it comes, I love trying to work them out myself, or, what usually ends up happening, with Matt.
Matt and I live very, very close to two major casinos on the Northeast, Foxwoods (bleh) and Mogehan Sun (amazing).
We’ll be the loud ones screaming “IT’S TWO-WAY YO TIME, SHOOTA!” at the craps table.
I have this uncanny knack for always rolling the same number twice (always is a bit overboard. To say that means 100% of the time and though recent events would suggest that this is pretty close to 100%, I don’t want all you notes people camping out in my driveway to go on a get rich quick trip to the casino though we’d love to see you all!), before making a point value.
So I got to thinking, just HOW amazing of a feat, if at all, is that?
I started talking to Matt about it. We quickly discovered that we needed to clarify the actual question. For example, ‘what are the odds of rolling two numbers in a row’ and ‘if I roll a 7 on the come out roll, what are the odds that I’ll roll a 7 again?’ are two entirely different questions.
By the way, click 'continue reading' at the end for a quick lowdown on how Craps works, by Matt.
The first question doesn’t care what the first roll is, only that the second roll comes up with the same number as the first. The second question means that it has to include for odds that the 7 MUST come up on the first roll.
(on a side note, that first question could be misinterpreted… this is usually the root of my confusion when Jess asks me a question. I say there is a 100% chance of rolling 2 numbers in a row. However, rolling 2 numbers that are the same is an entirely different story. Granted, over time, I came to understand they way she thinks and just answer the “real” question) Matt’s a smarty-pants.
What I tend to do that’s unusual, is before establishing a point (4,5,6,8,9 or 10), I will always roll either two 12’s, two 7’s, or two 11’s, etc.
At this point I think I’ll “hand the dice” (craps joke, har har) over to Matt because this is where he wrote up a document for me that I didn’t understand. So let’s see if he can explain it a little bit better for me (and you of course).
Ok, to answer this question you first need to understand what the odds of rolling each number is.
NUMBER(s) | ODDS |
2 or 12 | 1:36 |
3 or 11 | 2:36 |
4 or 10 | 3:36 |
5 or 9 | 4:36 |
6 or 8 | 5:36 |
7 | 6:36 |
Simplified the 3 and 11 are a 1:18 chance, the 4 and 10 are a 1:12 chance, the 5 and 9 are a 1:9 chance, the 6 and 8 are a 1:7.2 chance and the 7 is a 1:6 chance. This table also shows that there are 36 possible outcomes of rolling the dice (keep in mind that all values on the left in the odds column are doubled EXCEPT for the 7… you do the math unless you want me to get funky with combinatorics. )
Now onto the real question asked by Jess. “What are the odds that I don’t roll a point on my come out roll and the second number I roll is the same as the first?” ( I still did not understand this question until she started writing up this blog. I still don’t understand the answer… let’s see if his continued rant will help!)
So the first question we need to ask is what are the odds of not rolling a point. Having already established the 4,5,6,8,9, and 10 as points, we can see that there are 24 ways of rolling a point. That leaves 12 ways to NOT roll a point. Jess has a 1:3 chance to not roll a point on the come out roll. Now it is time to get all mathematical on yer asses. The numbers in question are 2,3,7,11 and 12. The odds of rolling a 2 or 12 on the first roll are 1:36. The odds of rolling it again on the next roll is 1:1296 (or 1 in 36 squared chance). This is because the second roll is based on the first roll. The odds on the 3 and 11 are a 1:324 chance and the 7 has the best odds which is 1:36.
This squaring holds true only for numbers that have the same odds for coming up. It does not suggest that the odds of rolling a 7 followed by a 12 will be 1 in 1296… the odds for this are 1:216 which is the odds of rolling a 7 times the odds of rolling a 12. (ok, enter a bit of combinatorics. This is where I stopped understanding when he sent me the document. The number of possible outcomes on a single die is 6 (1,2,3,4,5, or 6). The number of possible outcomes on two dice is 36 or C(6,1)*C(6,1) where C is defined as 6 choose 1 and has a mathematical formula of 6!/(6-1)! or generically, C(x,y) where 0<=y<=x equals x!/(x-y)! and ! is defined as factorial.) *** LADIES AND GENTLEMEN… SHE UNDERSTOOD IT!!! *** Well, he still had to explain it out loud after writing it. (please see SAT = Stupid Annoying Test for more on <-( Say it fast it sounds like MORON) that.)
Well I hope my open parens have matched my closing ones, that always gets me when I write up code. Too bad I can’t compile my document before I sign off on it. I also hope that my math is correct. I in no way make a claim that I am, or ever will be, a master of combinatorics… that stuff is like a bad hangover (please see my trip to Japan for MORON my hangovers).
At least it’s not heartburn.
Quick Craps Primer:
To the person who has only “seen” craps, they, more often then not, think that it is the most confusing game at the casino. Between the dice rolling, the players shouting, and the chips flying across the table, it is no wonder why this is the assumption. Well this couldn’t be any further from the truth. Here is the low down.
There is a round puck on the table with the word “OFF” on one side and “ON” on the other. This is a marker. When it says “OFF”, the person with the dice, a.k.a. the shooter, has not yet rolled a point. This is known as the “come out” roll. When it says “ON”, it is placed on the “point” that the shooter rolled. A point is a 4,5,6,8,9, or 10.
Now there are 5 numbers missing and depending on what the puck shows, they behave differently. When the puck shows “OFF”, a 2,3, or 12, a.k.a. “craps”, are usually bad, and a 7 or 11 are usually good. When it shows “ON”, a 7 is usually bad. I say usually because you can bet with the house or the shooter. Most, if not all, players at the table are betting with the shooter and if they are not, I don’t play at the table. As a result, the rest of this “low-down” will be describing how to play with the shooter.
The first bet you should make on the table is called a “Pass Line” bet. This one is really easy to do. When your standing at the table, simply take an amount of chips totaling no less then the table minimum, and place it on the pass line in front of you. If you have never seen a craps table before, don’t worry, the pass line is clearly marked. If a 7 or 11 is rolled, all bets on the pass line pay 1:1 (ex: if you put $5 on the pass line, you win $5). However, if craps is rolled, all pass line bets are collected by the house and you must place a new bet on the pass line. Any other number rolled is a point.
Once a point is rolled, you can place an amount of money behind your pass line bet, also known as backing your bet. Depending on the odds the house gives on the specific numbers can determine how much you can back it with. For instance, at Foxwoods and Mohegan Sun, you can back the 4 and 10 with up to 3 times your pass line bet, the 5 and 9 with up to 4 times your pass line bet and the 6 and 8 with up to 5 times your pass line bet. What you are betting on is that the shooter will roll their point again before they roll a 7. If they do, pass line bets win and if the shooter should “seven out”, the house collects all bets on the pass line.
Well, that is a brief introduction into craps and there are plenty more bets that can be made on the table. From one time bets like craps and yo, to place bets and hard ways, the table always offers plenty of excitement. Just remember, go with money you can lose and not money to gamble to make enough for the mortgage.
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No kidding! Why do you think I didn't understand it to begin with? :-)
Though it was fun, we were both ripping the keyboard away from each other to 'interject' into the blog. So that entire post wasn't scripted or anything, heh.
