Craps & probability

This is a follow up to my post from the other day on craps. Before we get into actual betting, I want to talk about probability. In craps, you are rolling two dice, each with six sides. This means that there are 6^2 (36) possible combinations of the dice: 1 and 1, 1 and 2, 1 and 3, and so on and so forth.

The reason this matters is that this makes each roll of the dice a random event: each combination is as likely to occur as any other. This is an important concept. If I flip a coin 100 times, there is no way to predict the next result of a coin toss because each event is random. ‘Heads’ is just as likely to come up as ‘tails.’ The coin doesn’t care if the last ten flips were all heads, the next toss still has the same odds of coming up heads: 50%. If you keep track of the result each time that coin is flipped, the more you flip it, the closer you will be to a 50/50 split.

What causes the “streaks” and “runs” of a random system is due to something called ‘distribution variance’ and is the reason why you see people say that a number is “due” for one reason or another. This is because people tend to see patterns even when there aren’t any. It is a random system, and each result is as likely as the other.

The same is true with dice. If I toss them enough times, you will see a pattern emerge. Out of each 36 attempts (on average), two will come up once (a one and a one). So will twelve (a six and a six). Seven will make an appearance six times (1&6, 2&5, 3&4, 4&3, 5&2, 6&1) and is the most likely number to come up. If I make a chart, it will look like this:

  • 2: 1/1
  • 3: 1/2 2/1
  • 4: 1/3 2/2 3/1
  • 5: 1/4 2/3 3/2 4/1
  • 6: 1/5 2/4 3/3 4/2 5/1
  • 7: 1/6 2/5 3/4 4/3 5/2 6/1
  • 8: 2/6 3/5 4/4 5/3 6/2
  • 9: 3/6 4/5 5/4 6/3
  • 10: 4/6 5/5 6/4
  • 11: 5/6 6/5
  • 12: 6/6

This makes the math pretty easy. Let’s go back to the first roll of the dice:

If the shooter rolls a 7 or an 11, they win. There are 8 chances of each 36 rolls on average that will result in a win on the come out roll.

If the shooter rolls a 2, 3, or 12, they lose. There are 4 chances out of each 36 rolls that the shooter will lose.

Any other number becomes the point. That means that 24 of each 36 rolls will result in setting the point.

Now seeing that, you would assume that betting on the shooter would result in you winning twice as often as you lose, and you would be right, if the come out roll was viewed in isolation. The catch here is that if the point is set, the bet must remain in play until the shooter either rolls that number again (and wins) or rolls a seven (and loses). Since seven is more likely than any other number, it is more likely that you will lose your money than it is that you will win. Still, with all of that, betting on the come out roll (called a pass line bet) is the best bet in the casino.

Why is that? Because the come out has the smallest house advantage of any other bet you can make in the entire casino- that includes slots, Blackjack, Roulette, any other bet in any other game. For example: In Nevada, slot machines over the long term pay out 80 cents of every dollar that is wagered. The house keeps 20 cents of every dollar- 20%. This is called the house edge.

In roulette, the house edge is the 0 and 00 spaces on the wheel. This means that the house edge (if you bet black/red or odd/even) is 5.26%. The house keeps 5.26 cents of each dollar wagered.

In Craps, the house edge for a pass line bet is 1.41 percent. That is, out of each dollar, the casino only keeps 1.41 cents.

Still, if the house ALWAYS has an edge, why gamble? Because you CAN win in the short term, thanks to distribution variance. If you find yourself in one of those “hot streaks” you can make a good bit of money. If you are in a cold streak, you can lose a LOT of money.

Let’s go back to our example of flipping a coin. Let’s say I flip a coin 10 times. Even though the odds are 50/50 for heads or tails, it is likely in such a small number of flips that you will see a streak like this: 7 heads, 3 tails. If you are betting heads, you make a lot. If you had bet on the tails, you could lose a lot. This is what makes gambling fun, if you don’t go buck wild. In future posts, I will explain betting and how to do well playing this game.

Uniform aggravation

When I began my new job, I was told that I needed to wear scrubs. I could wear any color except black, denim, camouflage, or pediatric prints. So I got blue and dark red. Five sets, at $40 each set.

Two months later, and the announcement was made that they are changing the color schemes. We are going to be color coded by our job. I will be required to wear teal. The change goes into effect October 1.

So now I have $200 in scrubs that will not be wearable, another set of unreimbursed scrubs to buy, and employee expenses are no longer tax deductible.

The press is the enemy

In comments to this article:

My comment, which I don’t think violated the TOS, was moderated and will not appear on the site. No bias here, nope.

EDITED TO ADD: I showed this to my wife, and her reply was “It’s their website, they can do what they want.”

I don’t want anyone to think that I support making their bias illegal. I am, however calling them out for being lying hypocrites for making the claim that the press is an unbiased purveyor of the truth. I am also calling social media for blocking so-called “false news” when their version is no closer to the truth than any other.

Inflation

Peter over at Bayou Renaissance Man says that readers claim inflation isn’t here. Let me show you how it sneaks up on you. A Denny’s commercial from 1997:

Note that one of those breakfasts was this one:

2 strips of bacon, two link sausages, two eggs, and two pancakes. This is the breakfast that Denny’s calls the “Original Grand Slam.” For $1.99.

How much is this breakfast now? $9.29, or 467% more than it was 24 years ago. That works out to an annual inflation rate of 6.7%. The published rates for that period were anything from negative 0.2 all the way to 3.0. The official inflation rates say that this breakfast should only cost $3.28 today.

When I was in high school nearly 40 years ago, I remember being able to go to McDonald’s and eat my fill for less than $4. A Big Mac was only $1.09. Krystal Hamburgers were 25 cents. Compare them to today’s prices.

It isn’t just food. In 1999, you could purchase gasoline for less than $1 a gallon. The hit is even larger than that- because in 2005, Congress mandated that all gasoline be diluted with alcohol.

But wages haven’t kept pace. In 2000, the starting pay for a Paramedic right out of school was $14 an hour. Today, that same new paramedic would start at – $13 an hour.

Prices have been increasing at a rate of 6 to 7 percent per year, while wages have remained static.

Black gun stores are racist

Amid all of this talk about how white supremacy is the largest threat to America, we see this article. To date, we hear about how the gun culture is filled with whites who hate the fact that black people want guns. This article shows something different.

Blacks are arming themselves because they don’t like whites, if this story is to be believed. The black gun store owner showcased in the story had this to say:

“It was a terrifying, horrible experience, not just because I was buying the gun; it was because of how I was treated,” Solomon told NBC News. “I looked around the room and there was nothing but white men behind the counter. There wasn’t even a woman there.”

She claims to have been treated badly, but the only thing she can point to is that there were no women or blacks working there. The story then doubles down:

After watching report after report of police killings of Black people and her experience living in a predominantly pro-Trump neighborhood, she decided to buy a gun.

Still a third black woman had a gun buying experience:

The class of 20 new gun owners was predominantly Black — exactly what fellow student Erin Wood was looking for. “It’s just nice to have people that look like you in the group. It just makes you feel a little more comfortable to have the instructors be from your community,” Wood said, emphasizing that she sought out Redstone Firearms specifically because it is Black-owned.

Had this story been reversed, and a white gun store owner or gun buyer would have said they want to buy guns and take classes from people who look like them, Biden’s DHS would be dropping a JDAM on the store by now.

This gun case was a waste of time

This gun case was a win for the gun owner, but a waste of time. A teacher in Florida was told that he could not have a gun in his car because the school district forbade it through a rule that had been adopted by the school board. Someone had anonymously informed the school on several occasions that he had a gun on campus, the school had searched him and his vehicle several times without finding a gun.

State law generally prevents people from carrying guns on school grounds. But the law has exceptions, including allowing people to have guns in cars if the firearms are secured. However, school districts can approve policies that prevent guns in campus parking lots, as long as that policy is in accordance with state law. The teacher argued that the rule as adopted by the board was not in compliance with the law, and filed a lawsuit. He specifically said that the rule, which stated that:

“No person except law enforcement and security officers may have in his/her possession any weapon, illegal substance, or dangerous substance.”

Was vague and did not specifically prohibit firearms.

The trial court agreed that the rule was not in compliance with the law, but also ruled that the teacher was not entitled to damages or relief because he had not suffered any damages, since he hadn’t been fired, suspended, or otherwise disciplined.

The state’s Fifth District Court of Appeals ruled that the “courts generally have not required individuals to subject themselves to penalties to establish an adverse effect” in order to be able to challenge a law. The court went on to say that “[the teacher] was an employee of the high school and subject to the challenged policy. Furthermore, [the teacher] actively sought to keep a firearm in his vehicle. However, [the teacher] refrained from doing so because his employer informed him that the policy was enforced and a violation of the policy would subject him to discipline, up to and including termination. Under these facts, [that teacher] was affected by [the rule against firearms in a vehicle], and adversely so.

So now the school board has been told that the rule in place that prohibits, expect them to rewrite it to specifically include firearms. I don’t really understand what this win accomplished. It seems like it was a complete waste of everyone’s time and resources. It’s almost like the lawsuit was filed by an SJW who wanted to make sure the rule against guns was improved.