A continuation of my Craps posts. As I have been saying: There is no way to beat math. There are some who will tell you that you can “call your shots” by throwing the dice a certain way. That is balderdash that the casinos actually encourage people to believe, because it makes the gullible actually gamble more.

Why isn’t it possible? The rules of the game include a proviso that the shooter must throw the dice far enough that they hit the back wall of the table. The wall is covered in a rubber bumper that has little pyramid shaped bumps on it. Those bumps are designed to deflect the dice in unpredictable directions. If you are good enough to nail those in the same exact spot every time, you need to be playing professional golf or basketball, you will make more money than at the casino.

No, the winning strategy doesn’t involve the way you play the game. It involves the way that you bet.

I enter the casino with a daily budget. Let’s say that I am spending a weekend at a casino. I have budgeted $500 to gamble with. Since I will be there for 2 evenings, I will lose no more than $250 a day. I walk into the casino with $250 each evening, and once that is gone, I am done for the evening.

So let’s say that I enter the casino and due to random variation, I enter the casino on Friday evening with $250. I leave the casino with $375. When I enter the casino on Saturday, I do it with $250. Win or lose, yesterday’s play is yesterday. By doing this, I limit my losses while making my wins unlimited. This works pretty well. There are days that I have lost the $250 in less than an hour, and that stings. There are also days that I have walked in with $250 and then left the casino with more than $4,000.

First, don’t take the sucker bets with YOUR money. Use the casino’s money. I only take sucker bets (low chance of winning, high payout, high house edge) when I am far ahead. What this means is that you don’t make the risky bets until you have doubled the money that you started with. If you walked into the casino with $250 for the day, don’t make risky bets until you have more than $500.

Second, the best bets on the table are the pass line bet, place bets on the 6 or 8, and taking odds on your pass line bet. (I don’t like to play the “dark side” bets like “Don’t Pass.” Yes, they are bets with a low house edge, I just can’t have fun winning while the table is losing.) Personally, a sound bet to me is any bet with a house edge of 2% or less. Here are the tables for calculating house edge on multi roll bets. Stay away from single roll bets until you are gambling with their money.

Third, if the table is cold- walk away and come back later. Tables tend to run cold and hot. I know that mathematically, this shouldn’t be true- but it seems to work that way.

Lastly, make sure that you frequent one chain of casinos and make sure that you are in their player’s club. The free comps you get may well be the best part about gambling and the only way to come out ahead. Free rooms, free drinks, free food, and more. I always stick with MGM casinos and have spent my way into Platinum status there. I get free hotel rooms, sometimes free airfare, and other perks. A four night stay in a room at the NYNY Hotel in Las Vegas normally costs $500, so getting a free, four night stay is a win.

My next trip out to Vegas is already booked. They are giving me a four night stay for free (we are paying for a 5th), plus $100 resort credit for meals, plus $200 in casino credit to gamble with. (I am not specifically endorsing MGM resorts- any of the big name casinos would work just as well.) My budget for gambling for the 5 days is $1,500, but I am getting $800 in perks.

Just remember, win or lose, I play because it is FUN. Also remember my rules for gambling:

  • 1 I know that I will lose money over the long term. It is mathematically certain. So budget your gambling and stick to it.
  • 2 I gamble because it is fun and entertaining. If I ever find myself gambling while desperate to win because I need the money, it is time to quit.
  • 3 Don’t ever gamble with money you can’t afford to lose. If you are gambling your rent or grocery money, that isn’t entertainment, it’s desperation.

Bad bets

This is a follow up to my series on Craps. The last post was on good bets, and this one will be about bad bets. The worst bets on the table are what I refer to as sucker bets. A few of them here:

The one set of bets that are horrible are all of the “one roll” bets. Bets where you bet on the outcome of a single roll are all found in the center of the table. They all have a house edge of between 11.1 and 16.9.

These bets include “any craps” which is a bet that the next roll of the dice will be a 2, 3, or 12. If the dice come up as a 2, 3, or 12, the payout is 7 to 1. The house advantage is 11.1. Similar is betting on either the 3 or the 11. Either bet pays 15 to 1, and the house advantage is still 11.1. You can bet the “Big 7” which pays 4 to 1, but has a house advantage of 16.9.

So how exactly do we make money on Craps, if all bets are losers? There are many theories and tactics. Some people recommend things like trying to control the dice and can make them land on a certain number. That won’t work. The game can’t be rigged, it can’t be cheated, and it can’t be beat in the long term.

It CAN be beat in the short term by being a smart player. That is where we find the fun. More on that later.

Craps: Good bets

This post is a continuation on my discussion of Craps and gambling. My last post on this topic was about probability. Now we will talk about good bets.

The best bet in a casino is called “pure odds.” This is a largely theoretical bet where the probability of that event occurring is the same as the payout. (For a discussion of probability, see my last post on this.) For example, let’s say that you are betting that a ‘6’ will be rolled on the dice. Out of 36, there are 5 ways to roll a six (and win) while there are 6 ways to roll a ‘7’ (and lose), so your probability of winning would be 5 to 6. In a “true odds” bet, a five dollar bet on the six would pay you 6 dollars if you won. However, casinos want to make money, so the payout is structured in such a way that the casino makes more money. In the case of our example of betting on the six, a six dollar bet would win you seven dollars. This ‘house edge’ is the casino’s cut, called the ‘vigorish’ or ‘vig’.

So obviously, a good bet is one that has the smallest house edge. There are some bets that have a small edge, and others with a large one. Let’s start with the good bets, the ones that are the closest to true odds.

The Pass Line Bet

The most basic bet you can make in Craps is the pass line bet. You are betting that the person shooting the dice will win. (Refer to the basic rules of the game here) A pass line bet is placed before the shooter rolls the dice for the first time (this is called ‘coming out’). If the shooter rolls a 7 or an 11, he wins. If he wins, all Pass line bets win as well, and they pay at even money. (A $10 bet pays $10) If the come out roll is a 2, 3, or 12, the shooter loses, and so do all pass line bets. Any other roll ‘sets the point’ meaning that this is the number that the shooter must roll again before he rolls another seven in order to win. Once you place a pass line bet, it must remain in place until the shooter either wins or loses. You place a pass bet by putting your chip down on the pass line, just like the $10 (red) chip in this picture.

For example: You place a $10 bet on the pass line. The shooter rolls a seven. You win $10. Congratulations, pick up your $10 in winnings. The shooter rolls again. Since no point was set, it is again a ‘come out roll.’ He rolls a 12. You lose. Easy come, easy go. Replace the $10. The shooter again comes out, and this time he rolls a 9. The 9 is now ‘the point’ and the shooter must roll another 9 to win. If he rolls a 7, he loses and passes the dice to the next shooter. (This is called “sevening out”) The house edge for a pass line bet is 1.41.


“Taking odds” is mathematically the best bet in the casino, and is a part of the pass line bet. However, it can be a good bet, or a bad one. Taking odds is a way of increasing your pass line bet, but at true odds. You can take odds by betting more money after the point is set. If a 7 is rolled, you lose your pass line bet AND your odds bet. If the point gets made, you win the pass line bet AND the odds bet pays at true odds.

Let me explain. You place this bet by putting more money behind the pass line. If the point is a 9 (as in our example above) and the 9 hits, the odds bet pays out at true odds. True odds can be found below. To place an odds bet, after the point is set, you put more chips behind the pass line bet (where the blue chips are in the picture above). Odds bets can be placed or taken down at any time, as long as the dice are not actually in play. (The dealer will say “Dice are out- no more bets, watch your hands.” whenever the dice are in play)

Place bet

A place bet is where the gambler bets on a particular number being rolled. The bet pays each time the number is rolled. (see the “True odds” section below) If a seven is rolled, the bet is lost. You place a place bet by putting your chips on the playing surface between you and the closest dealer (while the dice are not in play) and tell him “$xx on the number 6”. The house edge on a place bet varies with the number you are betting on. For a 6 or 8, the house edge is 1.52. For a 5 or 9, the edge is 4.0. If you are betting on a 4 or 10, then the house edge is 6.7.

True odds:

  • If the point is a 6 or 8, true odds is 6 to 5. Place bet pays 7 to 6.
  • If the point is a 9 or 5, true odds is 3 to 2. Place bet pays 7 to 5.
  • If the point is a 4 or 10, true odds is 2 to 1. Place bet pays 9 to 5.

The good bets.

So the long and the short of this is:

The best bet on the table is the pass line bet. With a house edge of 1.41, this is the best bet to make. However, if this is the only bet you make, you are going to get bored.

The next best bet to make is a place bet on the 6 or the 8. The house edge on this bet is 1.52. When I play, I will put a $30 bet on the six or the eight, then every time that number is rolled, I collect $35. Of course, once a 7 is rolled, I lose the $30. The hope is that a 6 or 8 will get rolled at least once before a 7 makes an appearance, and I make money.

Later, we will talk about the mediocre bets, dark side bets, then some betting strategy.

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.

Aw, Craps

If you have read this blog for any time at all, you know that one of my vices is that I like to gamble. It all began when I had to take statistics in college, where my professor used casino games to teach us statistics. For that reason, I learned several casino games, and the one that really stuck was Craps.

It is a straightforward game of math, and once the rules are understood, fairly easy to play. The math can be done in your head pretty quickly. I get tired of always talking about the decay of our society, so I thought that I could do a few posts that were more fun (for me) to write to break things up a bit.

The rules for Craps are easy, but since it is a fast moving game and there are lots of bets that can be made, people who watch the game get easily confused and are often scared away from the game. Let me tell you though, that a busy table with a hot shooter is pretty exciting and makes for a fun game.

The rules are simple: The shooter picks up two sixed sided dice and rolls them to the other end of the table. (Most casinos have the rule that the dice must hit the wall at the opposite side of the table.) The first time the shooter rolls is called the “come out roll.” If the dice show a 7 or 11, the shooter wins. If the dice show a 2, 3, or 12, the shooter loses. Any other number becomes the “point” and the shooter continues to roll until they either roll a 7 (which causes the shooter to lose) or again rolls the point (for which the shooter wins). As long as the shooter continues to win, they continue to roll the dice. If the shooter loses on the come out roll, they can try again, but if they lose by rolling a 7 after the point is set, the dealer passes the dice to the player on the losing shooter’s left, and that person becomes the new shooter. That’s it for the rules of the game.

Everything else that happens on the table is betting that the shooter will win or lose, or is a bet on what numbers will appear on upcoming rolls of the dice.

Upcoming posts will deal with the math of the game and what the odds are for different outcomes.

Let me close out this post by pointing out something which many people will try to lie about: The only winner in casino gambling is the owner of the casino. The math is set up so that the longer you play, the more likely you are to lose. It’s math- there is no way around it.

Even games like blackjack, where people try to convince you that they “count cards” and have a system to always win, are set up so the casino comes out ahead. If it weren’t, everyone who plays in the casino would soon adopt this system and the casino would go out of business. I don’t play to make money, I play because it entertains me. I also know that over the long term, I lose money in the casino. I just try to maximize gains and minimize losses. Here are my rules for gambling:

  • 1 I know that I will lose money over the long term. It is mathematically certain. So budget your gambling and stick to it.
  • 2 I gamble because it is fun and entertaining. If I ever find myself gambling while desperate to win because I need the money, it is time to quit.
  • 3 Don’t ever gamble with money you can’t afford to lose. If you are gambling your rent or grocery money, that isn’t entertainment, it’s desperation.

My wife initially didn’t like it, but then she came to realize that I Am responsible with it. Although the first time she came to the table and saw that I was making individual bets of over $100 and had more than $1200 on the table, she was a little nervous. At the time, she didn’t realize that it wasn’t my money I was gambling with. More on that in a future post.

Answer to this week’s logic problem

So the answer to this week’s logic problem: There would be the same number of boys as girls.

Here is the explanation:

This is a common misconception. It is the same misconception that makes gamblers believe that a certain number is “due.” As they say, the dice have no memory. For example:

Let’s say that 1 million couples have a child in round one. Half will have boys, half girls. So now there are 500K each of boys and girls.

The couples with girls must stop, the 500,000 with only boys are required to try again. So the 500,000 couples who had boys in round one have children, again half are boys and half girls. So now there are 750,000 each boys and girls.

The third round, the parents who had a girl stop, the 250,000 parents who don’t yet have a girl try again. So now another 125,000 boys are born, as are 125,000 girls. So now the running count is 875,000 boys, and 875,000 girls.

So as this progresses, the ratio will always be 50/50.

Logic Problem

Kamala Harris finally lives her dream and winds up becoming the President of the United States. She decides that the US will be better off if there were more women, so she signs an executive order:

Henceforth, all child bearing couples will be required to keep having children until they have a girl. To prevent overpopulation, once they do have a girl, they must stop having children.

Here is the riddle: After 20 years of this policy, what will be the ratio of boys to girls under the age of 18 in America?

Third Trump Impeachment

My apologies to Monty Python.

Pelosi: We have found an insurrectionist, may we burn him?
McConnell: How do you known he is an insurrectionist?
SWALLWELL: He looks like one!
Pelosi: Bring him forward
Trump: I’m not an insurrectionist! I’m not an insurrectionist!
McConnell: ehh… but you are dressed like one.
Trump: They dressed me up like this!
Democrats in unison: naah no we didn’t… no.
Trump: And this isn’t my nose, it’s a false one.
(McConnell lifts up carrot nose)
McConnell: Well?
PELOSI: Well we did do the nose
McConnell: The nose?
PELOSI: …And the hat, but he is an insurrectionist!
(all: yeah, burn him burn him!)
McConnell: Did you dress him up like this?
PELOSI: No! Yes. a bit! But he has got a wart!
Joe Biden: We’re gonna need more troops.
McConnell: What makes you think he is an insurrectionist?
AOC: Well, he had me assassinated!
McConnell: Assassinated?!
AOC: I got better.
Swalwell: Burn him anyway! McConnell: There are ways of telling whether he is an insurrectionist.
PELOSI: Are there? Well then tell us!
McConnell: Tell me… what do you do with insurrectionists?
P3: Burn’em! Burn them up! (burn burn burn)
McConnell: What do you burn apart from insurrectionists?
AOC: Books!
McConnell: and what are books made of?
Rep Hank Johnson: More troops!
McConnell: So, why do insurrectionists burn?
SWALLWELL: Cuz they’re made of… wood?
McConnell: Gooood.
McConnell: So, how do we tell if he is made of paper?
PELOSI: Print money on him!
McConnell: Ahh, but can you not also make money out of thin air?
PELOSI: Oh yeah…
McConnell: Does money sink in water?
AOC: No. It floats!
PELOSI: Let’s throw him into the swamp!
McConnell: What also floats in water?
Hunter Biden: Hookers!
SWALLWELL: Chinese women!
Hunter: Hookers!
Bernie Sanders: Free Tuition!
Rep Johnson: Won’t more troops tip Guam over?
PELOSI: Cherries
Biden: A Duck!
McConnell: Exactly! So, logically…
Pelosi(thinking): If he weighs the same as a book… he’s made of wood!
McConnell: And therefore,
(pause & think)
Pelosi: An insurrectionist!
McConnell: We shall use my largest scales.