But at the same time, I would argue that "lucky" gamblers who believe in cosmic forces have more fun (and heartbreak) then the people who understand the math and the odds.

Take baccarat for example. For me, it is one of the most boring games in the world as essentially you are playing a coin toss. In his latest Travel Channel program, the Wizard even stated that you should take the Banker every single time (slightly better odds). Sure your money lasts longer, but what fun is betting only the Banker?

In contrast, consider all of those baccarat players who may not understand the math behind the game and only believe in luck and fate. They write down every single result on a sheet of paper, consult with one another, and debate heatedly about what will happen next, only to say firmly, "No bet this hand. The pattern is unclear."

Or those wonderful and superstitious craps players who make 100% of their decisions on things that have no outcome on the dice. It really doesn't matter if an ugly man walks by, a beautiful woman is wearing a low cut dress, or if the dice hit a player's hand. However, I argue that those same gamblers have a lot more fun and excitement then the mathematician who know that the dice/cards/ball have no memory, that there is no god of luck to pray to, and that everything evens out in the end.

Now, I am not saying that people who understand the math and odds have no fun at all. On the contrary, I love casinos, the atmosphere, the people watching and playing at the tables. I am just saying that people who do not understand the math and odds have more fun. I argue that math seems to take some of the fun out of gambling.

In the case of harmless beliefs [such as varying your betting pattern based on nonsense but still always betting the same amount on Banker in Baccarat] you may be right.

However, I find I have fun following superstitious patterns that I have determined are harmless, and the knowledge that it is nonsense is merely in the background.

Actually, the first time I stepped foot in a casino many years back, I did have no clue what the odds were. And I barely played, and I certainly didn't care for it much, mainly because I felt uneasy about some of the bets I made. Afterwards I educated myself and immediately started enjoying the experience, knowing I was making some reasonable bets (even though they were usually still at a disadvantage).

So for me, the opposite is true. I need the math to enjoy it. Now does a clueless gambler with a personality that allows them to enjoy the superstitous aspect of it all generally have more fun than me? Maybe, even probably, but I certainly don't envy them.

Reading this, it is clear that knowing the odds keeps me away from the Big 6 wheel and hard ways, I guess. Otherwise, I'm as much a sucker as anyone else!

The low cut dress does make a difference, it always makes a difference ... just not for the dice.

My first time at Baccarat I had the Wizards advice ringing in my ears but the cards listened to the Wizard only two out of over a dozen times.

I think a basic understanding of the odds is necessary for intelligent play, but a slavish adherence to the odds is neither necessary nor fun.

Big Red is 16.67 percent against me. So I don't bet it.

Pass Line is 1.414 percent against me so I do bet it.

Its not the math, its common sense applied to the math.

If its a pleasure trip, you should be having fun. If you are with some friends, you should be in a festive mood and not try to apply some mental calipers to every decision and carry things out to the tenth decimal point.

Quote:gamblerPersonally, I have a strong math background and know exactly what the odds are for every single bet that I make. I also understand that most people on the Wizard of Vegas forum have a strong math background so I am sure that this thread will be very biased.

But at the same time, I would argue that "lucky" gamblers who believe in cosmic forces have more fun (and heartbreak) then the people who understand the math and the odds.

Or those wonderful and superstitious craps players who make 100% of their decisions on things that have no outcome on the dice. It really doesn't matter if an ugly man walks by, a beautiful woman is wearing a low cut dress, or if the dice hit a player's hand. However, I argue that those same gamblers have a lot more fun and excitement then the mathematician who know that the dice/cards/ball have no memory, that there is no god of luck to pray to, and that everything evens out in the end.

Anyone who REALLY understands the math, and I'm not talking just about the house advantage, also understands that everything DOES NOT even out in the end for the individual player. For the "aggregate player", yes, but no individual plays enough craps to have no chance of getting and staying ahead. Unfortunately, most people stop learning when they understand how to figure the house advantage. Of course, it's important and it's always there, but variance is equally, if not more, important. The chance of overcoming the house advantage is a function of variance, the more variance the better chance for any given house advantage. Understanding that, I know that I can go to the casino with a chance to win; understanding that, I can figure the chances of busting my bankroll, too, as variance, of course, works both ways.

Quote:gamblerNow, I am not saying that people who understand the math and odds have no fun at all. On the contrary, I love casinos, the atmosphere, the people watching and playing at the tables. I am just saying that people who do not understand the math and odds have more fun. I argue that math seems to take some of the fun out of gambling.

That may be true for yourself. I enjoy craps as much as anyone, and I enjoy it more now than when I was a newbie, because of my increased understanding.

Cheers,

Alan Shank

Quote:gamblerOr those wonderful and superstitious craps players who make 100% of their decisions on things that have no outcome on the dice. It really doesn't matter if an ugly man walks by, a beautiful woman is wearing a low cut dress, or if the dice hit a player's hand. However, I argue that those same gamblers have a lot more fun and excitement then the mathematician who know that the dice/cards/ball have no memory, that there is no god of luck to pray to, and that everything evens out in the end.

Now, I am not saying that people who understand the math and odds have no fun at all. On the contrary, I love casinos, the atmosphere, the people watching and playing at the tables. I am just saying that people who do not understand the math and odds have more fun. I argue that math seems to take some of the fun out of gambling.

If you look at the number of posts that I've had, I enjoy posting on this site because I love math, statistics, and problem solving. Stepping into a casino for me is like taking my mathematical and statistic abilities and apply it into something very real (my bankroll). That's why I love gambling and why I have so much fun.

I have tons of fun at the casino BECAUSE I know the best games to play. If I know the smart bets it means on average that my bankroll lasts longer, that I can stay for longer, and have more fun. I enjoy the camaraderie as much as anyone at the craps table but I get my kicks laughing with the superstitious. My superstitious buddies will laugh at me as my bets get wiped away after they took their bets off after a crap roll, just as much I'll laugh at them when the dice bounces off someone's hand and ends up being a point or the new girl at the craps table sevens out after the third roll.

I enjoy a game more if I understand it, including a rough notion of what my chances are. I can manage my gambling budget better with that rough notion. It doesn't mean I won't play games with lousy odds for the player if I enjoy them, but I will play without any illusions.

Oh, sure, knowing the numbers may help me feel better about not bothering to play some of those carnival games, but does that stop me from throwing a couple bucks at a hard way if I 'feel' it? Hell no!

I often say about the FireBet, that if you've got your money spread out when somebody hits it, you're gonna be doing good whether you bet the FireBet or not. And I know that the FireBet is a high HA bet. Do either of those thing prevent me from dropping a buck on the fire? Hell no!

Does knowing the HA on hop bets prevent me from hopping the two remaining numbers on every come out when the shooter has hit four numbers? Hell no! I did that twice where I gave back $24 of the $25 that the FireBet was paying me. Will my history, or the math, prevent me from doing it again? Hell no!

Does Mathematics Take Some of the Fun out of Gambling? HELL NO!

Quote:DJTeddyBearNah. Gambling is fun. Plain and simple.

Oh, sure, knowing the numbers may help me feel better about not bothering to play some of those carnival games, but does that stop me from throwing a couple bucks at a hard way if I 'feel' it? Hell no!

I often say about the FireBet, that if you've got your money spread out when somebody hits it, you're gonna be doing good whether you bet the FireBet or not. And I know that the FireBet is a high HA bet. Do either of those thing prevent me from dropping a buck on the fire? Hell no!

Does knowing the HA on hop bets prevent me from hopping the two remaining numbers on every come out when the shooter has hit four numbers? Hell no! I did that twice where I gave back $24 of the $25 that the FireBet was paying me. Will my history, or the math, prevent me from doing it again? Hell no!

Does Mathematics Take Some of the Fun out of Gambling? HELL NO!

Very well put!

The math knowledge allows me to make low HA bets until (and if) I'm ahead enough to afford some of those more expensive (i.e. higher HA) bets. Sometimes they work, and I make even more money. Sometimes they don't, but I still leave the table with more money than I started with.

Quote:DJTeddyBearNah. Gambling is fun. Plain and simple.

Oh, sure, knowing the numbers may help me feel better about not bothering to play some of those carnival games, but does that stop me from throwing a couple bucks at a hard way if I 'feel' it? Hell no!

I often say about the FireBet, that if you've got your money spread out when somebody hits it, you're gonna be doing good whether you bet the FireBet or not. And I know that the FireBet is a high HA bet. Do either of those thing prevent me from dropping a buck on the fire? Hell no!

The Fire Bet is like the lottery, in a small way. For a buck, which you won't miss, you buy a very small chance at winning $1000, or whatever is payout is for six points. That is some "serious variance", isn't it?

Quote:DJTeddyBearDoes knowing the HA on hop bets prevent me from hopping the two remaining numbers on every come out when the shooter has hit four numbers? Hell no! I did that twice where I gave back $24 of the $25 that the FireBet was paying me. Will my history, or the math, prevent me from doing it again? Hell no!

Does Mathematics Take Some of the Fun out of Gambling? HELL NO!

Too many players consider only the HA. Take the bets on 2 and 12, or any of the 30 to 1 payouts for 35 to 1 shots: if your luck is average, you're going to lose 5 units in 36 bets, but it only takes one extra win to be ahead $26. One extra loss is only one more unit lost. The high variance gives you a shot at overcoming the HA.

Cheers,

Alan Shank

---------------

For instance if you understand the mathematics it makes sense when you are playing craps to play the "base bets". If you want the thrill of shooting for bigger payouts, you should switch over to the roulette table.

This sounds profound. I don't follow the math on this "lose five units in 36 bets". Just what bets are we talking about and just how is this 5 in 36 calculated?Quote:goatcabinToo many players consider only the HA. Take the bets on 2 and 12, or any of the 30 to 1 payouts for 35 to 1 shots: if your luck is average, you're going to lose 5 units in 36 bets, but it only takes one extra win to be ahead $26. One extra loss is only one more unit lost. The high variance gives you a shot at overcoming the HA.

Quote:gamblerDoes Mathematics Take Some of the Fun out of Gambling?

This is a question for the ages. For lack of a better response, "it all depends on you and what you enjoy."

:)

Quote:FleaStiffThis sounds profound. I don't follow the math on this "lose five units in 36 bets". Just what bets are we talking about and just how is this 5 in 36 calculated?Quote:goatcabinToo many players consider only the HA. Take the bets on 2 and 12, or any of the 30 to 1 payouts for 35 to 1 shots: if your luck is average, you're going to lose 5 units in 36 bets, but it only takes one extra win to be ahead $26. One extra loss is only one more unit lost. The high variance gives you a shot at overcoming the HA.

Really, it's just arithmetic. The odds against rolling a 12 are 35 to 1, since there's only one way of rolling 12 out of the 36 possible combinations. Most casinos pay 30 to 1 (31 for 1) on this bet, the 2 and any of the "hardway hopping bets". So, here is the expectation:

35 losses = -35

---

-5

The total of the bets is 36 units, so the HA is -5 / 36 = -.1389, or -13.89%.

You can do this for any bet. Take the place 6, which pays 7 to 6, with 5 ways to win and 6 to lose.

6 ways to lose 6 = -36

----

-1

Total bets are 11 * 6 = 66, and -1 / 66 = -.01515, or -1.52%.

So much for the HA. So, how do we figure the variance? The variance is a measure of "dispersion", IOW, how much the different outcomes differ from the mean outcome. For each possible outcome, you take the difference from the mean outcome (expected value), square it and weight it by its probability or the number of ways it occurs. Let's figure it for the bet on the 12:

-1 - -.1389 -.8611 .7415 * 35 = 25.9523

+30 - -.1389 30.1389 908.3533 * 1 = 908.3533

---------

934.3056 / 36 = 25.9529

That's the variance, but it's exaggerated, because we squared the differences to get absolute values for the differences; so, we take the square root of the variance and we get the "standard deviation".

SD = sqrt(25.9529) = 5.0944

So, the standard deviation for the bet on the 12 is over five times the amount of the bet.

Let's do this for the passline bet, for comparison:

-1 - -.01414 .98586 .97192 * 251 = 243.952

+1 - -.01414 1.01414 1.02848 * 244 = 250.949

-------

494.901 / 495 = .9998 = variance

.9996 = standard deviation

So, the standard deviation for a pass or come bet is, basically, the amount of the bet.

You can see that the bigger the difference between the bet and the payout and the bigger the difference in their probabilities, the bigger the variance/standard deviation.

Technically, the variance is the sum of the weighted squares of the differences, and the standard deviation is the square root of the variance. However, the word "variance" can also be used in a general way to describe variability, or volatility, and I use it in that general sense. The standard deviation is the more useful measure.

If the amount bet does not change, we can "draw a picture" of the distribution of possible outcomes of any number of bets of various types, because we know the expected value of each bet and the standard deviation. The important point is that the expected value increases with the number of bets, but the standard deviation only increases with the square root of the number of bets. This is because the more bets that are resolved, the more likely the results are to be to the mean. This is why, by the way, the casinos can rely on the HA, while the individual player can still hope to win.

So, we can figure likely outcomes for different numbers of passline and boxcar bets like this:

For passline:

number of bets | ev | SD | ev/SD |
---|---|---|---|

1 | -.014 | .999 | .014 |

5 | -.071 | 2.236 | .032 |

10 | -.141 | 3.162 | .045 |

25 | -.354 | 4.999 | .071 |

100 | -1.414 | 9.999 | .141 |

As you can see, the ratio of the ev to the SD keeps getting larger, because the ev grows faster. At some point around 5000 decisions, the ev will become larger in magnitude than the SD. This means that the player's results have to be at least one standard deviation better than expectation in order to be ahead after that many bets. In other words, he/she has to have experienced positive variance of at least one standard deviation to overcome the HA. Keep in mind that it's just as likely to experience negative variance of one standard deviation. We call that "bad luck". >:-)

number of bets | ev | SD | ev/SD |
---|---|---|---|

1 | -.139 | 5.094 | .027 |

5 | -.694 | 11.391 | .061 |

10 | -1.389 | 16.110 | .086 |

25 | -3.473 | 25.472 | .136 |

100 | -13.889 | 50.944 | .273 |

The ratio ev/SD tells you how lucky you have to be to be ahead after a given number of bets. You can see that, although the HA on boxcars is almost ten times as high as on the passline, the ev/SD after 100 bets is only about double that of the passline after the same number of bets.

In terms of our chances to overcome the house edge and win, variance is our friend; without variance, we would always lose. That's why hedging, which reduces variance by offsetting one bet against another, reduces one's chances of winning; however, it also reduces the amount lost when one's luck is bad. The other side of the "variance coin", however, is that it works both ways, increasing the magnitude of losses.

With some exceptions, the higher the variance of a bet, the higher the HA, i.e. you PAY for variance, because it gives you a chance to win. The house would be very happy to see people play like this:

bet equal amounts on pass and don't pass, never taking or laying odds

This "system" has very little variance, the only varying factor being the number of times the 12 shows. The player can NEVER WIN, only lose one of the bets when the 12 shows.

One big exception to the "more variance, higher HA" rule is the odds bets behind pass, come, don't pass and don't come bets. Since the casinos pay the actual odds, the expected value of those bets is always zero. For example:

take odds on 6

6 ways to lose 5 = -30

---

0

lay odds against 4

3 ways to lose 20 = -60

---

0

These bets add variance without any increase in the expected loss, which attaches only to the flat part. Let's examine the ev/SD for a pass bet with double odds:

number of bets | ev | SD | ev/SD |
---|---|---|---|

1 | -.014 | 2.857 | .002 |

5 | -.071 | 6.389 | .011 |

10 | -.141 | 9.036 | .016 |

25 | -.354 | 14.286 | .024 |

100 | -1.414 | 28.574 | .049 |

So, the ev/SD for 100 pass bets with double odds is about the same as for 10 pass bets without odds, meaning you have about the same chance of being ahead after 100 of those bets as after 10 pass bets if you don't take double odds. Never, ever forget, however, that this also means that you will lose almost three times as much with negative variance of one standard deviation.

The more odds you take or lay, the more variance, the better chance to win, the bigger the losses. IOW, everything is exaggerated, except the expected loss, which never changes if the flat bet stays the same.

One thing to keep in mind: any money on the flat bet is subject to the 1.4% "tax", so betting $10 and taking single odds has only half the expected loss of betting $20 and not taking odds.

Cheers,

Alan Shank