Math math math . . .

[heavy]

Okay, let's have some fun with this. I'll post a series of questions related to casino math (or probablity math) on this thread. I'll string them out over the course of the next few days. Meanwhile, you guys jump in with the answer (as you see it) with whatever explanation you deem necessary. And don't expect ME to have the right answer. Those of you who have been around for awhile know that I am not a math guy.

In a random game:

Question - Set-up #1: You bet a $1 Hard Six with the intent of parlaying the first hit to $10, parlaying the second hit to $100, and taking $1000 and down on the third hit. What are the odds of you successfully completing this bet.

Question #2 - Follow up: Which strategy would be the most cost effective way to win $1000 on the hard six? Playing the parlay method mentioned above - or simply starting out with a $100 hard six?

Thoughts?

[wudged]

1. The probability of winning hard 6 is 1/11 (1 way to win and 10 ways to lose) The probability of winning it three times in a row is 1/11*1/11*1/11 = 1/1331 = 0.075% (no, that's not 7.5%)

you can expect to bet $1331 before finally hitting a triple parlay for $1000, for a net loss of $331.

2. As stated above, the probability of winning once is 1/11 = 9.091%

you can expect to bet $1100 before finally hitting for $1000, for a net loss of $100.



In addition, for betting $10 and parlaying the first hit and keeping $1000 on the second hit:

the probability of winning twice in a row is 1/11*1/11 = 1/121 = 0.826%

you can expect to bet $1210 before finally hitting for $1000, for a net loss of $210.

[Mad Professor]

Just to add a bit more gilding to Wudged's gold-star answer in case you didn't pick it out of the equation above:

~The chances of three randomly-tossed Hard-6 wins in a row is around 1-in-1331.

~The chances of two randomly-tossed Hard-6 wins in a row is around 1-in-121.

...which begs the question:

Who still thinks that parlaying your H-way wins on random-rollers is a good solid-investment idea?


MP

[rollinbones]

Who still thinks that parlaying your H-way wins on random-rollers is a good solid-investment idea?

MP

Ha, now that's funny. I INVEST in the stock market and GAMBLE at the casino. Just that some bets are better than others. Unfortunately, same with my investing

[heavy]

Soooooooo, are some (apparently random) shooters inherently "better" at tossing hardways than others? Nudge nudge?

and part two . . .

If the hardway bets are so bad why does the casino limit them to . . . say $500 each (at least a most of my local joints). Seems like they should encourage players to bet all of their action on the hard boys.

[wudged]

The casinos want people to stay longer so they can outlast any positive variance the player may come across - not give out the entire vault on one roll of the dice.

The $3500/$4500 payout on a $500 hardways bet is comparable to $3000-$5000 passline max that is commonly found.

[rollinbones]

Soooooooo, are some (apparently random) shooters inherently "better" at tossing hardways than others? Nudge nudge?

I sure as hell don't know but, like the 4's and 10's, they sure seem to come in bunches! Unfortunately, as my old man used to say I'm usually "a day late and dollar short" when it happens

[alanwr]

Here a parlay method I found on starchips. If you want to go for a thousand just take $125 from your $450 profit and you'll still be ahead.

Hard 6 or 8

Here is a method to risk a little money to make a lot. Take $5 and try to win $500 by parlaying the hardway # 6 or # 8.
Bypass the come out roll then put $5 on either the # 6 or the # 8 your choice.
Lets say you hit the # 6, it pays $45 plus your $5=$50.
Tell stickman to parlay the $50.
2nd hit payoff is $500 take down profit.

Another Variation is:
When you put $5 on the hardway also PUT A PLACE BET $6 on the same number so if it comes out easy you will have a push.
Lost $5 hardway, won $5 easy way. Put bet back up seen this a lot of times back to back.

Here is another Variation:

SET THE DICE WHERE THERE IS NO WAY TO MAKE A EASY SIX OR EASY EIGHT. ONLY THE HARDWAY SIX OR HARDWAY EIGHT LIKE using the ( parallel 6's ) That is where the first dice has on the left side of the dice the number 2--5 and the second dice has the same side number 2--5 with the PARALLEL Sixes facing you.
I been using the hardway set like all hardways over the four faces of the dice.
bigkahnman@aol.com

Best Alan

[heavy]

Man, I miss "bigkahnman." Last I heard he was struggling with some health issues. I hope he's still out there somewhere running his progressions.

[heavy]

The laws of probability often confound gamblers. Things that sound correct "logically" really aren't when looked at from a mathematical perspective. Let's think, for example, about the odds of the seven showing up on the next toss of the dice. There are six combinations of dice faces that add up to seven - out of a total of thirty-six possible combinations of the dice. So the odds are essentially one in six that you'll see the seven show up on the next toss of the dice. Let's say that happens and now we're looking at the NEXT toss of the dice. What are the odds that the seven will show up on this toss? Well, the odds of that happening are STILL one in six. But the odds of the seven showing up twice back to back like that are what? One in thirty-six? Two in thirty-six? One in three? Oh, what webs we weave?

Odds of the seven showing back to back?

Once you've determined that . . . let's go out to the other extreme. It's been eleven rolls since we've seen the seven. What are the odds the seven will show on the next toss? How about after roll seventeen? What about roll twenty-three?

Okay, it's a very short step from here to get into "due number" theory, which is a whole 'nuther animal on its own. I'll leave it at there for now and get a little input from you guys. Meanwhile, I'll ask a couple of you old timers to put on your thinking caps and see if you can recall anything about "Global Expectancy Rates" and "Seven Survival Rates" from way back when. And yes, this will play into the entire regression theory.

[Mad Professor]

And in case any of you need a refresher-course on "Global Expectancy Rates" and "Seven Survival Rates"; all of the original material on that subject is found in my Regression Avoids Depression series.


MP

[rollinbones]

MP - thanks for the link.

Which led me to perhaps the best article I've read on betting:
http://www.diceinstitute.com/2009/06/id ... three.html

Good stuff.

[heavy]

Man, you guys are spoiling all of my fun. I had hoped to get to those links after a few comments from the gallery. Well, there you go. I will go so far as to mention that (with his permission) I included major elements of MP's Regression Avoids Depression article - in particular those Global Expectation and Seven Survival Rate charts - in my betting strategy seminar a few years back. Good work on his part.

Now, back on the subject at hand. I'd like us to go into what is commonly referred to as "due number theory" or (as the math guys like to call it) "gambler's ruin." And rather than focus on a common number like the seven - I'd like us to consider a strategy that (if memory does not fail me) was put forth years ago by our old pal Larry Edell. That strategy looked at one specific number - the eleven - as its key. Under this strategy you wait for (get this) eighteen consecutive tosses without an eleven showing. Then you bet the eleven every toss until it shows. I seem to recall some sort of negative progression being involved. You bet this way because, according to the theory, the eleven is "due" at this point. After all, out of thirty-six rolls you should expect to see two elevens, right? Riiiiiiight.

The problem with this theory is simple. The dice don't have a clue about how many tosses it's been since the eleven showed up. The odds of the eleven showing are exactly the same as they were on the first toss - and the eleventh toss - and the three hundredth toss, for that matter.

Now let's switch gears and get back to our old nemesis, the seven. This theory - that the odds of a number showing up never change - is a real problem for a lot of players. For example, we all know that there is not an infinite number of tosses to be had on any given hand. The seven is lurking out there somewhere. It can jump up at any time. We just don't know when. But after ten tosses we KNOW that we're ten tosses closer to the seven than we were when we started out hand. WE know that. The dice don't.

Thoughts?

[rollinbones]

This theory - that the odds of a number showing up never change - is a real problem for a lot of players. Thoughts?

Fun topic, but this really sums it up.

This is one time where the K.I.S.S principal applies and in craps it can be boiled to this:
It's a negative expectation game.

[Dylanfreake]

I think bigkahnman had eyesight problems.

He could surely come up with some heart-stopping presses and plays; and I think he used them.

[Kelph]

Heavy,

The numbers are generated from the dice which have six faces each with one to six pips per face in the same order. Players see the meaningful number depending on which faces are up when the dice finally stop moving. Because of the various possible numbers that can form by these two top faces (2 to 12 using simple addition) it is possible to have more combinations that make specific numbers than others. All known stuff and sorry to go through it but it sets up my response.

Regardless of how many times we see too many or too few of any number within a space of time or number of rolls (if you’re counting) the number of faces on a die or the amount and arrangement of the pips doesn’t change. Each possible number is still as likely or unlikely as the first roll assuming the dice are honest.

All numbers in Craps are due…..eventually. If I played for hours and never saw a single 9 I might begin to wonder about the dice. Even though the dice often mirror long term expectations in the short term they don’t have to always do so and it neither bends or breaks the probability math when such aberrations occur. The dice have no schedule to keep in the short term. Short term results can look quite chaotic.

Many times what one refers to as a “due” number actually comes in and the player looks smart. Sometimes it continues its hiatus and the player gets to a point where the increasing negative progression stops (nice size loss here), the player’s nerves give out on the next increased bet (nice loss here) or the bankroll is depleted (maximum loss). Due numbers and negative progressions……………betting that what’s has not been happening will happen. Better guess right because the price can be high.

I prefer to go with what is happening and repeating and that it will continue because it's easier on my nerves and more fun. Can I be wrong and lose? Hell yeah but I know the changing result quickly and I’m off it rather than continuing to sink greater amounts of money into the pit waiting to see if it ever happens.

Kelph