Craps Streaks and Math (A little different perspective)

I have been toying with the ideas behind streaks. Anecdotally, they do happen. Everyone that has played has seen them, anyone who walks past the roulette wheel can easily see them on the board. However, I know that each occurring action in a non-memory game is an independent event.

What I have seen is that there is an issue of "Due" theory (6 hasn't come up for a while, therefore it should do so soon) or "Abundance" theory (Those dice sure have a lot of 6's in them, so I there must be a bunch more coming). I am not for either of them per-se, but something I can't quite put all the math to.

Streaks, being the recurring of the same event, have odds for and against them. There should be some unlikely"ness" of things that can be quantified.

For example, let's take a coin flip. The chances are 1/2 that it will be heads or tails. The odds of the same value coming up twice in a row then go down (not because the first one was rolled but now we are looking at a different event '2 flips') That is .5^2 or 1/4 and so on up the pipe

If I flip a coin 8 times (twice * 4) it is likely I will get two heads at least 1 time.

So .5^6 like 0.015625 (1.5625/100) for getting it to come up heads 6 times in a row.

So if flip a coin (6 times * 1.56... * 50) (so I don't have to say 1.56... times) 470 times it is likely that at least one time in that series I should see 1 series of 6 heads.

With pass line bets in the 244/495 (I think) this makes for some much more interesting math but let's assume the numbers are simply X and Y and go with me for a moment.

The chances of 6 in a row on any First throw are 1.5625 in 100. However, if you have already thrown 5 of them the odds that you will now throw 6 in a row are 1/2. As are each subsequent roll. Of course the chances against it are the same too :)

Unfortunately, I don't know of a bet that capitalizes on that concept. However, in the same vein, at the beginning of a roll the chances that you will flip heads 6 times in a row is whatever 98. whatever the math is... and even when there have already been 5 of them the chances are 1/2 that you will not flip a 6th heads.

Again, I don't know of any wager that capitalizes on this.

Looking at streaks this way seems to take the fun and excitement out of them. But one can take either side (and still be wrong) and say the chances of rolling some number 6 times in a row are so low I will bet against it happening again, or just as well on the other side with well if it happened this many times it just might happen a few more... I say choose the one that sounds more fun to you and go with it....

Paging Mister Martingale

There have been lots of streaks of 12 spins in a row turning out to be Red. You walk up, you glance at the annunciator panel, see that the last 12 spins have been red and figure a Black is somewhere just round the corner ...
but there have been lots of streaks of 13 Reds in a row too!

But it's been RED 12 times in a row, Hold that Black spot open, dealer, Don't roll the ball till I get back from the ATM !

Why would you bet against the trend? Just wondering.

I think I would bet with the trend of red or six's rather than bet against it. Kind of like a sports team that is hot; why bet against them when they are on a win streak?

As a wise pit boss told me while I was losing money hand over fist obstinately betting on banker while an enormous player run was occuring: "Never bet against the streak."

Martingale?

Well this is usually one of the proofs that debunks the Martingale system. The idea being that as long as there are table maximums you are likely to hit them in 6 losses. At that point the MS is a loser because you can't effectively double the previous bet anymore. Of course, even if it does win you have risked an awful lot to win quite a small return.

I am amazed that I can look at the AP and see 5 reds, 1 black 6 reds 1 black 1 red 5 reds... and my gut tells me just play red and how can you lose. But the math doesn't support that. What would work is jumping in my time machine and going back 1 hour and playing for those streaks, knowing that they were coming.

But the fact remains, if there are 5 reds on the board the odds are the same that a red will come up next as they are for a black to come up next. (and of course a bit less that a greenie will do its thing)

If you really want to bet the streak, then you have to parlay it. Bet red, let it ride... lather rinse repeat for 5 (or more) in a row, as long as you can effectively stop before the red comes up. Only problem is unless you could do that really accurately, your payoff vs your exposure is about even except for the HA.

Quote: Absinthe

Bet red, let it ride... lather rinse repeat for 5 (or more) in a row.

Nothing prevents someone from betting on streaks ... its making the assumption that the math supports such things that is the error. Alot of people leave the casino with cash because they bet on streaks that were mathematically unsupported.

I am not sure if you are joking or serious, but I kind of feel that way for real. I know in my brain, that the chances of continuing the trend are just the same as ending it but somehow it is happier to bet with it than against it.

I tell people that 3 is a random number. The series of 3,3,3,3,3,3 is just as random as 3,2,5,1,6,2 (just the distribution is different).

There is something in our brains that says trends have to stop. But there is something in our hearts that wants them to continue.

In a perfect world, you would flip a coin H,T,H,T,H,T,H,T ad infinitum. But you would be just as unlikely to bet that and win as you would betting for H,H,H,H,H...

When someone is going to have a 3 hour roll at the craps table, it would be great to be there at their initial come out roll, with a huge bet and lots of odds and place/buy all the points and have the fire bet. But at 2 hours and 59 minutes the next roll of the dice has the same chance of sevening out as any other specific roll. But if you have collected all your winnings and you have not parlayed them on each point and stuff who cares if it sevens out when you are risking $1900 on the put buts and $1100 on the pass line if you have already collected $125000 or more on the 3 hour run :)

I usually tell people not to count on the streak, but don't bet against it :) Kind of useless advice, but it sounds profound :)

I think people see more streaks on some of the online games or their downloaded programs because the RNG's they have in them are not so widely distributed. There is one online craps game (free) that i can pretty much 4x my bank roll before getting bored and quitting by just playing $100 pass line and the maximum 345 odds on each bet. There is another one that if I play that I am usually out of money in the first 15 minutes. If I could do that in LV or AC I would be a rich and could write books :) I guess I could do the latter anyway, seems like the thing to do for some folks. Point is, just playing one online game system I could come up with a system that works but it will fail on another one like it, or in the real world.

Best example ever (for me). I was out in Vegas not too long ago. I was on the craps table and the dice finally came around to me. I personally am a bit superstitious about a few things. I call for 'same dice', I set them and if my SO comes over and asks "how are you doing" I cash out immediately. But i digress. Anyway, one strange thing is that once I set a point I don't like changing bets or really much of anything other than tossing the dice. I had as my last point a 17 toss long roll before I sevened out. I got a few come out 7/11 type things, and hit a few points. But the amazing thing was that I threw 8 nines in that 17 toss roll. The guy next to me parlayed my nines into something with at least 1 or two purple and a bunch of black chips and I could hear other delighted screeches every time I hit that nine, so I know others were raking it in hand over fist. I never placed a bet on the 9. Was that a natural streak, or did my dice setting have something to do with it? I don't know, but I didn't do it again, and no one else that night had 8 of the same number through a roll that i was aware of. I actually lost money that night, funny thing, if I knew there would be a streak, I may not have done so. Of course the guy next to me had no way of knowing. He kept pushing the 9. But who knows how much he has lost on the 9 during other rolls and other nights. There was a lot of money trading hands that night, I watched someone 3-parlay the hard 6 as well (not on that roll) as well. But I can't count the number of times I have been at a choppy table or just ice cold and seems like no one could make a point unless someone was betting wrong.

I like the idea of betting with the streak, but I don't try and fool myself into believing that I have any better chance of winning with it than betting against it.

And that is both "why it is called gambling" and "what makes it fun!"

A lot of people also leave casinos with much less than they started with, both by betting mathematically unsupported bets as well as well supported mathematical bets.

Here is where the math problem still pokes me in the side.

On a coin flip the chances were 1.5625 for every hundred 6 tosses that you could do 6 in a row. Which suggests that if there are 5 showing chances are good that the next will not be heads. (That is the mental math that is fouled.) The chances are 1/2 no matter what has already been flipped.

But a person may say, I have never seen 6 (or whatever number) in a row on the AP so if there is 5 then I will bet against another one coming up. That is wrong math, but it makes smug people feel good and say "I told you so" with some mathematical proof when it works. However, "just 'cuz you ain't seen it yet, don't mean it ain't goin' ta happen!" How many time a day do people say "Wow, I have never seen that before?" And if a whole bunch of people are feeling the same way, there is a whole bunch of 'good feelings' and 'hope' and 'prayer' going on to keep it going. If you believe in any of those giving an edge then perhaps it won't come up green :)

So here is a roulette betting system. Watch the AP and wait for a 5 in a row streak. Bet against it. It won't increase your odds much, but you will lose much less money than if you bet ever roll. (Because you are betting much less often.) but your odds are still 48/100 (I think) Does that help comps? Not sure, but it sounds like a boring way to play.

I still want to believe on one side or the other that the streak will continue or that it is due to break... But I can't. My brain has been ruined with the silly math facts. Damn facts.

That same silly math is what allowed the casino to be built in the first place. And pays a certain frustrated old man his salary. LOL

Well, mine too :)

The psychology behind streaks is awesome. Ask someone to write down a 'random' series of coin flips, and they will write a pattern that does NOT have many streaks in it (that is they will flip between H & T too much, like HHTHTHHTTTHTH, which has 8/13 breaks in streaks). But there should be longer streaks in a number of coin flips that long.

We see patterns where there aren't any, it's a survival instinct to pick a leopard out of a bush. Better to be wrong than dead. But because we look for patterns, it bothers us to see something we know is random take on what appears to be a pattern.

Long streaks happen more than we expect, but they can't be predicted, especially in independent trials. We try to make sense of that, and the outcome is often losing $$$.

I'm tired of explaining this, but this quick hypothetical seems to convince some people, so here goes:

1) Imagine you flip a coin 1000 times. The average result is 500 heads and 500 tails. Let's just call that 50.00% heads, exactly what it should theoretically be.
2) Now imagine you flip a coin and it is on a streak and you get 4 heads in a row. It has, to this point, favored head. 100.00% heads.

Now imagine that we do #2 followed by #1. We get 504 heads and 500 tails. That's 50.2% heads. So despite the streak, we can still get back to the theoretical odds on a %age basis just by doing a lot more coin flips, despite starting out 100.00% on heads.. We don't have to get any "extra" tails to make up for the heads.

Quote: kmcd

We don't have to get any "extra" tails to make up for the heads.

I'm not sure I understand this fully but will think about when I sober up. Meanwhile... which will the next toss be?

Quote: FleaStiff

I'm not sure I understand this fully but will think about when I sober up. Meanwhile... which will the next toss be?

It'll be the 1005th toss :)

Quote: dwheatley

The psychology behind streaks is awesome. Ask someone to write down a 'random' series of coin flips, and they will write a pattern that does NOT have many streaks in it (that is they will flip between H & T too much, like HHTHTHHTTTHTH, which has 8/13 breaks in streaks). But there should be longer streaks in a number of coin flips that long.

We see patterns where there aren't any, it's a survival instinct to pick a leopard out of a bush. Better to be wrong than dead. But because we look for patterns, it bothers us to see something we know is random take on what appears to be a pattern.

Long streaks happen more than we expect, but they can't be predicted, especially in independent trials. We try to make sense of that, and the outcome is often losing $$$.

Your comment here is very much on target.

In your example "HHTHTHHTTTHTH" there is no streak longer than three. There is a 58.374% probability that there will be at least one streak longer than three. While this is certainly enough to confidently say if you faked the data or not, I could ask you to make a string of 26 coin flips.

If there is still no streak longer than three, now there is an 86% probability that there will be a streak longer than three if the data was truly random. I have much more confidence in saying you faked the data.


I also liked your earlier statement about streaks. It is utter bullshit, but it does have a reassuring sound to it. Are you a pitchman?