Craps Streaks and Math (A little different perspective)

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?