Probability issues - a coin toss

It's an error in thought process. As you noted, the odds of any one coin toss ending up "heads" is 50/50. People tend to confuse that with the odds of multiple coin tosses in a row coming up all heads.

Obviously, if you toss a coin 100 times the odds of it coming up heads every time is miniscule but people tend to think in those terms instead of thinking about the act that each and every toss is still 50/50.

I just read up on this from a sientific point of veiw. The coin has no memory. Each toss is it's own event and has nothing to do with the last one.

But if you had to place a bet on a coin toss and the last five were 'Heads' how would you bet?

Amigo, the previous toss would have no effect at all on my bet...the odds are exactly 50/50...I would just as likely take into account the colour of my underwear.

Your response is exactly what intrigues me....how would you bet and why?

I've also seen people researching which lotto numbers "tend" to be drawn more often ...and then choosing those numbers to play..... which seems to be similar but OPPOSITE reasoning as the coin toss betting.

The chances are 50/50 if and only if the coin is fair.

If a coin toss was heads five times in a row, I would bet heads for the sixth since there is a chance that the coin is fixed and if it was just random, then it is 50/50 and no harm done. But the "gambler's fallacy" you refer to is well known. People also tend to extend it to things that are not random. I was sitting in a meeting discussing hurricanes. Two had hit locally, so one person said that it was unlikely that a third would hit since the chances of three in a year were slim. The opposite was true. The likelyhood of the next hurricane hitting was greater than normal since macroscopic weather conditions were sending hurricanes up the Atlantic cost rather than into the Gulf.

It's on this mistaken idea of probability that casinos rake in so much cash.


shhhh...don't tell anyone.

That's illogical Chai but it's alright because I like illogicality in fun feminine packaging.

The profit a casino,or any bookie,makes is derived from what is known as the "over-round".The over-round in national lotteries is usually set at about 150 and in the top enclosure at Royal Ascot about 103.It represents what is "in the bag" for each 100 paid out to winners.The odds in a casino have no need to vary as the process for deciding the winner is always the same whereas with horses it isn't due to trainers being human and horses and jockeys being animals.I gather casino over-rounds are between 103 and 104.

But I wouldn't bother your little head over such matters if I was you.It's a bloke thing really.

The chance that this paternalistic, protective statement will pass without comment is slim.

Actually each coin toss should be random - but 5 heads in a row could easily indicate the coin is not random - but ill-balanced in favour of heads or a two headed coin.

Yes, the chances of 5 heads in a row is 1/32 (assuming fair play) but the chance of throwing another head after that is still 1/2

Coin tosses aren't actually 50/50. I figured that out as a kid when I could get a coin to come up 75% of the time to what I wanted. Science has since proven it to be true.

Source

Sorry Noddy, just got back from getting my nails done and eyebrows waxed.

The wax getting yanked off made me a little dizzy, so I'm not sure what you're referring to.

Goodness what us ladies must do to keep up our appearance. It just takes up my entire day.

Time to condense that routine -

mud wrestling

All the benefits of a mud bath, exercise, and it keeps the men in your life interested all in one easy session.

oooooo - sounds super.

and I have a few girlfriends that need to condense their beauty regime too!

maybe I should tell them about this idea next time we go shopping.

I would certainly bet that you are right.

But yeah, to echo an earlier poster, 5 head tosses in a row indicates the coin is not fair and I would not assign 50/50 odds to the next coin toss.

It might indicate the coin is not fair, or it might indicate that a low probability (one in thirty-two) came up.

Well, that's kind of the whole point. We make a guess based on the previous 5 events. Either an unlikely result occurred, or the coin isn't balanced (or being tossed fairly). At worst, your odds are 50/50, but if the coin isn't fair, then they are somewhat better in favor of heads (using the current example). So the probability of heads coming up is greater than or equal to that of tails. I'd bet heads.