Thanks, this was very informative as someone who knows nothing about statistics and probability. I was interested in what you said about the forces or "fate' aspects of Casino gambling. My immediate thought about being wary of it was because it is probably rigged (which it is by the very set up but also by possibly being run by dishonest people).
There are three quite different situations. Changing lanes on a 'stuck' highway, the cost of changing is minimal and the benefit is also minimal. You absolutely know that if you change lanes, the one you left will then get clear and leave you 10-20 cars behind. You do it anyway because of your frustration.
The lottery is huge because I take a ticket each week and the cost to me is marginal. But if I do win then the benefit is HUGE. Of course the fact that I get to spend the week in fantasies about spending a few million has a great impact on relieving the fear and drudgery of everyday existence. Of course I won't win, but occasionally someone does. So I buy a ticket.
The casino you know the odds are against you but they are bearable. 1:38 chances to win 36 times your bet. Yes you will lose in the long term, but tonight may be your 'lucky' night and you go home with more money than you came with. People do you know. Play computer roulette, sometimes I go from $2,500 to more than $50,000. When you login again or continue, the computer numbers will bring you down to zero eventually, but in the meantime just maybe you have discovered the perfect system that will work in the real world.
I knew someone who taught statistics at a university, as well as developing time series forecast for private businesses. I remember being surprised that he enjoyed casino gambling, knowing that the odds were always against him. I, on the other hand, could not have been less interested.
I now wonder, 25 years later, if he was looking for evidence of unknown forces, acting on his fate.
The statistics I understand but it's the psychology that gets me about the casino analogy.
In casino games, the odds are intentionally stacked against the player in a way that guarantees the house will win more money over time. This is not necessarily true of most real-life decisions where outcomes are uncertain. So, given an unlimited amount of time and money, we and the casino know that if you keep playing, no matter how many winning streaks you go on, it will ultimately level out in their favor. Knowing this, the gambler does not wish to play the game indefinitely. They know there will be certain winning streaks somewhere in the gameplaying series, and that is what they are attempting to capitalize on. So possibly the gambler's psychological premises are what are the odds that when he starts playing for a short period, he will likely get on a winning streak for X length of time before he's comfortable calling it quits vs. just hitting losing streaks.
Daily choices and uncertainties often don't involve an opponent or entity deliberately setting the odds against you for their own gain, as the casino does. Are natural probabilities more "balanced"?
I'd like to add another thing which may be of interest. A thought experiment. Say a casino had a coin flipping game. But what they do is they hide the dealer behind a wall such that you cannot see them flip the coin. An interesting caveat we could add is that the casino lets you know that on some days there's some dealer back there flipping the coin the old fashioned way flicking off his/her thumb. But on other days the dealer back there is instead using the Briggs coin flipping machine.
The only other information you have to go on when you arrive at the table and start playing is a record, which the Casino loves including with various games because they know that the Roulette wheel, dice, and cards don't have a "Memory" that effects odds but our intuitions about our odds are influenced by that.
So with that information how does it impact what we think the odds are? I would imagine most people would first make the assumption it is supposed to be 50/50 so they'll look at the record and if it is roughly 50/50 in the past they'll assume there's a guy back there doing it by hand. But what if we see the record is a bunch of heads in a row? We might assume today is the day they're using the Briggs flipping machine. But actually it is just the guy back there flipping the coin consistently in such a way that heads happened to be coming up a lot in that period. My understanding of odds is that it still is technically 50/50 even though you may at the moment see a streak of heads or tails in a row and if you keep this series going infinitely a 50/50 chance would mean that eventually the head streak will end and things "even out".
So you plop down some money and bet the next one will be heads, but the dealer back there just happens to stretch out his hands, readjust his stance, etc. or he is relieved by another dealer that takes over the manual flip and the dealer flips again. Because of the minor physics the coin lands on tails and you lose. But you keep trying but notice the head streak is over and it looks roughly equal for a good long while after that.
..."rather, the payout"...
Perhaps you are missing the "fun" I think.
Perhaps you see that as part of the payout, but for those who enjoy gambling, something analogous to the "thrill of the chase" is definitely a factor.
Thanks, this was very informative as someone who knows nothing about statistics and probability. I was interested in what you said about the forces or "fate' aspects of Casino gambling. My immediate thought about being wary of it was because it is probably rigged (which it is by the very set up but also by possibly being run by dishonest people).
There are three quite different situations. Changing lanes on a 'stuck' highway, the cost of changing is minimal and the benefit is also minimal. You absolutely know that if you change lanes, the one you left will then get clear and leave you 10-20 cars behind. You do it anyway because of your frustration.
The lottery is huge because I take a ticket each week and the cost to me is marginal. But if I do win then the benefit is HUGE. Of course the fact that I get to spend the week in fantasies about spending a few million has a great impact on relieving the fear and drudgery of everyday existence. Of course I won't win, but occasionally someone does. So I buy a ticket.
The casino you know the odds are against you but they are bearable. 1:38 chances to win 36 times your bet. Yes you will lose in the long term, but tonight may be your 'lucky' night and you go home with more money than you came with. People do you know. Play computer roulette, sometimes I go from $2,500 to more than $50,000. When you login again or continue, the computer numbers will bring you down to zero eventually, but in the meantime just maybe you have discovered the perfect system that will work in the real world.
I knew someone who taught statistics at a university, as well as developing time series forecast for private businesses. I remember being surprised that he enjoyed casino gambling, knowing that the odds were always against him. I, on the other hand, could not have been less interested.
I now wonder, 25 years later, if he was looking for evidence of unknown forces, acting on his fate.
Seen it many times. Especially with East Asians.
That is interesting. I am continually surprised by the things I have missed.
The statistics I understand but it's the psychology that gets me about the casino analogy.
In casino games, the odds are intentionally stacked against the player in a way that guarantees the house will win more money over time. This is not necessarily true of most real-life decisions where outcomes are uncertain. So, given an unlimited amount of time and money, we and the casino know that if you keep playing, no matter how many winning streaks you go on, it will ultimately level out in their favor. Knowing this, the gambler does not wish to play the game indefinitely. They know there will be certain winning streaks somewhere in the gameplaying series, and that is what they are attempting to capitalize on. So possibly the gambler's psychological premises are what are the odds that when he starts playing for a short period, he will likely get on a winning streak for X length of time before he's comfortable calling it quits vs. just hitting losing streaks.
Daily choices and uncertainties often don't involve an opponent or entity deliberately setting the odds against you for their own gain, as the casino does. Are natural probabilities more "balanced"?
All good points, thanks.
I'd like to add another thing which may be of interest. A thought experiment. Say a casino had a coin flipping game. But what they do is they hide the dealer behind a wall such that you cannot see them flip the coin. An interesting caveat we could add is that the casino lets you know that on some days there's some dealer back there flipping the coin the old fashioned way flicking off his/her thumb. But on other days the dealer back there is instead using the Briggs coin flipping machine.
The only other information you have to go on when you arrive at the table and start playing is a record, which the Casino loves including with various games because they know that the Roulette wheel, dice, and cards don't have a "Memory" that effects odds but our intuitions about our odds are influenced by that.
So with that information how does it impact what we think the odds are? I would imagine most people would first make the assumption it is supposed to be 50/50 so they'll look at the record and if it is roughly 50/50 in the past they'll assume there's a guy back there doing it by hand. But what if we see the record is a bunch of heads in a row? We might assume today is the day they're using the Briggs flipping machine. But actually it is just the guy back there flipping the coin consistently in such a way that heads happened to be coming up a lot in that period. My understanding of odds is that it still is technically 50/50 even though you may at the moment see a streak of heads or tails in a row and if you keep this series going infinitely a 50/50 chance would mean that eventually the head streak will end and things "even out".
So you plop down some money and bet the next one will be heads, but the dealer back there just happens to stretch out his hands, readjust his stance, etc. or he is relieved by another dealer that takes over the manual flip and the dealer flips again. Because of the minor physics the coin lands on tails and you lose. But you keep trying but notice the head streak is over and it looks roughly equal for a good long while after that.