Obsessing about how 'close' one's lottery numbers are to winning is akin to the Gambler's Fallacy ... or should be, I think.
I agree that there is a parallel to be made.
But could you explain what is "obsessive" about bringing up or discussing this subject ?
Yes Hofstadter wrote a lot of interesting stuff about these type of closeness or similarity questions. That is one of the reason I started this thread, it has noting to do per se with lottery. Lottery was just an example.
Debunked is as a volatile concept as closeness.
This is a strange thread. Personally, I only consider something "close" if I can repeat/refine my behavior to get close/closer the next time. In the case of lottery numbers there is nothing I can do to improve my odds for the next drawing. Thus for me, there is no concept of closeness.
That said, when it comes to something like slot machines, "closeness" results in an adrenalin rush. If the first reel comes up a red 7, I get an instant shot of adrenalin. If the second one comes up a red 7, that's another rush (they are timed to not come up all at once). If the third one comes up red 7 above the pay line, there's another rush. I then look at the payout charts and think, "Damn! I could have won $2,500!" Of course, I won nothing, but it's certainly more fun than seeing three low-payout symbols all hit above the pay line.
The reality is that the moment I pulled the reel it was decided whether I would win or not through random number generators. I was simply enjoying the reveal - a tease, if you will. I also know that the number of red 7s decreases from the first reel to the last reel. Statistically I know that if I don't get a red 7 on the first reel, I will not win the jackpot. If they allowed betting between reels, it would make sense to raise my bet after getting the first red 7 even if the next two reels were determined when I made the pull. Statistically over time I would come out ahead (well, less behind).
When it comes to the next pull, the number of red 7s I got on the prior pull is irrelevant since each event is independent. It doesn't matter how "close" I came.
That said, when it comes to something like slot machines, "closeness" results in an adrenalin rush. If the first reel comes up a red 7, I get an instant shot of adrenalin. If the second one comes up a red 7, that's another rush (they are timed to not come up all at once). If the third one comes up red 7 above the pay line, there's another rush. I then look at the payout charts and think, "Damn! I could have won $2,500!" Of course, I won nothing, but it's certainly more fun than seeing three low-payout symbols all hit above the pay line.
The reality is that the moment I pulled the reel it was decided whether I would win or not through random number generators. I was simply enjoying the reveal - a tease, if you will. I also know that the number of red 7s decreases from the first reel to the last reel. Statistically I know that if I don't get a red 7 on the first reel, I will not win the jackpot. If they allowed betting between reels, it would make sense to raise my bet after getting the first red 7 even if the next two reels were determined when I made the pull. Statistically over time I would come out ahead (well, less behind).
When it comes to the next pull, the number of red 7s I got on the prior pull is irrelevant since each event is independent. It doesn't matter how "close" I came.
Say you buy 2 lottery ticket on saturday. The drawing is done and one of the two tickets is the winning ticket. It is Sunday morning and you do not know that one of the 2 tickets is the winner.UncaYimmy;665340[IMG said:
Later that day, you keep one ticket and give the other (which happens to be the winning one) to your friend.
You did not win, but did you not came "close" to winning ?
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No.
You did not win. Full stop.
Let's put it another way. You take one of two possible routes to work, chosen at random each day. Route 'A' parallels route 'B' and is separated from route 'B' by one city block. One day, you chose route 'A'. Upon arriving at work, you discover that there was a horrible multi-vehicle accident that killed everyone along route 'B', and that took place at the exact time and at the exact place that you would have been had you taken route 'B'.
Did you come close to dying? Were you almost killed? Did you have a "near-death experience"?
If you follow my reasoning, you should be able to answer that question. Can I change my behavior next time around to better my odds? Yes. I can check the results before giving away a ticket. Now, it may take many, many years to be in possession of another pair of tickets where one is the winner, but my new strategy will most definitely increase my odds of keeping the winning ticket should I have one. However, there is no strategy I can adopt to increase my odds of having one winning ticket in any given pair that I buy.
If a killer fires one shot (at random) from a tall building, at a crowd. You are in this crowd and the person next to you is shot dead. I would say you came close to dying (or at least being seriously injured).
Closer to dying than say a person at 3 km from the victim.
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Wrong again, by false analogy.
"Coming close to dying" and "being in close proximity to a person who died" are two entirely different things. 'Live' or 'Die' - there is no 'Almost'.
Vorticity
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Once again: The question in the opening post is not a mathematical question. For those who think such questions are meaningless, take a look at Analogies and Roles in Human and Machine Thinking by Douglas Hofstadter, which is contained in his collection of SciAm articles Metamagical Themas: Questing for the Essence of Mind and Pattern. Here is a link to it on Google Books.
From that article we find, for example, the following:
Now, an overly literal person might simply reply "Well, there's a 4 in B, so clearly '4' plays the role in B that 4 plays in A."
As for me, my "cognitive gut" immediately gives me a different answer: "Clearly, '3' plays the role in B that 4 plays in A."
To those of you who argue that the question of the OP is meaningless, since there is no "close" in lotteries... well that's one way of looking at it, which is literally accurate.
But which of the possibilities in the OP feels closest? Don't use mathematics (at least not explicitly) to arrive at your answer...
As for me, I'm not sure. I'll have to think about it.
From that article we find, for example, the following:
Now, an overly literal person might simply reply "Well, there's a 4 in B, so clearly '4' plays the role in B that 4 plays in A."
As for me, my "cognitive gut" immediately gives me a different answer: "Clearly, '3' plays the role in B that 4 plays in A."
To those of you who argue that the question of the OP is meaningless, since there is no "close" in lotteries... well that's one way of looking at it, which is literally accurate.
But which of the possibilities in the OP feels closest? Don't use mathematics (at least not explicitly) to arrive at your answer...
As for me, I'm not sure. I'll have to think about it.
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Vorticity
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No finite number.
False analogy ?? The person next to you did not die of a heart attack.
Then consider the close proximity with the bullet that can kill you.
The closer you are to the bullet that hits the crowd the more chance of dying or being injured.
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Now that makes sense to me.
By the same token, then, the poor lottery loser did not come close to winning, but instead was once in close proximity to the winning lottery ticket.