tag:blogger.com,1999:blog-3722233.post6138760775046652444..comments2024-06-22T00:23:11.174-05:00Comments on Computational Complexity: Would you take this bet (Part 2) ?Lance Fortnowhttp://www.blogger.com/profile/06752030912874378610noreply@blogger.comBlogger11125tag:blogger.com,1999:blog-3722233.post-54212101339406859522021-07-30T15:03:26.610-05:002021-07-30T15:03:26.610-05:00In my opinion: More fundamental than the supply of...In my opinion: More fundamental than the supply of money (which can easily be changed by switching currencies) or utility (which is subjective) is the requirement for potentially infinite number of repetitions (to realize the expectation). This directly assumes infinite time, which is not necessarily "supplied" by modern physics. I would be interested in others' opinions.Petar Maymounkovhttps://www.blogger.com/profile/08703852824477094824noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70677615344991623302021-07-24T11:05:07.706-05:002021-07-24T11:05:07.706-05:00I would do both of those. But usually when they of...I would do both of those. But usually when they offer a chance to win something, they don't tell you the expected value, and it is probably pretty low. But, I agree the distribution of the payoffs is relevant in general.David Marcushttps://www.blogger.com/profile/07084520656051241766noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-81217275784330896952021-07-22T18:41:26.123-05:002021-07-22T18:41:26.123-05:00Many such paradoxes are resolved simply by observi...Many such paradoxes are resolved simply by observing that one's utility does not scale linearly with the amount of money one has.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-56224221514155096572021-07-17T07:21:57.246-05:002021-07-17T07:21:57.246-05:00If I had infinite money to play infinitely long an...If I had infinite money to play infinitely long and an infinite lifetime and a time machine to return to when I started with my winnings then I would play.Jnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-57780425042823572512021-07-15T10:34:14.054-05:002021-07-15T10:34:14.054-05:00To answer your question #1, I like Shapley's a...To answer your question #1, I like Shapley's argument. It matches my intuition that games like these are a bad idea. One doesn't need to go to an "all the money in the world" extent, merely the extent of the finances of the "house" (the organization offering the game). This is lovely because it also can finesse the problem of dealing with infinitely long, but very low-valued (locally) tails whose sums diverge.<br /><br />And I very much agree with anonymous on really hating giving windfalls to lucky winners. Drug development is sometimes like that: lots of people work along similar lines, and the one bloke who figures out the trick (or the group whose guess pans out) makes a fortune, and no one else does, even though they all did really good science. (Apparently Pfizer ran multiple Covid-19 vaccine development programs in parallel, so they finessed this problem, although calling brute force "finesse" is esthetically problematic.)<br />DJLhttps://www.blogger.com/profile/04036156397398405817noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-42505015278478347542021-07-14T06:41:45.977-05:002021-07-14T06:41:45.977-05:00@=(v)( ')> No, if at flip #1 (and you can ...@=(v)( ')> No, if at flip #1 (and you can come back to it after some previous tosses) you get Head you receive $1 (no matter what you paid) and the game is over; and you can play only once in your life.<br />The idea of this variant is: if you're lucky enough your luck will increase ... but is the game worth $1000? Or what is the maximum amount you'll pay to play it?Marzio De Biasihttps://www.blogger.com/profile/18441670787376943932noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-70189034969161748082021-07-13T16:12:59.536-05:002021-07-13T16:12:59.536-05:00No, "flip #1) if HEADS you get 1 dollar and t...No, "flip #1) if HEADS you get 1 dollar and the games ends here, sorry" means you don't just get to choose how much money you want.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-34518623719700309482021-07-13T16:11:39.861-05:002021-07-13T16:11:39.861-05:00If I knew that I'd get $10 for doing a questio...If I knew that I'd get $10 for doing a questionnaire about a book, I would probably do it.<br /><br />If I knew that two lucky winners would get $500 each for doing the questionnaire and my "expected value" was $10, I likely would not do it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-64071804137650150042021-07-13T11:42:24.371-05:002021-07-13T11:42:24.371-05:00Ignoring the amount of time it takes to play, in t...Ignoring the amount of time it takes to play, in this version you get to choose how much money you want so you should play no matter the cost. Considering the time it takes to play you may spend your whole life playing this boring game depending on the cost.=(v)( ')>https://www.blogger.com/profile/16860809630209858215noreply@blogger.comtag:blogger.com,1999:blog-3722233.post-5397992021716769972021-07-12T18:14:37.755-05:002021-07-12T18:14:37.755-05:00I think there's actually a somewhat deeper que...I think there's actually a somewhat deeper question here that is not entirely addressed by simply observing that there is a maximum payoff in the real world. Namely, under what circumstances does it make sense to use expectation maximization to guide our behavior?<br /><br />When people calculate expected value, there is often a tacit assumption that the scenario will be repeated often enough that there will be a high probability of realizing the expected payoff. If this assumption is violated then it's not clear that maximizing expectation is a sensible thing to do. Would you rather that I give you a one-time opportunity to win $100 million by rolling a 100-sided die, or would you rather that I give you $900,000 outright? I think most people would opt for the guaranteed $900,000 and I don't think they're being irrational.<br /><br />Determining the expected value of a game is an important first step, but it is not the only consideration. It is also important to ask yourself what your real goals are. The Wikipedia article on the Kelly criterion has a nice illustration of this point. Suppose you are given $25 and may place even-money bets on a coin that lands heads 60% of the time. You can bet any fraction of the amount of money you currently have, up to a maximum of $250. You have time to place about 300 bets. What do you do? Expectation maximization tells you to bet your entire bankroll every time, but this strategy virtually guarantees that you will go broke. But if you bet 20% of your bankroll each time then you are highly likely to come out far ahead at the end of the session.Timothy Chowhttp://alum.mit.edu/www/tchownoreply@blogger.comtag:blogger.com,1999:blog-3722233.post-45220213042948132192021-07-12T05:52:08.354-05:002021-07-12T05:52:08.354-05:00A more tempting variant:
flip #1) if HEADS you ge...A more tempting variant:<br /><br />flip #1) if HEADS you get 1 dollar and the games ends here, sorry<br />if TAIL I flip again ("goto flip #2")<br /><br />flip #2) if HEADS you get 2 dollars and the games ends here OR we revert to flip #1 (you decide)<br />if TAIL I flip again<br /><br />flip #3) if HEADS you get 4 dollars and the games ends here OR we revert to flip #2 (you decide)<br />if TAIL I flip again<br /><br />flip #4) if HEADS you get 8 dollars and the games ends here OR we revert to flip #3 (you decide)<br />if TAIL I flip again<br /><br />... and so on (the flips are like a "stack")<br /><br />You're allowed to play the game only once in your life ... it will cost you $1000? Do you wanna play? Marzio De Biasihttps://www.blogger.com/profile/18441670787376943932noreply@blogger.com