This is not the classic lottery paradox. Details of that are available at Epistemic Paradoxes (Stanford Encyclopedia of Philosophy

Suppose there is one lottery with 100,000 tickets and one prize. I have bought one ticket. I know that the probability of each ticket winning is 1:100,000, that the probability of each ticket losing is 99,999:100,00, and that after the draw each ticket will have definitively won or lost.

My rational expectation has to be that my ticket will lose, so buying a ticket seems irrational and if I knew it would lose, I would not buy it.

However, buying a ticket can be justified because the odds of a small loss are balanced against a large gain. There’s no objective criterion for that balance, so buying a ticket is not rational, but also not irrational.

Here’s the paradox:-

  1. If my ticket loses, my expectation is true and justified. So it appears to be knowledge.

  2. If my ticket wins, my balanced decision is true and justified. So it also appears to be knowledge.

This is not a direct contradiction, but it does seem odd that after the draw, I will have known the outcome whatever it is.

There are three possibilities: -

  1. We could accept that in some cases justified true belief is not knowledge.

  2. We could adjust the definition of justification.

  3. We could adjust the definition of knowledge.

How can this be resolved?


At present my position is that: -

  1. Probability statements can be known.

  2. Probability statements can never justify claims to know unqualified statements about single events. But they can justify beliefs about them and those beliefs may be true.

  3. Probability statements can justify decisions to act but only in combination with a calculation or estimate of expected utility and therefore only in the context of the person expecting the utility.

I'm looking for critical evaluation of this position.

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    – Philip Klöcking
    Commented Mar 7, 2023 at 12:16
  • I think, shortly put, you're asking if knowledge from probabibility fits in with JTB since? As in, the knowledge from probability doesn't care for the truth or falsity. Commented May 26, 2023 at 12:53
  • I believe the reason people misunderstood the question was due to lack of technical terminology Commented May 26, 2023 at 12:54
  • Do you mean mine or theirs? On the whole I try to minimize technical terminology. And I'm not sure what's generally understood on SE. As to the question, perhaps you'll allow me to have another go, just for fun? The interpretation of justification that is less than conclusive is very tricky in the context of epistemology. Probability might sometimes justify a belief. If that belief turns out to be true, would it count as knowledge? A bet, which takes account of expected utility, can justify an action, if that action turns out well, might it justify a claim to knowledge? Is that any clearer?
    – Ludwig V
    Commented May 26, 2023 at 14:55
  • @Hopeful Whitepillar Thanks for changing the question. This version is better. It had me foxed for a while, though. I couldn't work out why I had two questions when I was sure I only posted one. Perhaps I'll get a new and better answer.
    – Ludwig V
    Commented May 26, 2023 at 20:01

12 Answers 12


There is no paradox here. What you knew for certain before the lottery was that there were 100,000 possible outcomes, in only one of which you would win. The result of the lottery does not change the truth of the knowledge you had beforehand. Suppose that you win- that does not not invalidate your earlier expectation that you would most likely lose. Suppose you lose- that does not invalidate your earlier willingness to place a small bet on the remote possibility of a big win.

  • Thank you for this. You are quite right. But it does not answer my question, which I am about to edit in order to clarify and focus it better.
    – Ludwig V
    Commented Mar 6, 2023 at 7:58
  • @LudwigV excellent. A clarification would be v helpful, as I felt I was stabbing in the dark somewhat when answering the initial version. Commented Mar 6, 2023 at 8:08
  • I bought a lottery once, only once, from this guy. Should've asked his name, but he looked like a Balthazar. Obviously, I didn't win.
    – Hudjefa
    Commented Mar 9, 2023 at 7:45

In a lottery, the expectation that you will definitely lose is not justified. The expectation that you are very likely to lose with a tiny chance of a huge win is justified.

Now the fact that you will have knowledge in the future that could help you today is useless. Fact is you don’t have that knowledge know, so whether your decision to play or not to play is a good decision, that is independent of the actual future outcome.

Say you are drunk. You are also hungry so you think about driving totally drunk to a fast food place through heavy traffic. Unbeknownst to you there is a fatal failure in your homes gas supply; five minutes from now your home will explode and kill everyone inside.

Driving to get food is the wrong decision. Even though that wrong decision will save your life, it is still the wrong decision.

Back to the lottery: For one dollar you can buy the hope that you might be a rich man by the end of the week, and that hope is what the lottery company sells. And you buy the emotional high when you watch the lottery draw and check your ticket. Is the hope, plus the emotional high, plus the chance of winning, worth the dollar for the ticket? You decide.

  • 1
    I can buy coffee for a dollar and feel better immediately for sure. This is why I drink coffee twice a day.
    – Scott Rowe
    Commented Mar 6, 2023 at 0:44
  • 3
    You're extremely lenient when you say that the lottery company sells a hope. I would argue it sells a lie.
    – Stef
    Commented Mar 6, 2023 at 14:24
  • @Scott Rowe - You can buy coffee for a dollar? Where do you live? In the UK I can't even buy a cup of tap water for that sort of price. Commented Mar 6, 2023 at 18:58
  • 1
    @Stef The company would not prey on hunger, it would prey on its unexpecting customers. And they would not buy if they knew that the box would be empty. But with a lottery, there is no black box: The rules are out in the open, the chance of winning is calculable, the gain of the company / average loss of the customers is calculable. They actually sell the chance of winning, even though everybody knows that they won't get anything back in almost all cases, and even that their expected gain (probability of winning times price money minus ticket price) is negative. Commented Mar 7, 2023 at 21:43
  • 1
    @Stef Or, more to the point: A lie requires intent to deceive. And lottery companies do not deceive. If you want to attack their business model, you have to attack it on other grounds than calling them liars. Commented Mar 7, 2023 at 21:48

It is irrational to buy a lottery ticket, not simply because the chance of winning are low. The expected value of the money you gain is negative. In other words, if you had enough money to buy all tickets to ensure the win, you would lose money. If you buy one ticket for every draw for the rest of eternity, you would (with probability approaching 1) lose money.

This is however only true if you value losing money and winning money the same.

If you value losing money more than you do winning money, it becomes even more irrational.

If you value winning more than you do losing, it might become rational to play until you win, depending on how much more you value the win.

  • 1
    And when you win, you should quit while you are ahead. You're ahead now.
    – Scott Rowe
    Commented Mar 6, 2023 at 10:42
  • I agree with that. I'm considering a philosophical question about what knowledge is in the context of probability.
    – Ludwig V
    Commented Mar 6, 2023 at 13:27
  • The expected value, in amounts of money, is not the whole story, especially since all money is not used the same. For instance, winning a lottery with a prize of 150.000.000€ or winning a lottery with a prize of 200.000.000€ is effectively the same; both events would transform my life in the exact same way, even though one of the events has 50.000.000€ more.
    – Stef
    Commented Mar 6, 2023 at 14:29
  • 5
    While this is typically true, there are times where the expected value of the lottery goes above 1. That is, the net payout is greater than the cost of purchasing every possible option. There was a case where an Australian syndicate purchased a large number of tickets in a Virginia lottery (and won) for this exact reason.
    – JimmyJames
    Commented Mar 6, 2023 at 16:56
  • 1
    @StevenGubkin For myself the expected utility would increase at least until it reached the amount where the money invested as close as possible to risk free would take care of the needs of myself and my loved ones indefinitely.
    – Andy
    Commented Mar 8, 2023 at 22:20

I think that if you speak strictly in terms of probability, point 2 is wrong and buying the ticket is an irrational decision. If your probabilistic model is what you describe, then the odds are extremely poor and if you end up winning it's just luck, you knew you wouldn't win, according to that model.

However, if you want to model the potential gain and the risk of buying a ticket, then probability theory is not enough and you have to switch to decision theory, where you can model the expected utility of either decision (buy a ticket or not) with an influence diagram, and there, depending on your model, you would arrive at the solution with the best utility, that is the most rational one under your modelling constraints. But these are augmentations of standard probability theory that take into account extra contextual information such as the economic gains you mention. In fact, methods for maximizing the expected utility (such as the influence diagram) have been pretty used in economics.

  • That's an interesting possibility. Thank you. But I don't think it helps my actual question.
    – Ludwig V
    Commented Mar 6, 2023 at 5:06
  • @LudwigV The point was that I don't think a question can follow from the initial analysis, which I pointed in the firs paragraph.
    – user64708
    Commented Mar 6, 2023 at 6:11
  • The analysis is in paragraphs 2 and 3 and 4. And the paradox stems partly from the fact that my belief that I will lose is justified, and I do lose, so I knew I would lose. If you include other factors losing financially may be off-set by other factors, but those considerations are independent of the argument that I knew I would lose. And the point is that one can know something that is justified only by a probability.
    – Ludwig V
    Commented Mar 10, 2023 at 11:44

You are making an assumption that it is irrational to play the lottery when you say that it makes no sense to buy something with a low probability. Then, you say, that because the gain is really high, the minimal cost is worth it. However, the latter case would still be a situation where you have a low probability of winning. This creates a contradiction in your scenario from the out go.

Either it is rational to bet on things even with low probabilities or it is rational to do so in some cases. Now, the question of whether or not it is rational is ultimately subjective. It also depends on the context. A person who has tons of money lying around may argue that it is rational to play lotteries since he does not have much to lose.

Ultimately, it depends on what you define as rational. As long as that definition is coherent, there is no contradiction.

  • Then there is Pascal's Wager...
    – Scott Rowe
    Commented Mar 6, 2023 at 0:42
  • Am I right to think that you have in mind the similarity that Pascal's wager is also a situation where a small(-ish) outlay might win huge rewards? That's true. But I don't see how it helps.
    – Ludwig V
    Commented Mar 6, 2023 at 4:58
  • 1
    @thinkingman You are right. What I should have said is the probabilities need a calculation or an estimate of the expected utility of the favourable outcome compared to the expected disutility of the unfavourable outcome.
    – Ludwig V
    Commented Mar 6, 2023 at 8:31
  • I always thought that 'rational' and 'subjective' were sort of opposite, but if 'subjective' just means that my individual circumstances figure in to the decision, then the word 'rational' begins to seem empty and pointless. There is apparently no impersonal point of view, so there is no overall 'rational' in that case. And personal rationality begins to seem like "private language". It is baffling.
    – Scott Rowe
    Commented Mar 6, 2023 at 10:49
  • 1
    @Scott Rowe I am also very puzzled about expected utility. I believe it was invented to provide some kind of objectivity for what look like subjective judgements. Very puzzling.
    – Ludwig V
    Commented Mar 6, 2023 at 16:36

The fallacy is thinking that if you win, your decision to buy a ticket was true and justified (or the best decision of their live as some would say it). If you win, you should think: considering the expected value, I was underpaid.

This is how good poker players can still improve after making a bad bet, even if they win. They are able to reflect on their decision and calculate if their win matches the risk they took and avoid that mistake in the future. Bad players feel their strategy was validated and will repeat that mistake even after continuing to lose.

The difference in Lottery is of course that you likely will play much fewer games in life than you could play poker hands. But collectively, all participants play enough games to apply probability theory. It's just that the bad decision is shared among them (including the winner).

  • You have put your finger on an important point. A decision to buy may or may not include a prediction that I will win. It does involve some beliefs, such as the belief that I will enjoy the excitement, but that's different. It could also be argued that my expectation that I will lose is not the same as a belief that I will lose, So although when I lose, my expectation is confirmed, that's not the same as having a belief confirmed.
    – Ludwig V
    Commented Mar 8, 2023 at 10:06

My rational expectation has to be that my ticket will lose, so buying a ticket seems irrational and if I knew it would lose, I would not buy it.

However, buying a ticket can be justified because the odds of a small loss are balanced against a large gain. There’s no objective criterion for that balance, so buying a ticket is not rational, but also not irrational.

You argue in your 2nd statement that there cannot be an objective criterion for that balance yet at the same time argue in your first statement that it's almost knowledge that you will lose and that it's irrational to do so? Why?

Like if it was just about how much money you make then there is an objective criterion to measure that balance: the expectation value. Meaning in the limit of infinite games the 1:100,000 ratio becomes reliable and so you can calculate jackpot-100,000 cost of ticket = net win/loss after 100,000 games. Divide that by 100,000 and you end up with the expected return per ticket.

As most lotteries only give back 2/3 of the ticket prices or less, that per game return is almost definitely negative. So regardless of winning or losing on average you'll lose money playing the lottery.

So if you look at the lottery as a reliable source of income, that would be irrational, because reliable it's only a source of income for the host of the game not the player.

There could be other motivations like thrill, hope, temporal high or other precursors to a gambling addiction. But in that case winning or losing might become a secondary motivation.

But you could also imagine the scenario that you owe money to the wrong people who vow to kill you tomorrow if you don't give them the money. But the money that you got is far less than expected and to little to run away, but enough to buy a few lottery tickets. So the odds of the lottery saving you are vanishingly low but so are your odds of survival in general and dead that money you have left is without use to you.

Now these are the ideal costumers for a lottery because they look for luck as a last resort and doing so makes them even more dependent on luck (as on average it's a money drain not a source).

Nevertheless it might be rational to buy the ticket because a low probability is still a positive probability.

TL;DR your choices in the context of statement 1 and 2 are not independent. If you think the balance is worth it, than 1 is not irrational despite the low odds. And if you think that 1 is not worth it because of the low odds than the balance in 2 is also negative.

Like even if the valuation is subjective it's likely still consistent for any given individual and you seem to apply a more general assumption on 1 but an individual for 2 which is likely not how this works.

Also the outcome of a single probabilistic event cannot be known or justifiably believed. So seeing the result doesn't change the knowledge (unless you believed it's impossible/inevitable and were wrong about that). If it was unlikely to begin with, you'll still see it as luck if you win and wouldn't be surprised if you lose. It only becomes a certainty in the limit of infinite trials of a fair game. In that case you'd gain knowledge about the probability distribution and the games expectation value. Though you'd still be clueless about an individual game, yet you could estimate if the odds are in your favor or against you.

  • Expected value applies if you are playing an infinite number of games. So it's not much help if you are playing one game, as you note. Are you telling me I don't know what the outcome of the game is after the draw? There's something odd about that.
    – Ludwig V
    Commented Mar 6, 2023 at 13:25
  • 1
    @LudwigV Expected values aren't completely useless for the application on one game as they tell you what is more or less likely, but they aren't knowledge but rather a heuristic. Oh you will know the outcome of that game, but as you started not with certainty but just with an assumption, the outcome isn't rationally effecting that assumption.
    – haxor789
    Commented Mar 6, 2023 at 13:55
  • Both comments are fair. And that tells me something about the relationship of probability even with expected utility to knowledge. So thank you.
    – Ludwig V
    Commented Mar 6, 2023 at 13:58

You are quite simply mixing up propositions (i.e., general knowledge about how lotteries work and how likely it is to win versus the concrete result of a single draw) in the layout of your argument.

Only because you know whether you won or lost after the draw, does not mean that you buying a ticket beforehand meant that you somehow "knew" that you would win (and were rational) or that you somehow knew that you would lose (and thus behaved irrationally).

This has nothing specific to do with lotteries but goes for anything that required an experiment or observation. Let's say I wish to know how many cars pass my street today. I can just guess a number. Then I can sit all day and count the cars. Me guessing the right (or wrong) number says nothing whatsoever about me "knowing" beforehand what the result would be. But back to your question.

To be more formal, for something to count as knowledge, you need some aspects, described e.g. on the Gettier Problem page of Wikipedia:

A subject S knows that a proposition P is true if and only if:

  • P is true, and
  • S believes that P is true, and
  • S is justified in believing that P is true

In your case, the fact of whether you guessed the right number of cars, or whether your ticket one, is just the first bullet point. The second bullet point, in your example, is of little importance (you do not assume to know which ticket will win before the draw). The third one is the jackpot. Even if you believe that ticket #6654 will win, and even if #6654 eventually is drawn, at no point could you claim that you were rationally justified that this would be the case (assuming it is a normal lottery which always has a negative expectation value). So no matter what you do, you would not count the fact that you won as "knowledge" that you somehow had beforehand.

Finally, all of this has nothing to do with whether it is rational or irrational to buy a ticket - this would depend on many factors (i.e., if the prize money becomes excessively large, then mathematically the expectation value could become positive, and there would come a point where it would be wise to play on the off-chance that you're the winner; or if you draw a lot of pleasure out of playing, even though you knew you would never win, and certainly wouldn't win back your money, it could still simply count as entertainment and could be worthwhile if you judge it so).

  • Probabilities justify expectations. My question is whether probabilities also provide a basis for knowledge. You are saying No, not even if the odds in my favour are very high indeed. Fair enough. But some people belief that the justification for knowledge does not have to be 100% certain. So it's a bit more complicated than you seem to recognize. The Gettier problem is a basis for rejecting the JTB analysis of knowledge , and that basis relates closely to this problem.
    – Ludwig V
    Commented Mar 6, 2023 at 16:32

Probability statements can be known.

This is true. It's the same thing as knowing the shape of the die being tossed. How many sides it has. It is not the same as knowing how it will land.

Probability statements can never justify claims to know unqualified statements about single events. But they can justify beliefs about them and those beliefs may be true.

This is known as anecdotal evidence. "I lost 50 pounds eating nothing but rutabaga for a week" may be true for them but that doesn't mean it will work for you.

Probability statements can justify decisions to act but only in combination with a calculation or estimate of expected utility and therefore only in the context of the person expecting the utility.

Oh you need much more than that. For one you need a fair game.

A classic game is the Monty Hall Problem. You have to choose one of three doors. Behind 1 is a valuable prize. Behind the other two are cheep stuffed goats. When you chose a door another one is opened and you're shown a goat. Now you're offered a chance to switch doors or stick with the one you picked.

Unsuspecting mathematicians will tell you it's always better to switch. It gives you 1 in 2 odds. Staying only gives you 1 in 3. So your choice is clear.

When you're sure you aren't being scammed.

What the game shows you is that the one conducting it knows exactly where the prize is. What you don't know is if you are only being given the chance to switch because you already picked the valuable prize. You can preach about the odds all you like but this is really about trust. Trust me when you shouldn't and I can stick you with a goat every time. And since I never told you we were playing Monty Hall I'm not even cheating.

If my ticket loses, my expectation is true and justified. So it appears to be knowledge.

All you know is that you lost.

If my ticket wins, my balanced decision is true and justified. So it also appears to be knowledge.

All you know is that you won.

This is not a direct contradiction, but it does seem odd that after the draw, I will have known the outcome whatever it is.

But what you don't know is why that outcome happened. It could be that your great uncle Stanly wants to give you 10 million dollars but doesn't want you to know. So he set up a fake lottery and got someone to sucker you into playing.

Outcomes only teach us when the game isn't rigged. Science fanatically checks against bias for exactly this reason. If the game is fair the law of large numbers takes over once you have enough trials, that is, outcomes to have reasonable confidence that your data is really telling you something you can trust. So long as no one has their thumb on the scale.

Even when the game is fair, outcomes only teach us when we do the math right. When we construct a model correctly. Get unlucky enough you can confirm a bad theory that you would have disproven if you'd have just thrown the die one more time. Which will be true no mater how many times you throw it.

One outcome only teaches you that that outcome was possible. Not exactly how likely. And only if you know what you're looking at.

We could accept that in some cases justified true belief is not knowledge.

I think therefore I am. For everything else I just hope I'm not worth the effort to fool.

We could adjust the definition of justification.

OK sure. I can justify playing the lottery regardless of the odds. I pay $1, buy a ticket, lose, and decide that was fun. Fun enough to buy another ticket. So long as no one tells me the game was so rigged I was never going to win, regardless of how lucky I got, it doesn't matter. I'm still having fun. Blissfully ignorant fun.

That's why people play the lottery. It is rational. It just has nothing to do with the math. Which is how they get ya.

Since the odds of winning the lottery are so low, and you have to get so lucky, lets use that imagined luck to give us not only a lot of money but the best lottery winning story ever.

We can use the same justification to play a different lottery. I'm playing it right now. Hold out your hand. Imagine a winning lottery ticket falling into your hand. Now snap your fingers and open your hand. Did a ticket fall into it? No? Well sorry you lose. But if you had fun it was worth it and cost you nothing but a moment of time thinking positive thoughts. It's the You-Don't-Have-to-be-In-It-to-Win-It Lotterytm. You played it just by reading this.

We could adjust the definition of knowledge.

Be careful with this. Our brains are pattern matching machines that can see rubber ducks in clouds.

This is not a direct contradiction, but it does seem odd that after the draw, I will have known the outcome whatever it is.

No, you don't really. Because a flipped coin can land heads, tails, on edge, or roll into a storm drain. However weird you think the universe is, it's weirder. But since we're not dead there must be some normal hiding somewhere.

  • 1
    Thanks for this answer. It is not unhelpful. Taking into account all the possibilities that could intervene in an actual lottery makes things very complicated. So I was working with the rules and their consequences. That means that the probabilities defined by the rules. They are not empirical for the purposes of what I'm trying to do. Whether you think that's a productive approach is another matter.
    – Ludwig V
    Commented Mar 7, 2023 at 8:37
  • It’s a productive way to teach probability. It’s a terrible way to run a casino. Commented Aug 6, 2023 at 15:09
  • I don't disagree with that. Working out the knowledge that probability gives us is very different in an empirical situation. But my question could be asked of that situation as well. Whether there is anything approaching knowledge that can be derived from a Bayesian calculation is another issue, distinct from both.
    – Ludwig V
    Commented Aug 7, 2023 at 7:59

The notion of probability is not well defined in purely physically terms, this is an unsolved philosophical problem as pointed out by David Deutsch here. There is no known way to rigorously define probability in terms of physically realizable systems, all attempts end up invoking probability in a self-referential way.

  • Thanks for this answer. I'm a bit confused about what you mean by "in purely physical terms." I did check out the link and I may have misunderstood, but it seemed to me that the propositions being discussed were not empirical, but theoretical. If you try to take account of everything that physically could happen, you do indeed get a very complicated situation which is hard to get a grip on. That's why I wasn't trying to do that.
    – Ludwig V
    Commented Mar 7, 2023 at 8:40
  • David Deutsch does have some very good points there. However, there is one thing that he misses: When you do a probabilistic experiment, you get a result with certainty. You do not know what result it turns out to be, but you know that you will have one. I.e. the sum of the probabilities of all possible outcomes must add up to exactly one, and that corresponds with the certainty above. I.e. when you throw a dice, you know that you will either get a 1, 2, ..., 6, and you will get that with certainty. And if you have six people betting on the six different outcomes, exactly one of them will win. Commented Mar 7, 2023 at 22:10
  • This is the fundamental connection between the factual world and probabilistic statements. The rest of stochastics follows from assumptions of some of the outcomes being equally probable. I.e. all six die results are equally probable, they must add up to 1, so each result must have a probability of 1/6. Still, after rolling a six 100 times in a row, you still cannot conclude that the die is loaded based on this result. Simply because that outcome is actually possible. Very low probability, but still possible. Just like winning the lottery. Commented Mar 7, 2023 at 22:15

In this statement:

If my ticket loses, my expectation is true and justified. So it appears to be knowledge.

The "knowledge" comprises your expectation combined with the observation, after the fact, that the ticket did lose. Prior to the lottery draw, all you had was a guess; afterwards you have empirical knowledge about the winning ticket, plus a guess.

If you are considering this from an outside viewpoint -- an omniscient being, say, or a person reading about it in a novel -- then there may be other things at play. In that case the gambler's expectation could be foreshadowing, or it could affect the narrative in some magical way.

But if it's you buying the ticket, then what constitutes "knowledge" is constrained by the way your subjective universe works. Your thoughts about the ticket are thoughts about a hypothetical, fictional future world, and whether your guess proves correct or not, the imaginary world you knew about remains distinct from the real world where the draw took place.

Your mental model parallels the real world to the extent that you can "know" the draw will happen on Saturday. Granted, this is a probabilistic kind of knowledge too, since the machine could always be hit by a comet. Indeed, there are ways you could be wrong about what color your own eyes are. But the categorical difference between knowing you're unlikely to win the lottery, and knowing you won't win, is that the latter stipulates a specific outcome; until you know what ticket will win, you don't know it won't be yours.

  • You are quite right. But consider this:- I arrive at the station in time to catch the 9:20 train to my destination. My belief is based on my having checked the timetable, so I know that it is due. In due course, the train arrives. Did I know the train would arrive? Most people would say that I did. You are a philosopher, so you probably won't. You will only accept conclusive justification as a basis for knowledge. Then most of what you think you know, you don't know. Are you comfortable with that? Many philosophers are not.
    – Ludwig V
    Commented Mar 9, 2023 at 11:21
  • @LudwigV I'm happy to stipulate that our knowledge of the world can only ever be contingent. "The train will be on time" and "the train will derail at 9:15" are both guesses with a nonzero chance of being proven correct. But the difference is not just one of degree; when you say you know one of these things, you have chosen that belief to be in a different category. To talk objectively about whether you know something or not, we'd have to consider how your choice-making process relates to the outside world, but at the very least that process has to exist.
    – bobtato
    Commented Mar 9, 2023 at 18:29
  • That's an interesting comment and I would agree with most of it. You take the two beliefs to both be guesses. But I don't think they are. I think I have good grounds for believing that the train will run on time - I have have checked the timetable. Most people in normal times would probably agree that I know it will. In some circumstances, when, say, the trains have been unreliable for months, they would not. But I have no reason at all to suppose that the train will derail at 9:15. No-one would think that I know it - even if it does derail.
    – Ludwig V
    Commented Mar 10, 2023 at 11:30
  • The lottery is like that. I have good reason to believe I will lose, and I do lose. So, surely, I know it? Or maybe not? That's the question. It you think I don't know it, I would hope that you would explain why.
    – Ludwig V
    Commented Mar 10, 2023 at 11:32

You totally miss the point.

We play in the lottery for amusement, not financial profit.

The potential financial profit adds some sort of thrill. Some people are more addicted to than others. The "profit" is thrill and excitement; the cost is (usually) rather small, so the thrill is not overshadowed by great risk.

While your positions are indeed valid, the assumption that rational thinking is the only driving force is wrong.

Or you could simply say that lotteries exploit a human weakness where our mind suspends rational thinking (naturally, there are human who are more vulnerable to lotteries than others). Knowledge of that human weakness makes a lottery rational for the lottery institution which can predict a financial profit.

  • 1
    That's a good answer to the question why people play lotteries. But it depends on a particular weighing of the balance between cost, benefit and risk. Rationality cannot determine the weighing of those different factors against each other, so you are right observe that it is not wholly rational. Lottery players have a different view from us, but in my book it's not irrational or rational, just different.
    – Ludwig V
    Commented Mar 10, 2023 at 11:14
  • 1
    I was told going to a game casino is like going to the movies - you go back home with less money in your pocket than when you left. As long as you realise that, and enjoy the time in between, you are fine.
    – gnasher729
    Commented May 26, 2023 at 14:47

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