So yes, I like the example I skimmed through, as well. It's all based on well-researched probabilities, and will never be completely objective, but does help decide between "smarter" and "less smart" outcomes with help from mathematically sound formulas.pbuk said:This is called a "maximax" strategy.
This branch of mathematics is called "decision theory".
You are asking under what circumstances adding an asset with a negative expected return will add value? you need more info - expected variance and covariance of the assets. The framework for this is the Sharpe Ratio - the return over the available risk-free rate divided by standard deviation.Arqane said:TL;DR Summary: Though buying a lottery ticket will almost always be a loss on average, the possible percentage return dwarfs any other type of investment. So when is the risk really worth it?
So let's say we have a lottery out there which costs $2 to buy a ticket, and currently has a $1B prize. Let's say the average return is $1.80 on that $2 (90%). Objectively, for every dollar spent, investing long-term in the stock market is mathematically better. But that doesn't take into account the maximum possible returns over a certain amount of time. A big lottery win absolutely dwarfs the amount of the greatest stock market return, so it ends up being high risk, but extremely high reward. The risk someone takes with an investment usually depends on a few circumstances, and often includes subjectivity. If you had $10,000 to invest, put only $9,998 into the stock market and bought a lottery ticket with the extra $2, the math would say that you're likely to lose $0.40 from my lottery example compared to investing the entire $10,000. With the possibility of winning $1B, the 5,500% return for Bitcoin one year looks tiny. So I guess you could do a probability graph, but what variables would be the best to include? And although I think it would still stay subjective even with the probabilities, could you come up with a reasonable rule of thumb to tell people where the probabilities cross (like saying that you should buy one lottery ticket for about every $10,000 invested in the market)? I find it an interesting exercise between the usual objectivity of math and dealing with subjective feelings of risk.
Trying to keep things simple - the same principles apply if you are dealing with lottery type binary payouts, adding fat tails just abscures the key fact that allocating to a negative expected return with zero correlation to stocks adds no value. Allocating any amount reduces the return expectation. If you disagree, then try quantifying your argumentArqane said:@BWV I'll have to translate that a bit to make sure I'm reading it correctly, but I'm not sure it would fully apply here. Here's a quote from the efficient frontier portion of that, which this formula seems to be trying to show:
"The efficient frontier and modern portfolio theory have many assumptions that may not properly represent reality. For example, one of the assumptions is that asset returns follow a normal distribution.In reality, securities may experience returns (also known as tail risk) that are more than three standard deviations away from the mean. Consequently, asset returns are said to follow a leptokurtic distribution or heavy-tailed distribution."
Of course, they're using the tail risk more as the possibility of losing more than 3 standard deviations (hence the risk part, I guess), but lottery curves tend to have insane deviation. And that was part of the point of a few of my posts. It's harder to fit a lottery win into certain formulas then you'd think, and very easy to dismiss. The shortcomings (high risk) would easily be balanced out if stocks or other investments could attain similar numbers. But unless you already have a significant amount to invest, along with substantial time, big lottery wins are out of the scope of being able to compare them directly to other investments. There has to be something in there to compensate to make a fair comparison, I think. What you wrote is pretty similar to a standard possibilities schedule in economics, it looks like. Just in this case, you'll have a pretty normal curve with one attainable point way, way out on the side.
James Holzhauer, Jeopardy! champion and professional gambler, made some good money betting on baseball while exploiting inefficiencies in the odds of gambling houses. There is an informative interview in this episode of the Effectively Wild podcast: https://blogs.fangraphs.com/effectively-wild-episode-1371-what-is-sabermetrics/PeroK said:I've not studied this in detail, but when there is a head-to-head sports contest (any soccer, tennis or cricket match or boxing match etc.) there are mutiple online betting sites that gives the odds for both sides. No individual site will give odds that add up to more than 1, but what if two different sites favour the different participants? Say online betting site A gives odds of 5/4 on team X and betting site B gives odds of 5/4 on team Y. Then, you could bet the same amount on each team on the different sites and guarantee positive return.
I have occasionally checked this out and it does seem that the different sites align with each other in this respect. I.e. the best odds on team X across the Internet plus the best odds on team Y across the internet always adds up to less than 1.
I agree with that of course, but my question is, regarding the progressive* mega-jackpots, is there a point where the expected return becomes positive and therefore there is a viable strategy to profit form it?BWV said:Trying to keep things simple - the same principles apply if you are dealing with lottery type binary payouts, adding fat tails just abscures the key fact that allocating to a negative expected return with zero correlation to stocks adds no value. Allocating any amount reduces the return expectation. If you disagree, then try quantifying your argument
The TX lottery, to my memory, had something like 1:20!million odds when it started back in the 80s, and the payout kept rolling over so it sometimes resulted in a payout over $20M - so a positive expected value, but the odds are still way low - there was an investor group that tried to buy one of every number in a VA lottery in the 90s as the expected value became significant positive, they weren’t successful getting one of each number, but did manage to winruss_watters said:I agree with that of course, but my question is, regarding the progressive* mega-jackpots, is there a point where the expected return becomes positive and therefore there is a viable strategy to profit form it?
The odds of winning the mega-millions are 1:302 million and the cost of a ticket is $2. So doesn't that mean that any jackpot over $239 million (tax adjusted, annuity option) is positive expected return?
I'm sure someone's thought this through and I have two potential ways that could fail:
1. Foiled by other players reducing the odds by also winning and splitting the jackpot.
2. Foiled by technical issues that make buying a large fraction of the tickets cumbersome.
*The point of these is that the value grows over time if nobody wins, so most people sit out until the jackpot grows big enough to be interesting, which improves the return. This could also apply to a progressive jackpot slot machine. A similar (reverse) concept would be scratch-and-win games where you can track the payout and buy tickets late if the high payout jackpots haven't been won yet.
Usually, yes, although some now incorporate ways to avoid that happening.russ_watters said:I agree with that of course, but my question is, regarding the progressive* mega-jackpots, is there a point where the expected return becomes positive and therefore there is a viable strategy to profit form it?
Yes, see for instance Stefan Mandel, Jerry and Marge Selbee etc.russ_watters said:I'm sure someone's thought this through