Risk/Reward Poll

[donjuan]

Compare (odds=+100, p=52.5%) with (odd=+1,000, p=13.636%) under full-Kelly.

Unless I'm missing something, these bets have different edges.

Does higher expected growth always imply lower risk? Isn't one advantage of logarithmic (full-Kelly) utility over quadratic (Markowitz) utility that the former takes into account higher-order moments? As such isn't it possible that due to (let's say) a sufficiently kurtotic outcome distribution the variance of a zero-growth +EV bet might nevertheless be lower than that of a higher growth bet with equivalent EV?

I looked around a little on the internet to try to find out what "kurtotic" means and the best guess I can make is that it would refer to an abnormal distribution. Is this correct? Also, not quite sure what you are referring to when you say higher order moments.

[Ganchrow]

Unless I'm missing something, these bets have different edges.

Whoops, my bad. I had misread your statement as "given two bets at full Kelly with the same Kelly stake".

The central question is, however, given identical edges, will a higher E(Growth) bet necessarilly be lower variance?

I looked around a little on the internet to try to find out what "kurtotic" means and the best guess I can make is that it would refer to an abnormal distribution. Is this correct? Also, not quite sure what you are referring to when you say higher order moments.

The first two "moments" of a distribution are the related to the expected value and the variance.

Higher order moments include skewness (related to the third moment of a distribution), and kurtosis (related to the fourth moment).

A positively skewed distribution (all else equal a "good" thing by Kelly standards) implies a relatively low probability of outperforming the mean, while a negatively skewed distribution a relatively high probability of outperforming the mean. An example of a positively skewed bet would be a lottery ticket. You risk a relatively small amount to have a relatively small probability of winning a large amount. An example of a negatively skewed bet would be going all-in pre-flop on a tight table with a garbage hand in deep stack NL Hold'em.

Kurtosis refers to what's known colloquially as "tail-risk". A highly kurtotic event is one where a relatively large (since kurtosis is always non-negative, usually one considers kurtosis relative to the normal distribution) proportion of variation comes from relatively rare occurrences. A kurtotic distribution is considered to have "fat tails". One frequently sees kurtosis in the stock market as a result of the improper identification of cross-correlation.

[Ganchrow]

That may be but, as in class, they just don't go by the lecture although I wish they would because it's easier... They have the nerve to make you prove it in a lab and that is harder...

I would like to see things proven is all... You might see or notice something you normally would not just by going the easy way...

Typically one uses experimentation to help verify unproven conjectures that can't readily be proven through first principles. The solution here is easily provable mathematical fact.

[durito]

I would think that regardless of the staking strategy, the underdog bet is more risky.

Specifically because of the fact that it will win far less often, there is much greater variance and a greater chance of not making a profit over X number of bets than with the large favorite bet.

[durito]

Hey Ganch-

Whenever I post to this thread, firefox tries to load anduin.eldar.org and displays one of your signature quotes all by itself on the page.

[Ganchrow]

I would think that regardless of the staking strategy, the underdog bet is more risky.

So would a risk-neutral staking strategy applied to a favorite necessarily be less risky than a fully risk-averse staking strategy applied to an underdog?

(A risk neutral strategy would seek to maximize EV irrespective of risk, while a fully risk-averse strategy would seek to minimize risk irrespective of EV.)

[Ganchrow]

And do the # of trials matter, say 1 vs 1000.

The same number in either case.

[HedgeHog]

I'm going to ask a stupid question. Since there is no chance of bankruptcy--an earlier given, and the fact that both have an identical 5% edge; wouldn't you "make more per bet" with the -1000 bettor because you're investing 10 times as much per bet with same edge--thus increased profitability.

PS In other words, if you bet $1000 @ 5% edge--you can expect $50 profit per bet long run; while just betting $100 @5% edge yields only $5 profit per bet long run.

[Ganchrow]

I'm going to ask a stupid question. Since there is no chance of bankruptcy--an earlier given, and the fact that both have an identical 5% edge; wouldn't you "make more per bet" with the -1000 bettor because you're investing 10 times as much per bet with same edge--thus increased profitability.

PS In other words, if you bet $1000 @ 5% edge--you can expect $50 profit per bet long run; while just betting $100 @5% edge yields only $5 profit per bet long run..

Of course.

If flat-betting you'd expect to make 10 times as much over any given number of bets.

[durito]

So would a risk-neutral staking strategy applied to a favorite necessarily be less risky than a fully risk-averse staking strategy applied to an underdog?

(A risk neutral strategy would seek to maximize EV irrespective of risk, while a fully risk-averse strategy would seek to minimize risk irrespective of EV.)

I wouldn't think so. If you were seeking to maximize EV irrespective of risk would you not find the bet with the greatest edge and then bet your entire bankroll on it?


I'm gonna stop talking out of my ass now, and go read some of the books I got myself for Christmas so I can perhaps make a more intelligent attempt at these questions in the future.

[Ganchrow]

Hey Ganch-

Whenever I post to this thread, firefox tries to load anduin.eldar.org and displays one of your signature quotes all by itself on the page.

Yeah I've noticed that that occurs when I use the Quick Reply. I thought it was just me.

Edit: I believe I've fixed this.

[Ganchrow]

I wouldn't think so. If you were seeking to maximize EV irrespective of risk would you not find the bet with the greatest edge and then bet your entire bankroll on it

Right ... so then what this tells us is that the staking strategy does matter when determining which of two or more candidate bets is riskiest.

[HedgeHog]

Of course.

If flat-betting you'd expect to make 10 times as much over any given number of bets.

So if there is no "risk" of bankruptcy, and both have the "same number of trials" as you claim, wouldn't you expect the -1000 bettor to be 10 times more profitable--because he's laying 10 times as much per bet?

[Ganchrow]

So if there is no "risk" of bankruptcy, and both have the "same number of trials" as you claim, wouldn't you expect the -1000 bettor to be 10 times more profitable--because he's laying 10 times as much per bet?

You got it.

[HedgeHog]

Even a blind squirrel finds a nut once in awhile.

[pico]

i hate socratic method of teaching. why don't you write an article of what you have in mind and use couple of examples to illustrate your point.


i think +1000 is more risky, but from my betting experience, i am more scared of making -1000 bets than making a +1000 bet.

p.s. i doubt anyone can estimate EV with good consistency and low variance over the long run. i am still skeptical of people calculating their bet size based on EV. IMO, the board has "strong information". unless you know some new development, it is like picking needle from the haystock when you cherry pick games to bet.

[Ganchrow]

i hate socratic method of teaching. why don't you write an article of what you have in mind and use couple of examples to illustrate your point.

I apologize. From now on I'll confer with you prior to making any more posts.

p.s. i doubt anyone can estimate EV with good consistency and low variance over the long run. i am still skeptical of people calculating their bet size based on EV. IMO, the board has "strong information". unless you know some new development, it is like picking needle from the haystock when you cherry pick games to bet.

As long a your estimates are unbiased, with accuracy uncorrelated to the strength of your forecasts, and without autocorrelation, then you don't really care about the variance of your estimator.

As the great poster TLD rather succinctly put it:

"It’s a mistake to think of flat betting as the default strategy, or the appropriate strategy for situations of uncertainty. When you flat bet, you aren’t being agnostic as to the degree of your edge; you’re taking a stand that the edge is equal for all bets."

[HedgeHog]

I like the brain teasers, especially the gambling related ones. You can keep posting them w/o my permission!

By the way, thanks for exposing the Bowl angle of Dec Dogs of +7 and more. I am 4-0 on it this year (overall it's 42-13 since '98). Simply remarkable.

[pico]

I apologize. From now on I'll confer with you prior to making any more posts.


As long a your estimates are unbiased, with accuracy uncorrelated to the strength of your forecasts, and without autocorrelation, then you don't really care about the variance of your estimator.

As the great poster TLD rather succinctly put it:

"It’s a mistake to think of flat betting as the default strategy, or the appropriate strategy for situations of uncertainty. When you flat bet, you aren’t being agnostic as to the degree of your edge; you’re taking a stand that the edge is equal for all bets."

unless you're a robot, kind of hard to make forcasts EV without autocorrlation or bias i bet most people have weekly patterns. the only way i can think of to overcome that is if you have a set of models that you use, using models for sportsbetting sounds kind of silly, not sure if a model even exist.

[Ganchrow]

the only way i can think of to overcome that is if you have a set of models that you use,

Now you're starting to get it.

[3put]

.

[pico]

Now you're starting to get it.

the thing is that i have never seen models for sportsbetting other than mlb. i guess simulation is a good approach for mlb because their data is way more robust than other sports. you can do montel carlo simluation and figure out the EV from that. i did look into couple of simple sabermetrics models.

for simulations, i saw espn has accuscore, and accuscore claimed that they used over 10,000 simulations to estimate the win probability(that is what they claim...i am guessing they're using montel carlo simulation). what is your take on accuscore? right now i don't really know whether to take them seriously.

i would like to know whether there are closed formed or recursive models that is not cooked up by bunch of touts.