The concept of over betting ones edge? Definitely an expert on that, would not recommend.

lolz

Iowa should be familiar overbetting kelly from golf. As he noted in another post if one bets 20 players to win that presents a form of hedging. From that it makes sense to overbet the calculated kelly ratios due to this natural hedge.

I've bet futures and had the star player of that team blow out his Achilles in the 1st quarter of the very next game. Assuming you'll be able to make a move down the line to cover your ass is folly.

It's not the same thing.

Betting multiple entrants is a form of hedging, i.e. a likelihood one loses and another wins. EG will go up if one bets optimal ratios instead of kelly ratios calculated independent of this natural hedge.

I think we are getting confused over general hedging vs. the specific ex ante hedge.

Yes but you aren't "hedged" until you actually place the hedges. You are advocating betting 20% of roll and then HOPING for the best for weeks on end. It's utterly ridiculous.

Not sure how you got to that conclusion.

What am I missing?

Yes, that is 1 permutation. It does not explain all permutations.

Where are the permutations where KC isn't 50%-comfortable fave in the SB?

My point which I clearly stated was that the hedge odds (and hence the win equity on KC) follows a stochastic. If that stochastic can be modeled, then it makes sense to take advantage of it with a projected hedge.

Simple example. According to your model 3 equal ability teams remain for SB, one from NFC (TB) and 2 from AFC (KC, BUF). Someone has offered you +310 for KC future win SB. You have $10k bankroll.

Let your stochastic model project the following probability distribution:
-KC will be 60% win equity: 1/3
-KC will be 50% win equity: 1/3
-KC will be 40% win equity: 1/3

KC future kelly bet is $81. If they get in SB, you would bet the following hedges:
-TB 40% win equity +150: $132
-TB 50% win equity +100: $165
-TB 60% win equity -150: $198

The expected growth for the above is 0.017%.

You can do quite a bit better than that if you know you are going to hedge prior to making the future bet.

What happens to your EG if you increase the probability of KC not reaching the SB by a few %? Everyone reads 0 ROR with Kelly and straps the dynamite to their chest forgetting that all of our models have p big error bars.

These are good questions, and just what I intend to find out.

Distribution of the actual win rates does not change the kelly calculation, so long as the modeled expectation equals the expectation given by the win rate distribution.

Example 1: One is offered +105 on a prop with actual win rate of 50%, e.g. expectation = 0. What is the kelly bet size with a bankroll of $10k?

Answer: $238.09

Example 2: Assume a model projects 50% win rate, but the actual win rate distribution is as follows:

30% (0.158)
50% (0.526)
60% (0.316)

Expectation = .3*.158 + .4*.526 + .6*.316 - .7*.158 - .5*.526 - .4*.316 = 0.

So the above expresses model error.

One is offered +105 on this prop with a $10k bankroll, what is the kelly bet size?

Answer: $238.09, the same as if the win rate were 50% with 100% certainty.

My new article came out today, in which I take a deep dive into these hotly debated issues, as well as define the difference between a sharp edge and a square edge. Please check it out!

In the real world ones projected odds are vastly more likely to be "wrong" relative to offered odds than "more right". Meaning, if I am offered +100 on something I think is 52%, the true odds are going to be 49-52% a huge % of the time (95%+) and almost never say, 54%. This is why people wreck themselves trying to bet Full Kelly. You didn't really address this aspect in your latest post even though I think you think you did.

If you're just talking being able to bet huge %s of bankroll on ridiculously off market odds and promos, w/e, go nuts, but if you bring these ideas into a market with real liquidity you'll wreck yourself.

If your true odds are 49-52% 95%+ of the time, then your 52% projection is obviously not correct.

That is my entire point. You are going to be wrong often, sometimes by a lot, and if you YOLO it with risk management you'll wind up having your biggest positions on your worst bets. Sound like a good idea?

You make a great point here about the regression to market of your model projection and the effect it can have on uncertainty in your edge, which is what can cause the traditional Full Kelly answer to be an overbet. I do address that my article (and it's much more thoroughly addressed in the "Toward a Theory of Everything" article I linked to), and noted that the situation you're talking about is a sharp edge. In my last paragraph I reiterate that this can be a dangerous thing and that if you used a sharp edge for your calculations then you should reduce your stake size accordingly.

Thing is, your warning applies equally well to betting 4% in a spot with +200 odds and an 8% edge (like in the Kansas City example) as it does to betting 10% in the same spot with a guarantee to be able to hedge out of the second leg for neutral EV. That's because the neutral hedge gambit combines the edge from slightly off market odds for both legs into just the first leg. It's like you've got an 8% edge on odds of -125, which is why you can bet so much more.

So if the parameter uncertainty that you're smartly concerned about means that you should be betting half Kelly instead, then you can either bet 2% on KC straight up or bet 4-5% with your ability to hedge and double your expected bankroll growth.

The sharp/square edge thing is dumb. I have nothing against market cappers, but if you think there is no margin for error in a no vig Pinnacle/CRIS line at any given moment in time, particularly one way futures markets well then, lol. The issue is the same regardless of how you derive your edge.

The hedging strategy SGspecial and I described is mathematically sound. It does not profess to correct those who are unable to quantify an edge.

How does one figure 52% win equity on a +100 if one estimates 95% chance the WE is between 49-52%? And betting half kelly using 52% somehow makes sense?

I appreciate your feedback sir! I never claimed that there's NO margin for error in a no vig line from any particular book. But if there's any truth to the theory of efficient markets, then the errors you encounter by deriving your true odds from a sharp book's line (or aggregate of other outs) are much more likely to be normally distributed than to be skewed like in your example. That's why a square edge can be much closer to an artificial generator than a natural one, and as likely to lead to under betting as over betting.

Your math is sound in the sense that 2+2 = 4 but you aren't telling the calculator that there is a decent chance one of the 2s is actually a 1, 0, or 3.

Why aren't we using the YOLO strategy for all our bets? Pretty much everything can be "hedged" before the game/in game/at half time etc unless it can't be and goes on to lose and in those permutations we just grab some more money from the trust fund, right?

The formula considers all permutations. I already posted that.
I think you are actually coming around on this, or at least a little bit.

What you call "YOLO" is a mathematically sound strategy for any AP who can quantify an edge and has resources to wager.

In regards to your question, the examples you state are clearly not perfect hedges, and the formula presented does not work without adjustments. But even you should understand that availability of a hedge increases EG.

For example, if I have a +100 full game bet with 52% win equity for team A, and you have a source who offers no vig 2H bets, you should bet more on team A than you would without the source. Again, the formula does not work because this is not a perfect hedge. But using some math the game bet size can be derived to max EG. Even you should see why this is so without going into the math.

Your hyperbole is misleading and does not lead to any useful direction. If you care to use math to show why the formula is incorrect I'm all ears.

You also did not address this: