To hedgers: Adding insult to injury

[pzhon]

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phzon,

you are wrong. the hedgers not only lowered their variance but also increased their EV quite significantly (over $200) through bonuses.

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Non-hedgers could get the same bonuses.

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So could people who hedged 90%, as I have pointed out repeatedly. The existence of bonuses does not justify the mistake made by hedging 100%.

[E.Z.]

this OP has lost his mind. spends all day writing these drawn out threads and cant even get the math right.

full hedge is 523.8 to win 476.2

where's the $50 that you speak of??

also, when 50% of these people didnt even know what a spread is or how to make a bet i think we can assume they wouldn't be signing up for every sportsbook known to man. they got a bonus and kickback from a site they never heard of or would sign up with anyway.

OP also fails to mention that those that got in -5 took the risk of injuries on either team before gametime.

what do you know, we had a team at gametime that was a coin-flip to win but us non-hedgers needed them to win by 6. save your time OP and get a life.

[pzhon]

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full hedge is 523.8 to win 476.2

where's the $50 that you speak of??

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The house advantage on the full hedge was roughly $25, not the $50 I had stated in the original post. That doesn't change my point, that making a 100% hedge was almost certainly incorrect for an advantage gambler.

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OP also fails to mention that those that got in -5 took the risk of injuries on either team before gametime.


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Wow, are you so confused that you think that is relevant? I bet you aren't actually that stupid, and that you are trying to distract attention from your inability to admit that you are trying to defend something that is clearly wrong.

I will ignore you henceforth.

[E.Z.]

OP needs to change topic to

to advantage gamblers that were planning on hitting up every sportsbook bonus and reload known to man before this mansion promo.

right OP?? for those few people i understand your point, but this thread says to hedgers and the majority that hedged made it EV cause they simply dont bet sports and would of never used the book they hedged with.

[thing85]

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If you recognize that hedging 100% was wrong, but decided it was too much effort to do better, that's ok. Not noticing that hedging 100% was wrong indicates a conceptual error that is likely to be repeated. Being unable to admit that hedging 100% was wrong after it is pointed out and explained by a mathematician is just being dense.

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I recognize the 100% hedge was not an optimal choice. The fact of the matter was, I've never bet on sports before and when this promotion came about, the 100% hedge was worded as a "risk-free" way to make a "guaranteed profit" of $X. Knowing that I lack the knowledge of sportsbetting, I accepted a wager that yielded a satisfactory return. Busy with other things, it simply wasn't worth my time to figure out the correct way to make the optimal hedge, squeezing out a little bit more in EV.

The argument that I'm making can't be quantified in terms of dollars gained or lost. Considering my level of risk tolerance, time constraint and lack of knowledge in sportsbetting, my decision, while technically suboptimal, was correct for me at the given time. This may seem to be drawn out way of me saying "I was stupid and accepted it," but that's basically what it was.

[pzhon]

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For sufficiently small fair coin-tosses for $x, the expected value (utility) of the gamble is about
-x^2 V"(0)/2
~ V(- 1/2 x^2 V"(0)).


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I made a sign error throughout this. The result should be V( 1/2 x^2 V"(0)).

V" should be negative for someone who is risk-averse, and more negative for those who are more averse to risk. Those with larger bankrolls should have a V" closer to 0.

[Ortho]

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The first half of the full hedge gives you 3/4 of the value, while the last half gives you 1/4 of the value. So, in some sense, the last half is 3 times as expensive as the first half.

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OP, could you elaborate on the above quote from your original post?


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In an expected utility context, there is something fundamentally quadratic about risk. Except in contrived situations, the cost of making a wager that is 2 times as large is about 4 times as great, at least for small wagers. Betting $100 on a fair coinflip is like making 10,000 $1 wagers.

More technicaly, let your utility function be V, normalize you initial bankroll to be 0, V'(0)=1 and V(0)=0, and consider the certainty equivalent of a fair coin-toss. For sufficiently small fair coin-tosses for $x, the expected value (utility) of the gamble is about
-x^2 V"(0)/2
~ V(- 1/2 x^2 V"(0)).

So, the certainty equivalent of wagering $x on a fair coinflip is about $-1/2 x^2 V"(0). That's the damage to our utility by wagering $x, expressed in $. The certainty equivalent of wagering $2x is about 4 times worse, $-2 x^2 V"(0). You should be willing to pay up to about $3/2 x^2 V"(0) to reduce the $2x bet to $x, but only about $1/2 x^2 V"(0) to reduce the $x bet to 0.

The first half of the hedge bet costs just as much as the second half of the hedge bet, but it gives you 3 times as much of an improvement in your certainty equivalent. The first 1/10 of the hedge bet gives you 19 times as much of an improvement as the last 1/10.

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I have only in the last few months learned about certainty equivalents, and this "different CE at different hedge levels" is a very interesting point for me.

Can you recommend a book where I can learn the basics of this stuff? At this point, the high point of my knowledge is understanding how to compute a CE given bankroll size, EV, probability of winning/losing, and bet size. I basically understand why that all works, but I hardly have it crushed. Do you know of a good starter text on this?

[JPT III]

OK, without taking any position as to who is arrogant, who is smart, who is dumb, or who's has the largest penis, I think the concept espoused by OP is correct, and important to keep in mind going forward. I'm not sure some of you guys are understanding it as expressed, and would like to set forth a simpler, less mathematical explanation that I hope some of you will consider when facing this scenario in the future. This, to me, is the real-life, practical application of the concept OP writes about. If I've got this wrong, I know he'll step in and correct me. Here's why you probably shouldn't hedge all the way in the future (and I'm going to use mathematical APPROXIMATIONS):

Suppose I offered to give you $475. As, say, a birthday gift. It's yours, keep it. Next year on your birthday, I'm going to do you one better. Since I know you like games of chance, but also like money, I'm again going to give you $475, but IN ADDITION I'm going to let you wager on a coin toss, in any amount you want up to $475, laying 10 to win 11. One toss, one wager, but for every 10 you bet, if you win I'll pay you 11. Feel free to wager part or all of the $475 gift I'm giving you, or wager none and walk away with the $475.

Now tell me, for your birthdays on years 3, 4, and 5 (upcoming), would you prefer I give the gift I gave you on year 2 or that which I gave you on year 1, or do you not care? Of course you'd take the year 2 gift every time, as you would likely take advantage of the 11-10 coin toss wager, for some marginal +EV. After all, you're getting $475 cash with each gift, why not invest in this +EV opportunity that comes with it?!

Now, the point here is that most of us would probably not risk the entire $475 to win $522, but most of us would not walk away without wagering something on the coin toss either. I think I'd wager, maybe, $100 (to win $110), locking in a profit of $375, but with a 50% chance of taking away $585. Some of you would wager $30, some $350, and so on. Most would not walk away from the +EV of the 11-10 wager, but also would not risk the entire $475 either.

This is exactly what happens with the Pitt/hedge/don't hedge scenario. Manison gave you gift of $475 (Approximating here!!). That's what you take away if you hedge the whole thing. And as OP pointed out, for every $10 you take away from your hedge wager, you stand to win (50% chance) $11 (because, on the hedge wager, you're laying 11 to win 10). So why not grab some of that +EV with your newly acquired $475 -- in whatever amount you're comfortable risking? After all, even the absolute cheapest, sluttiest, tramp of a bonus whore routinely undertakes risk for the benefit of +EV in the long run. With $475 to play with, we'd all probably jump at the chance to wager some part of it on a +EV wager. Those of us that did not hedge at all are the equivalent of those birthday present recipients that bet the whole $475 on a coin toss (Pitt) for a 50% shot at winning approximately $1,000. Those of us that hedged the whole thing are those that wouuld walk away from the coin-toss event without betting anything. In real life, if it were birthday gifts and coin tosses, rather than sports wagering, most would not walk away without wagering some part of the $475 on the coin toss.

While everyone's 11-10 coin-toss wager amount might differ, and ultimately be a function of each's personal risk aversion factor -- doubtless the wager is something most would take, in some amount or another.

This is why OP can say with certainty that to hedge the whole amount is almost always wrong (although not knowing what amount would make it right).

Note: Forget other bonuses, kickbacks, etc. That's not the point here (and they can be acquired regardless). Forget line changes and possible injuries, as they are a wash in the long run and impossible to predict. This is an "all other things being equal scenario."

Or do I have it all wrong, OP?

Now discuss, and be nice to one another...

[pzhon]

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While everyone's 11-10 coin-toss wager amount might differ, and ultimately be a function of each's personal risk aversion factor -- doubtless the wager is something most would take, in some amount or another.

This is why OP can say with certainty that to hedge the whole amount is almost wrong (although not knowing what amount would make it right).

Or do I have it all wrong, OP?

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We agree.

[econophile]

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Recall the notion of Pareto efficiency in a related (but not identical) context.

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Pareto efficiency has nothing to do with the optimality of hedging since the hedging decision involves only one person and Pareto efficiency applies to allocations of resources between multiple agents.

It is easy to write preferences for which a 100% hedge would maximize utility even if hedging sacrifices a significant fraction of the bet's expected value, despite what you think you've proven.

BTW, pz, do you have medical, house, car or fire insurance?