Betting against a Futures bet for a guaranteed win?

[Cardfan]

I bet $100 on Florida futures bet, to win $500 if they win the NCAA tourney.

I could now bet $205 on a OSU +190 moneyline

Then win $290 if OSU wins
or win $295 if Florida wins

So I'm guaranteed about $290, or risk the $100 to win $500.

[JC]

Take the points and go for the middle.

[leo2302]

ditto. i agree. if you take the points and Florida wins by less than 4 points, you'll win both bets

[ShamsWoof10]

I agree with either the ML and take the sure amount or buy points up and try for the middle but likely the 4 won't matter that is why I say go for the ML... Spreads don't matter that often I do not believe....

[EaglesPhan36]

I have a similar possibility, but with OSU as my futures wager. My buddy had this situation last night. If UCLA beat FLA straight up, he would have won $300 in an office pool that he bet $40 to begin with. I talked him into taking Florida -3 for $50 and he wound up covering the cost of his office pool despite not winning.

[TLD]

Ignore your futures bet entirely when deciding what, if anything, to bet on the game. It has no bearing whatsoever on what would be the right bet to make. The only effect it has is a psychological one on you.

People love to throw money away on these “hedges.” It’s why almost all amateur blackjack players insure every blackjack. “It must be a good bet; it guarantees me a win!” No, it’s an independent bet, and in the long run—except at certain counts if you’re a card counter—the math is against it and so you shouldn’t do it.

Same with sportsbetting hedges. Don’t bet Ohio State unless you’re convinced it would be the right side if you had no future bet active on this game. One has nothing to do with the other.

[LargeMouthBass]

People love to throw money away on these “hedges.” It’s why almost all amateur blackjack players insure every blackjack. “It must be a good bet; it guarantees me a win!” No, it’s an independent bet, and in the long run—except at certain counts if you’re a card counter—the math is against it and so you shouldn’t do it.

Are you saying never take even money?

[LargeMouthBass]

Cardfan, call me a donkey, a square, an amateur or whatever you want but I'd take the guaranteed money whether you choose OSU ML or OSU + the points... Not often do you get a chance to win guaranteed money.

[tacomax]

Cardfan, call me a donkey, a square, an amateur or whatever you want but I'd take the guaranteed money whether you choose OSU ML or OSU + the points... Not often do you get a chance to win guaranteed money.

Assuming that the parameters of the initial bet are unchanged the expected value of hedging is less than the expected value of letting the bet ride to a conclusion. Taking a guaranteed payment which is less than the expected value of the bet makes you a risk-averse gambler. Nothing wrong with that, but you're never going to maximise your returns by doing this.

[nep1293]

I've done this several times in the past. I had a Syracuse future the year they won. I had a Pats future against the Panthers in the Super Bowl. It's nice knowing you have a guaranteed win but I would have won both bets anyway so i did end up costing myself some cash.

maybe put $100 on the OSU money line, that way you can still have a chance at a bigger payoff but are still guaranteed a profit

[Ganchrow]

Ignore your futures bet entirely when deciding what, if anything, to bet on the game. It has no bearing whatsoever on what would be the right bet to make. The only effect it has is a psychological one on you.

...

Same with sportsbetting hedges. Don’t bet Ohio State unless you’re convinced it would be the right side if you had no future bet active on this game. One has nothing to do with the other.

This really is not the correct way to look at this these types of situation. Remember, we're trying to optimize return AND risk. So if the risk/return profile of a bet changes substantially it may very well make sense to reduce return in order to also reduce risk (in other words, to hedge). I'll give an example which should illustrate this:

Let's say that you buy a $1 ticket in a lottery that provides you with a 1 out of a ten million chance of winning $10 million dollars. Let's further say that you have a net worth of roughly $1,000,000. Let's say a pre-drawing of the lottery is conducted and it now turns out that you are one of 100 people selected and you now have a 1% likelihood of winning the lottery. The expected value of your position in the lottery has just jumped from $9 to $99,999.

I think it's fair to say that most people in this this type of situation would probably choose to hedge out at a portion of their risk so as to guarantee some sort of profit, and would even do so if it cost them a fair bit of expected value. Even if it an insurance company charged twice as much charged double the fair rate to allow hedge a lottery participant the ability to hedge, I'd bet that most individuals would still choose to hedge. Even Kelly bettors (who are not known for being particularly risk-averse) when faced with the proposition to receive $X with the understanding that they'd pay out $198X were they to win the lottery (a startling theoretical hold of 99%) would still choose to hedeg the tune of roughly $45,000 (meaning they'd only stand to win about $1,000,000.

This isn't all just about fear either. The fact is that by hedging one is able to increase the expected long-term growth of his bankroll. Indeed, this is what the Kelly bettor always seeks to maximize.

Assuming that the parameters of the initial bet are unchanged the expected value of hedging is less than the expected value of letting the bet ride to a conclusion. Taking a guaranteed payment which is less than the expected value of the bet makes you a risk-averse gambler. Nothing wrong with that, but you're never going to maximise your returns by doing this.

I think any serious advantage player is going to have to be at least somewhat risk averse. Would you place a $100,000 gamble on the flip of a coin? I know I wouldn't. I wouldn't even place a $10 bet on a 50/50 proposition.

[chano]

I would bet more on Florida.

[Ganchrow]

So given:

OS +187
FLA -207

OS+4½ -110
FL-4½ +100


it's not surprising that Kelly prefers the slightly lower vig money line to the spread (especially when you realize that due to middling the possibility, in this scenario the spread is an inherently inferior pure hedging tool than the ML).

Assuming a $500 total bankroll (including the $100 futures bet), Kelly recommends hedging with $199.67 worth of OSU ML.

Assuming a $1,000 total bankroll (including the $100 futures bet), Kelly recommends hedging with $193.74 worth of OSU ML.

Assuming a $2,500 total bankroll (including the $100 futures bet), Kelly recommends hedging with $175.93 worth of OSU ML.

Assuming a $5,000 total bankroll (including the $100 futures bet), Kelly recommends hedging with $146.26 worth of OSU ML.

Assuming a $10,000 total bankroll (including the $100 futures bet), Kelly recommends hedging with $86.91 worth of OSU ML.

Assuming an $18,000 total bankroll (including the $100 futures bet), Kelly recommends no hedging with OSU ML.

[TLD]

Sure, there are scenarios in which you should give up value when wagering. If I need $10,000 in the next five minutes to save my life from a loan shark and the only way I can get it is risking my last $6,000 to win $4,000 on a coin flip, then I’ll do it even though it’s a bad bet in a sense. I see the lottery example the same way.

Similarly with scalping, I might make a wager that I calculate to be slightly negative EV taken in isolation, because I’m doing it in combination with another wager in a scalp, and the elimination of risk allows me to bet on each far more than I would be justified in betting on just the side where the value lies.

But if we’re talking about a normal size wager for my bankroll—not something where I bet extra in anticipation of taking the other side later—and no convoluted scenario where the value of money is skewed by a loan shark or life-changing lottery winnings and such, and a situation arises later where I can back out of it for less than its value by betting the side with negative EV, I’ll pass.

Looked at from the other side, if I were a book I’d like having players that whenever they get a lead in a bet are willing to cash it in for less than its present value.

[tacomax]

I think any serious advantage player is going to have to be at least somewhat risk averse. Would you place a $100,000 gamble on the flip of a coin? I know I wouldn't. I wouldn't even place a $10 bet on a 50/50 proposition.

Of course, the larger the sums at risk and the sums to win, the more risk averse people would become as they move nearer and nearer to their total bankroll. But in the context of the bet placed, I wouldn't lose expected value by hedging the bet half way through. If I was so risk averse then I wouldn't place the bet in the first place and wager on straight bets instead of accumulators.

[Ganchrow]

Of course, the larger the sums at risk and the sums to win, the more risk averse people would become as they move nearer and nearer to their total bankroll. But in the context of the bet placed, I wouldn't lose expected value by hedging the bet half way through. If I was so risk averse then I wouldn't place the bet in the first place and wager on straight bets instead of accumulators.

-and-

if we’re talking about a normal size wager for my bankroll ... and a situation arises later where I can back out of it for less than its value by betting the side with negative EV, I’ll pass.

Looked at from the other side, if I were a book I’d like having players that whenever they get a lead in a bet are willing to cash it in for less than its present value.

Let me say this as directly as possible (often a difficult task for yours truly).

A completely rational advantage player placing "normal-sized" wagers, be they singles, accumulators, or futures, will at times find it optimal to place negative EV wagers in order to hedge positions based upon changes in the market. These changes may consist of both changes in price and changes in underlying circumstance.

Disagreement with the above represents an extraordinarily commonly held misconception regarding the nature of risk and risk management. But from an economic and mathematical perspective there really is no argument.

I'm just going to give a specific example and see if those interested can't work through it.

At the beginning of a golf tournament Tiger Woods is offered at +120 to win (implying a roughly 45.45% win prob). A bettor with a bankroll of $100,000, believes that Tiger's true probability of winning the tournament is really 50%, implying an edge of 10%. Being a quarter-Kelly bettor, he risks $1,136.36 on Tiger Woods to $1,250.

Tiger performs roughly to expectations and at the start of the last day of the tournament his market is currently ~ -235 (exact decimal odds of 1.425) to win and +185 to lose, implying a theoretical hold of 5% and a win probability of 66.67%. The bettor has no insight into the current market.

So what does our bettor do? Well my contention is that as quarter-Kelly bettor the proper play is to risk $150.49 (to win $278.41) on Tiger to lose the tournament.

So what's happened? If the player made the bet before, why should he expend capital on a negative EV bet to reduce his exposure now? The answer is that the event profile has changed. No longer is the outcome a 50/50 occurrence -- it's likelihood has increased by a third. This means the bettor now has what amounts to an unrealized profit. He wins $1,250 with probability 2/3 and loses $1,136.36 with probability 1/3 (an EV of ~$454.55).

Think about that outside of the framework of a sports bet. If you the reader had a bankroll of $100,000 and someone offered to pay you $1,250 if a rolled die came up 1-4, as long as you'd pay $1,136.36 if it came you up 5-6, you'd probably accept the bet, but at the same time (remembering your total bankroll itself is only $100,000) you might look for a partner with whom to share some of the risk. You might even go to an insurance company and buy an insurance policy against that 5 or 6 appearing.

Well that's what's happening in the case of the bet on Tiger Woods. The bettor is giving up ~ $7.52 in EV for a partial insurance policy ... one that allows him to transfer a small part of the profit he'd realize were Tiger to win, in order to cover a part of the loss he'd experience were Tiger to lose.

In theoretical terms what's going on is that as the probability of a bet winning increases, unrealized profit on the bet also increases and hence the odds received on that bet consequently decrease. As such, the bettor is essentially risking more on that bet than his risk parameters would dictate. This is often the result of having placed a compound bet (i.e. a parlay or a future), but it bears mentioning that this same exact conclusion can be derived even when placing single bets.

If a player were to bet an NFL game at +7.5, and an hour before kick-off, the line had moved to 6.5, it may very well make sense for him to place a bet on the the other side at -6.5 (or even sell it down to -7.5) even if he believed the spread should in fact be even lower.

[Ganchrow]

At the beginning of a golf tournament Tiger Woods is offered at +120 to win (implying a roughly 45.45% win prob). A bettor with a bankroll of $100,000, believes that Tiger's true probability of winning the tournament is really 50%, implying an edge of 10%. Being a quarter-Kelly bettor, he risks $1,136.36 on Tiger Woods to $1,250.

Tiger performs roughly to expectations and at the start of the last day of the tournament his market is currently ~ -235 (exact decimal odds of 1.425) to win and +185 to lose, implying a theoretical hold of 5% and a win probability of 66.67%. The bettor has no insight into the current market.

So what does our bettor do? Well my contention is that as quarter-Kelly bettor the proper play is to risk $150.49 (to win $278.41) on Tiger to lose the tournament.

In case anyone's interested, I talked about how to perform these calculations in this post: Using Kelly To Determine Optimal Hedging Strategy.

[tacomax]

Disagreement with the above represents an extraordinarily commonly held misconception regarding the nature of risk and risk management. But from an economic and mathematical perspective there really is no argument.

I'm just going to give a specific example and see if those interested can't work through it.

Agree completely with the examples. But in the Tiger Woods example you quoted, the bettor had a +ve EV when the initial place and laid off the bet in-play where he had no idea as to what the price should be. In the NFL example, the spread changed from +7.5 to +6.5 in the interim period of the bet being placed.

My assumption was that if there has been no changes to the parameters of the original bet (i.e. nothing had changed - no injuries, line movements, adverse news stories etc - in the bet between it being placed and now) then the bettor, again assuming that he has a sufficient bankroll to place the bet in the first place, should let the bet ride to maximise the expected value.

[TLD]

Thanks for the explanation Ganchrow. It makes it clearer when a hedging style bet can make sense mathematically (just as the negative EV side of a scalp can).

A few quick comments (which don’t constitute a disagreement with the math).

Most “real world” examples of hedging do not match what you are describing and are made for other—mathematically unjustified—psychological reasons as I alluded to earlier, e.g., “It guarantees me a profit, so it must be the right play!” like taking insurance on a blackjack.

“Hedgers” generally are trying to lock in a profit. So in your Tiger Woods hypothetical, for example, they would likely bet enough on that +185 second bet to win more than their original risk of $1,136.36, which wildly exceeds your recommended bet of about one-fifth that. So even an example chosen because it’s a decent size risk relative to bankroll and because the underlying circumstances changed significantly, generates a recommended “hedge” wager only a tiny fraction of common hedging practice.

Also, consider the parlay case. A person places a seven team parlay where the outcome of the first six legs will be determined before the seventh begins. He wins the first six and decides to lock in a profit by placing a straight bet on the other side of the seventh.

The right play? There’s a good chance it is, given your analysis. But I’d say all he’s really doing is mitigating the damage of an earlier error. Depending on the changes in the underlying circumstances, it may well be that hedging the seventh game (though again for a much lesser amount than people in real life tend to hedge) is better than letting it ride. However, wouldn’t betting a six game parlay in the first place have been better than either? That way you wouldn’t have to pay a penalty now to back out of that seventh leg.

Example:

Twin brothers A and B like a certain seven games at the Greek. Six start at the same time; one is a later game.

A bets $10 on a seven team parlay at 75 to 1, with the intention of hedging out of the seventh leg if he’s lucky enough to win the first six.

B bets $10 on a 6-team parlay at 40 to 1, leaving the seventh game for a later straight bet.

Assume the first six legs win. A the hedger is six-sevenths of the way toward a $750 winning parlay. He bets $396 to win $360 on the side he doesn’t even like in the seventh game. That way he’ll either win the parlay ($750 minus a loss of $396 on the straight bet) or win the straight bet ($360 minus a loss of $10 on the parlay), for a profit of about $350.

Meanwhile B has already won $400, and is free to make a straight bet on the seventh game on the side that he determined going in has value.

Maybe A is mathematically better off placing a small hedge (much smaller than $396 to win $360) on that last game than just letting the parlay ride, but I’d rather be in B’s position.

[Ganchrow]

the bettor had a +ve EV when the initial place and laid off the bet in-play where he had no idea as to what the price should be. In the NFL example, the spread changed from +7.5 to +6.5 in the interim period of the bet being placed.

My assumption was that if there has been no changes to the parameters of the original bet (i.e. nothing had changed - no injuries, line movements, adverse news stories etc - in the bet between it being placed and now) then the bettor, again assuming that he has a sufficient bankroll to place the bet in the first place, should let the bet ride to maximise the expected value.

Well that was just the way I told the story.

This could just as much apply in the case of a player who wagered on a futures contract (e.g. Florida to win the 2007 NCAA National Championships) and is then faced with a hedging decision at the doorstep of the final round. In other words, a player in exactly the same situation as the OP.

[Ganchrow]

Most “real world” examples of hedging do not match what you are describing and are made for other—mathematically unjustified—psychological reasons as I alluded to earlier, e.g., “It guarantees me a profit, so it must be the right play!” like taking insurance on a blackjack.

“Hedgers” generally are trying to lock in a profit. So in your Tiger Woods hypothetical, for example, they would likely bet enough on that +185 second bet to win more than their original risk of $1,136.36, which wildly exceeds your recommended bet of about one-fifth that. So even an example chosen because it’s a decent size risk relative to bankroll and because the underlying circumstances changed significantly, generates a recommended “hedge” wager only a tiny fraction of common hedging practice.

In fact I'm attempting to be prescriptive as opposed to descriptive. The example I gave was mild in that the change in odds was fairly slight. Had the change in odds been more drastic, the recommended hedge would have been larger and likely more in keeping with your expectation of the behavior of the typical hedger.

But the truth is that irrespective of real world examples this is the manner in which a player attempting to maximize the growth rate of his bankroll should behave.

Also, consider the parlay case. A person places a seven team parlay where the outcome of the first six legs will be determined before the seventh begins. He wins the first six and decides to lock in a profit by placing a straight bet on the other side of the seventh.

The right play? There’s a good chance it is, given your analysis. But I’d say all he’s really doing is mitigating the damage of an earlier error. Depending on the changes in the underlying circumstances, it may well be that hedging the seventh game (though again for a much lesser amount than people in real life tend to hedge) is better than letting it ride. However, wouldn’t betting a six game parlay in the first place have been better than either? That way you wouldn’t have to pay a penalty now to back out of that seventh leg.

Inn the example you've given there's a good chance the player should have behaved differently to start -- but that should in no way impact his proper decision ex-post and as such has no bearing on my own recommendation in this particular situation.

I'll add, however, that there are plenty of times that a player should bet a parlay, and plenty of times that after one or more legs of that parlay have been decided the player should hedge. We're not talking about wildly improbable scenarios, either. We're talking about situations that can and do occur all the time.

The OP described his situation and asked for advice. Regardless of his possibly questionable decisions for having made the bet in the first place, his growth-maximizing decision at the point in time the question was asked was (assuming a bankroll of less than about $18K) to hedge part of his bet. The fact (were it so) that he might have arrived at his situation due to a miscalculation should not be relevant to his decision making process.

Ignore your futures bet entirely when deciding what, if anything, to bet on the game. It has no bearing whatsoever on what would be the right bet to make. The only effect it has is a psychological one on you.

What I really want to do to is drive home the point that the above statement is simply untrue within the framework of a proper system of risk management. I've seen and heard plenty of extremely smart, highly quantitative bettors make this claim, but it's nevertheless inaccurate and ignores the risk side of the equation. And it's not just about about some subjective measure of risk either -- proper hedging will ultimately result in higher expected bankroll growth, and as such provides a concrete, objective measure of the effectiveness of a given series of hedges.

[TLD]

Didn’t mean to be disputing your prescriptive point; I thought you made a convincing case for it in your previous posts. I was adding to the conversation some related points, speculations, and questions; some of a descriptive nature.

I didn’t think hedging was justified even to the extent you’ve shown it is, so I stand corrected.

My concern though is that someone could come away from the thread thinking the gist of it was “Ganchrow endorses hedging” and not understand “only in some cases,” “usually for only a small portion of the original bet,” “often only as the lesser of the evils to undo an earlier error,” “though not for the reason that most hedgers hedge,” etc.

An optimum bankroll growth maximizing strategy, as you’ve shown, can include some negative EV hedging plays just as it can include some negative EV sides of scalps. But I strongly suspect that most real world hedgers hurt themselves more through their practices than I have hurt myself by refusing to consider hedging at all.

[Ganchrow]

My concern though is that someone could come away from the thread thinking the gist of it was “Ganchrow endorses hedging” and not understand “only in some cases,” “usually for only a small portion of the original bet,” “often only as the lesser of the evils to undo an earlier error,” “though not for the reason that most hedgers hedge,” etc.

I somehow doubt that I have so big an audience.

I strongly suspect that most real world hedgers hurt themselves more through their practices than I have hurt myself by refusing to consider hedging at all.

I would have to agree with that suspicion.

[TLD]

I did want to reiterate, though, that I concede that you’ve shown to my satisfaction that the absolutist anti-hedging position I originally stated is not the optimum approach for expected bankroll growth. I only wish that when people want to dispute something I (or anyone else) post, they could do so with your substance and tone, regardless of whether they succeed or fail in showing me to be in error. It would certainly make the forums a more civil and educational place to hang out.

[Cardfan]

I bet $100 on Florida futures bet, to win $500 if they win the NCAA tourney.

I could now bet $205 on a OSU +190 moneyline

Then win $290 if OSU wins
or win $295 if Florida wins

So I'm guaranteed about $290, or risk the $100 to win $500.

The question became would I be willing to risk $390 ($100 already at risk, + $290 guaranteed I could win) to win $500, and take Florida straight up to win the game.

I couldn't get that kind of bet anywhere, and I still liked Florida to win. I let it ride, and am much happier that I did.

Interesting discussion.