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To hedge or not to hedge, here is the math and why hedging is a bad idea....

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Posted: #551
Quote Originally Posted by vanzack:

You dont read my post but you dont agree with what I am saying?

How do you know what I am saying?

Unreal.

When vanzack writes (speaks) not everyone reads (listens)...lol

 
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Posted: #552
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Posted: #553
Quote Originally Posted by MLBguru:

Yea but there's a sound problem with this reasoning to a degree.
 
Let's say you take the 4th game off the parlay like you said...now you are left with 3 games.  Now say the first two win....now you're in the exact same situation as you were with the 4 game parlay.
 
You now have to choose whether to hedge or not.  And if you planned on doing it with a 4 gamer, what makes it any different with 3? 
 
Plus it's not likely after I cash my 3 gamer, that I would go and throw all of it into the 4th game...even if I like the 4th game.  It would still be smarter to bank some of it and just straight bet the last game.  And in that situation, you're still banking some in the interest of guarunteed money.
 
So really it's not that different.

 

It really sounds like you shouldn't be betting 4-team parlays in the first place.  A 4 team parlay is like giving your bookie an order to say double or nothing 3 different times.  Of course, with all the vig, it isn't "double or nothing", its more like "1.82 or nothing".  If you don't like doing that, you shouldn't be playing parlays. 

If you aren't comfortable with the idea of letting the entire 3-team parlay ride on the 4th game, you shouldn't be betting the 4-team parlay.  If you aren't comfortable letting the entire 2-team parlay ride on the third game, you shouldn't be playing 3 team parlays, etc, etc.

Hedging is just turning a 4-team parlay into a 3-team parlay (**at considerably worse odds than a traditional 3-team parlay)

The people arguing in favor of "guaranteed money" are really just arguing against playing 4 team parlays in the first place.  Its a reasonably good argument (I don't like parlays), but I can't help but wonder what in the hell they were thinking when they bought the ticket.  I mean I don't smoke and I don't recommend you smoke, but if you pay $5 for a pack of cigarrettes, you are better off smoking the damn things than selling them for $4 and going to buy another pack.

 

 
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Posted: #554
Personally, when I do hedge, its just to get the dollar amount back from the bet to wind up even or up. Not really a big parlay guy, but when I do, its house money. No sense in donating my hard earned cash...
 
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Posted: #555
Quote Originally Posted by tallguyindc:

 

It really sounds like you shouldn't be betting 4-team parlays in the first place.  A 4 team parlay is like giving your bookie an order to say double or nothing 3 different times.  Of course, with all the vig, it isn't "double or nothing", its more like "1.82 or nothing".  If you don't like doing that, you shouldn't be playing parlays. 

If you aren't comfortable with the idea of letting the entire 3-team parlay ride on the 4th game, you shouldn't be betting the 4-team parlay.  If you aren't comfortable letting the entire 2-team parlay ride on the third game, you shouldn't be playing 3 team parlays, etc, etc.

Hedging is just turning a 4-team parlay into a 3-team parlay (**at considerably worse odds than a traditional 3-team parlay)

The people arguing in favor of "guaranteed money" are really just arguing against playing 4 team parlays in the first place.  Its a reasonably good argument (I don't like parlays), but I can't help but wonder what in the hell they were thinking when they bought the ticket.  I mean I don't smoke and I don't recommend you smoke, but if you pay $5 for a pack of cigarrettes, you are better off smoking the damn things than selling them for $4 and going to buy another pack.

 

Very well said.

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Posted: #556
I will say this about parlaying and hedging. I think you're dead on with hedging. It never ever makes sense mathematically to hedge a parlay ever. That seems to be very well stated throughout this thread.

I do think though that there is mathematically an advantage to parlaying though.

Parlays should never be played by themselves, period. It doesn't make any sense and VanZack does a great job of illustrating that. If you like all the games you're parlaying, you're better off just playing them individually.

Yet, you're actually better off playing those games individually and also placing smaller wagers on the different combinations you can make with those games in parlays. Playing these games separately by themselves while at the same time parlaying multiple combinations of the games, increases your risk adjusted reward.

The less you like multiple games or think of have a slight advantage on a few games, the more the weight of the wagers should be placed on the individual bets with a small fraction devoted to the parlays. The greater you like two games, then the weight on the individual game wagers decreases and the weight of the bet on the parlay increases.

So with all the math that has been devoted towards proving why hedging isn't ever a good idea, I thought it should be brought up that declaring parlaying is never a good idea either is also wrong. Now there is a certain way to go about parlaying, as I said there is a certain responsibility that comes with it, which is knowing how much one should weight the parlay wager in relation to the individual wager.

Here is the most ridiculous but hypothetical example to prove this:

You have two wagers you know that have 100% chance of winning. Like I said, this is hypothetical. (Maybe you found a sports almanac from the future or something, but anyways).

Now someone who declares to never ever bet a parlay would be stupid to place these bets individually. Placing the bets solely individually in any distribution that uses 100% of your bankroll, will give you a return of 191% of your bankroll for a 91% profit. (at -110 odds) Yet, anyone in there right mind would parlay these two games with there entire 100% bankroll, which would return 361% of the bankroll for a 261% profit.

 
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Posted: #557
I meant to say 360% and 260% above there...

(And to clarify I stated that placing a parlay by itself is never mathematically right, but the only time it would be is if each better had a 100% chance of winning, never any other time, but that is why in my example only a parlay bet is used to maximize profit)
 
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Posted: #558

FreakyFresh -

If you have multiple +EV plays, you are better off parlaying them DEPENDING UPON THE PAYOUT OF THE PARLAY.

If you can get a true odds parlay, and your plays are +EV - then you are correct that you should parlay your plays.

But the problem is that most parlays payouts are so heavily juiced that it kills the +ev.  In other words, if you are getting 10-1 on a 4 team parlay (normal payout) when you should be getting 15-1, its hard to overcome that juice even if your 4 plays are individually +EV.

Overall, in theory, you are correct - but in practice - the average gambler has a very hard time (including myself) accurately figuring out EV percentages of plays before a game starts - and that is my problem with both Kelly and also in this parlay example.  It relies on accurate pre-game calcualtion of EV.

 

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Posted: #559
Van, ever hear the phrase "Never argue with a fool, because someone watching might not be able to tell the difference."  ?

We live in a country filled with innumeracy.  This is why people can't understand their mortgages or their retirements.  This is why BS mutual funds stay in business.  This is how Vegas keeps it's lights on.

Fundamentally, gambling is a risk/reward game ,and if you can't understand the VERY BASIC math behind it, you're not only a fool, but you're a sucker.  And you are certainly not an investor.

The bottom line is there is no "guarenteed" money.  You have "guarenteed" money at the beginning of the day, i.e. the money in your bank account.  After 3 games that money has increased.  You are now presented with a bet that will lose you money and a bet that will win you money, based on VERY SIMPLE and FUNDAMENTAL principles of probability that you MUST understand if you are going to gamble, and yet we have the idiots here who INSIST on the bet that will lose them money.

My point?  Why try to educated them, especially when they will be as stubborn as they are here.  Just let them bask in your ignorance, and enjoy their $$$.

 
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Posted: #560
Oh and another note, I am an engineer but I wasted most of my college playing poker.  I am now in a picks pool with poker friends and the entire pool is KILLING it.  There is nobody under .500 out of 15 and most are above .6.  Only about 3 even watch sports.

I am now completely convinced that the person who understands gambling will be far more successful at sports betting than someone who understands sports.
 
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Posted: #561
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Posted: #562
Calculating EV

The expected value (EV) of a wager is a measure of how much each dollar is worth over a series of wagers. It is not how much you win on a wager.

EV = Expected Value per dollar wagered
EG = Expected Gain/Loss
EQ = Expected Gain/Loss per dollar wagered

EW = Expected win for a series of wagers
EL = Expected loss for a series of wagers
AW = Amount won on a winning wager
AL = Amount lost on a winning wager
OW = Odds of winning a wager
OL = Odds of losing a wager
WA = Wager amount

OW + OL = 1
WA = | AL |

EL = AL x OL
EW = AW x OW

EG = EW + EL
(Note: EL is always negative or zero – if you use | AL | in the EL equation then EG = EW – EL)

EQ = EG / WA

EV = 1 + EQ

EV = [ WA + (AW x OW) + (AL x OL) ] / WA

One could find many examples of this formula in some form on the Internet that do not divided by WA. That is because they always assume a $1 bet. You must change the wager amount to $1 or divide by WA.

The assumptions used are very important since in reality they are generally not true.

1)       The odds of winning a bet on any single game are 50/50.
2)       The world in which we are calculating is statistically perfect. This means if the odds are 50/50 you are going to win a bet then lose a bet (or lose, then win) with the sequence repeating. Every 2 bets will result in 1 win each and every time.
3)       The first 3 teams on the parlay are guaranteed winners. Obviously the odds of winning a 3 team parlay are not 100% but for this discussion it is required.

Option1:

In this option there is no possibility of “losing” so AL and OL are both 0:

EL = $0 x 0 = $0

There are 2 possibilities both resulting in the same win amount and OW is 1:

AW = $424
OW = (2 / 2) = 1

EW = $424 x 1 = $424

The expected gain is the same as the expected win since there is no loss component:

EG = EW + EL = $424 + $0 = $424

The amount you can expect to win on every dollar bet:

EQ = EG / WA = ($424 / $676) = $0.63

The expected value (EV) of each dollar bet is:

EV = 1 + EQ = $1 + $0.63 = $1.63

This is easy to prove due to our statistically perfect world and the fact that there are only 2 possibilities.

Option1 possibilities (Bet $100 to win $1000 and bet $576 to win $524 although each bet is mutually exclusive):

1)       Parlay wins. Walk into sports book with $676 and walk out with $1100 ($100 + $1000).
2)       Parlay loses. Walk into sports book with $676 and walk out with $1100 ($576 + $524).

Total amount in pocket once the sequence is over = $2200
Total amount wagered for the sequence = $1352

$2200 / $1352 = $1.63

Each dollar wagered is worth $1.63.

Option2:

This option results in losing $100 half the time so:

EL = -$100 x (1 / 2) = -$50

This option results in winning $1000 half the time so:

EW = $1000 x (1 / 2) = $500

The expected gain of this sequence:

EG = EW + EL = $500 + (-$50) = $450

The amount you can expect to win on every dollar bet:

EQ = ($450 / $100) = $4.50

The expected value (EV) of each dollar bet is:

EV = $1 + $4.50 = $5.50

Again only 2 possibilities so the proof is easy due to our statistically perfect world.

Option2 possibilities (Bet $100 to win $1000 or lose $100):

1)       Parlay wins. Walk into sports book with $100 and walk out with $1100 ($100 + $1000).
2)       Parlay loses. Walk into sports book with $100 and walk out with $0.
 
Total amount in pocket once the sequence is over = $1100
Total amount wagered for the sequence = $200

$1100 / $200 = $5.50

Each dollar wagered is worth $5.50.

Option3:

As in Option1 there is no possibility of “losing” (see assumption #3) so AL an OL are both 0:

EL = $0 x 0 = $0

There is only 1 possibility so:

AW = $600
OW = (1 / 1) = 1

EW = $600 x 1 = $600

The expected gain is the same as the expected win since there is no loss component:

EG = EW + EL = $600 + $0 = $600

The amount you can expect to win on every dollar bet:

EQ = ($600 / $100) = $6.00

The expected value (EV) of each dollar bet is:

EV = $1 + $6.00 = $7.00

Even easier to prove with only one possibility as you walk in with $100 and walk out with $700. Each dollar wagered is worth $7.00.

Option1A:

I noticed quite a few posters stating they only hedge enough to cover the parlay bet. Let’s call that Option1A. So the hedge bet is $110 to win $100 which yields 1 win of $890 and 1 loss of $0.

AL = $0
OL = (1 / 2) = 0.5
EL = $0 x 0.5 = $0
AW = $890
OW = (1 / 2) = 0.5
EW = $890 x 0.5 = $445
EG = EW + EL = $445 + $0 = $445
EQ = EG / WA = ($445 / $210) = $2.12
EV = 1 + EQ = $1 + $2.12 = $3.12

Option1 possibilities (Bet $100 to win $1000 and bet $110 to win $100 although each bet is mutually exclusive):

1)       Parlay wins. Walk into sports book with $210 and walk out with $1100 ($100 + $1000).
2)       Parlay loses. Walk into sports book with $210 and walk out with $210 ($110 + $100).

Total amount in pocket when leaving sports book = $1310
Total amount wagered = $420
 
$1310 / $420 = $3.12

Each dollar wagered was worth $3.12.

Summary:

Option1 EV = $1.63
Option1A EV = $3.12
Option2 EV = $5.50
Option3 EV = $7.00

Since each value is per dollar wagered it is even more clear which option is better statistically.

The biggest issue is the assumptions in calculating these numbers. The concept of EV (as most everything in statistics) is based on the Law of Large Numbers.

It is the concept that everything will converge to the EV as the iterations go to infinity. Therefore the EV’s above are where this situation would converge as the number of times one was in this situation approaches infinity. One assumption was that the 3 team parlay was already won (in other words was guaranteed in the calculations). The actual EV for a 3 team parlay at 6/1 is $0.875. In order to reach this situation you must actually beat 8/1 odds. So on average you will be in this situation twice each football season.

The assumption of living in a statistically perfect world also mucks the waters. You may hit the first 3 teams on a 4 team parlay once this season, twice next season and take Option2 but each time the parlay lost and Option1 or Option1A would have put you ahead of the game at that point. Then you may go the entire next season without the opportunity.

The best statement is this:

If you are in the position to hedge, you have already made a fundamental error.

If you played a parlay in the first place you have already given up on EV so if it suits you go ahead and hedge the bet. It is your money so do with it as you please.

 
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Posted: #564
Quote Originally Posted by spiff:

Calculating EV

The expected value (EV) of a wager is a measure of how much each dollar is worth over a series of wagers. It is not how much you win on a wager.

EV = Expected Value per dollar wagered
EG = Expected Gain/Loss
EQ = Expected Gain/Loss per dollar wagered

EW = Expected win for a series of wagers
EL = Expected loss for a series of wagers
AW = Amount won on a winning wager
AL = Amount lost on a winning wager
OW = Odds of winning a wager
OL = Odds of losing a wager
WA = Wager amount

OW + OL = 1
WA = | AL |

EL = AL x OL
EW = AW x OW

EG = EW + EL
(Note: EL is always negative or zero – if you use | AL | in the EL equation then EG = EW – EL)

EQ = EG / WA

EV = 1 + EQ

EV = [ WA + (AW x OW) + (AL x OL) ] / WA

One could find many examples of this formula in some form on the Internet that do not divided by WA. That is because they always assume a $1 bet. You must change the wager amount to $1 or divide by WA.

The assumptions used are very important since in reality they are generally not true.

1)       The odds of winning a bet on any single game are 50/50.
2)       The world in which we are calculating is statistically perfect. This means if the odds are 50/50 you are going to win a bet then lose a bet (or lose, then win) with the sequence repeating. Every 2 bets will result in 1 win each and every time.
3)       The first 3 teams on the parlay are guaranteed winners. Obviously the odds of winning a 3 team parlay are not 100% but for this discussion it is required.

Option1:

In this option there is no possibility of “losing” so AL and OL are both 0:

EL = $0 x 0 = $0

There are 2 possibilities both resulting in the same win amount and OW is 1:

AW = $424
OW = (2 / 2) = 1

EW = $424 x 1 = $424

The expected gain is the same as the expected win since there is no loss component:

EG = EW + EL = $424 + $0 = $424

The amount you can expect to win on every dollar bet:

EQ = EG / WA = ($424 / $676) = $0.63

The expected value (EV) of each dollar bet is:

EV = 1 + EQ = $1 + $0.63 = $1.63

This is easy to prove due to our statistically perfect world and the fact that there are only 2 possibilities.

Option1 possibilities (Bet $100 to win $1000 and bet $576 to win $524 although each bet is mutually exclusive):

1)       Parlay wins. Walk into sports book with $676 and walk out with $1100 ($100 + $1000).
2)       Parlay loses. Walk into sports book with $676 and walk out with $1100 ($576 + $524).

Total amount in pocket once the sequence is over = $2200
Total amount wagered for the sequence = $1352

$2200 / $1352 = $1.63

Each dollar wagered is worth $1.63.

Option2:

This option results in losing $100 half the time so:

EL = -$100 x (1 / 2) = -$50

This option results in winning $1000 half the time so:

EW = $1000 x (1 / 2) = $500

The expected gain of this sequence:

EG = EW + EL = $500 + (-$50) = $450

The amount you can expect to win on every dollar bet:

EQ = ($450 / $100) = $4.50

The expected value (EV) of each dollar bet is:

EV = $1 + $4.50 = $5.50

Again only 2 possibilities so the proof is easy due to our statistically perfect world.

Option2 possibilities (Bet $100 to win $1000 or lose $100):

1)       Parlay wins. Walk into sports book with $100 and walk out with $1100 ($100 + $1000).
2)       Parlay loses. Walk into sports book with $100 and walk out with $0.
 
Total amount in pocket once the sequence is over = $1100
Total amount wagered for the sequence = $200

$1100 / $200 = $5.50

Each dollar wagered is worth $5.50.

Option3:

As in Option1 there is no possibility of “losing” (see assumption #3) so AL an OL are both 0:

EL = $0 x 0 = $0

There is only 1 possibility so:

AW = $600
OW = (1 / 1) = 1

EW = $600 x 1 = $600

The expected gain is the same as the expected win since there is no loss component:

EG = EW + EL = $600 + $0 = $600

The amount you can expect to win on every dollar bet:

EQ = ($600 / $100) = $6.00

The expected value (EV) of each dollar bet is:

EV = $1 + $6.00 = $7.00

Even easier to prove with only one possibility as you walk in with $100 and walk out with $700. Each dollar wagered is worth $7.00.

Option1A:

I noticed quite a few posters stating they only hedge enough to cover the parlay bet. Let’s call that Option1A. So the hedge bet is $110 to win $100 which yields 1 win of $890 and 1 loss of $0.

AL = $0
OL = (1 / 2) = 0.5
EL = $0 x 0.5 = $0
AW = $890
OW = (1 / 2) = 0.5
EW = $890 x 0.5 = $445
EG = EW + EL = $445 + $0 = $445
EQ = EG / WA = ($445 / $210) = $2.12
EV = 1 + EQ = $1 + $2.12 = $3.12

Option1 possibilities (Bet $100 to win $1000 and bet $110 to win $100 although each bet is mutually exclusive):

1)       Parlay wins. Walk into sports book with $210 and walk out with $1100 ($100 + $1000).
2)       Parlay loses. Walk into sports book with $210 and walk out with $210 ($110 + $100).

Total amount in pocket when leaving sports book = $1310
Total amount wagered = $420
 
$1310 / $420 = $3.12

Each dollar wagered was worth $3.12.

Summary:

Option1 EV = $1.63
Option1A EV = $3.12
Option2 EV = $5.50
Option3 EV = $7.00

Since each value is per dollar wagered it is even more clear which option is better statistically.

The biggest issue is the assumptions in calculating these numbers. The concept of EV (as most everything in statistics) is based on the Law of Large Numbers.

It is the concept that everything will converge to the EV as the iterations go to infinity. Therefore the EV’s above are where this situation would converge as the number of times one was in this situation approaches infinity. One assumption was that the 3 team parlay was already won (in other words was guaranteed in the calculations). The actual EV for a 3 team parlay at 6/1 is $0.875. In order to reach this situation you must actually beat 8/1 odds. So on average you will be in this situation twice each football season.

The assumption of living in a statistically perfect world also mucks the waters. You may hit the first 3 teams on a 4 team parlay once this season, twice next season and take Option2 but each time the parlay lost and Option1 or Option1A would have put you ahead of the game at that point. Then you may go the entire next season without the opportunity.

The best statement is this:

If you are in the position to hedge, you have already made a fundamental error.

If you played a parlay in the first place you have already given up on EV so if it suits you go ahead and hedge the bet. It is your money so do with it as you please.



@$#% SON!!! Hitting the nail on the head is an understatement...
 
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Posted: #565
Quote Originally Posted by DJNY:

All I have to say is Thanks to Van and that I cannot believe this post has gone on for over 2 years. It almost took me that long to read it and was so hard with all of the stupidity. The point that I am surprised was not made sooner in the post was.

You WIN the first 3 games to be able to hedge the 4th

You make the SAME parlay without the 4th team you have ALREADY WON the 3 teamer.

This is where they were so confused and hung up. They could not wrap their stupid heads around having already won in you only make it 3 teams instead of 4 lol....



TY man... it pays more to just parley the first 3 games, rather then parley 4 and bet against yourself on the last game. Hedging it not gauranteed money, because it's not gauranteed you even get to the point where you hedge... I don't understand how people cannot grasp this concept.

If there was such thing as 'gauranteed money' there would not be such thing as Las Vegas.
 
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Posted: #566

Wendysrox loves this thread.

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Posted: #567

 I have it bookmarked 

must read it sometime over the weekend

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Posted: #568
HI VAN ZACK, THE MATH WORKS, BUT IN THE BETTING WORLD TAKE MONEY WHEN IT IS FOR SURE.  I BET ONE  7 TEAM PARLAY EACH WEEK, I HIT ONE OVER 20 YRS BUT HAD 6 GOING INTO THE SEVENTH AND LOSS. ALL 6. BUT I MAKE MORE MONEY BETTING AGAINST MY SELF IN THE 7TH GAME IN ALL 6.   SURE MONEY PROTECTS BANKROLLS.
 
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Posted: #569

Quote Originally Posted by tomkarw:

HI VAN ZACK, THE MATH WORKS, BUT IN THE BETTING WORLD TAKE MONEY WHEN IT IS FOR SURE.  I BET ONE  7 TEAM PARLAY EACH WEEK, I HIT ONE OVER 20 YRS BUT HAD 6 GOING INTO THE SEVENTH AND LOSS. ALL 6. BUT I MAKE MORE MONEY BETTING AGAINST MY SELF IN THE 7TH GAME IN ALL 6.   SURE MONEY PROTECTS BANKROLLS.

ONE MORE ITEM, I ALWAYS PUT THE MONDAY NITE GAME AS MY 7TH TEAM AND AS LINE MOVES THERE IS ALWAYS A CHANCE TO MIDDLE THE PARLAY.  $$$$$$

 
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Posted: #570
of course hedging comes at a price but gurenteed win in sports betting ,gotta be the way to go when   its win 424 gurentteed or  risk it all just to win 600 ,It doesent pay to win nothing to go for 176 dollars  more in reality  .now if the win is double or more than maybe its worth and thats maybe
 
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Posted: #571

Quote Originally Posted by tomkarw:

HI VAN ZACK, THE MATH WORKS, BUT IN THE BETTING WORLD TAKE MONEY WHEN IT IS FOR SURE.  I BET ONE  7 TEAM PARLAY EACH WEEK, I HIT ONE OVER 20 YRS BUT HAD 6 GOING INTO THE SEVENTH AND LOSS. ALL 6. BUT I MAKE MORE MONEY BETTING AGAINST MY SELF IN THE 7TH GAME IN ALL 6.   SURE MONEY PROTECTS BANKROLLS.

So you bet a 7 team parlay, knowing you are going to hedge the 7th game.

You obviously didnt read this thread.

Simple question - why wouldnt you just bet a 6 team parlay?

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Posted: #572
Great thread
 
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Posted: #573

agre with vanzack - what hes tryin to say is that why hedge in gambling?  it's an oxymoron like a sure bet!

 
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Posted: #574
oh my god the fact that this thread is this long just confirms how dumb covers members really are....this thread basically should have had the first two posts explaining why hedging is stupid and then a few people should have agreed with it and the book should have been closed....man i want to be a sportsbook now just for the sole fact that i will be dealing with people this dumb and if they are that stupid there is no way they will win in the long run....hedging is idiotic and the first post clearly explains why...all those idiots saying guaranteeing urself money blah blah blah...u r f'ing guaranteeing urself more money without hedging.....if the last game of ur parlay happens much later than the other ones why the fck did u put the last game in there....u would have already won money without hedging just by leaving it out! THE PARLAY WOULD BE CLOSED COMPLETE PAID.....and then with the money it paid you have the freedom to decide how much or if you want to bet on the last game without paying vig twice to hedge
 
 
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Posted: #575

Quote Originally Posted by mick82:

oh my god the fact that this thread is this long just confirms how dumb covers members really are....this thread basically should have had the first two posts explaining why hedging is stupid and then a few people should have agreed with it and the book should have been closed....man i want to be a sportsbook now just for the sole fact that i will be dealing with people this dumb and if they are that stupid there is no way they will win in the long run....hedging is idiotic and the first post clearly explains why...all those idiots saying guaranteeing urself money blah blah blah...u r f'ing guaranteeing urself more money without hedging.....if the last game of ur parlay happens much later than the other ones why the fck did u put the last game in there....u would have already won money without hedging just by leaving it out! THE PARLAY WOULD BE CLOSED COMPLETE PAID.....and then with the money it paid you have the freedom to decide how much or if you want to bet on the last game without paying vig twice to hedge

Nearly 3 years after the original post in this thread, somebody sums it up.

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