How badly is this bookie screwing up with his odds?

[DVO]

And what should the true odds be?

Here is a cut and paste from an EM I sent a friend. It involves a friend who is using a local bookie. Said bookie usually uses Vegas' lines. I hope this is understandable. I'm just wondering if I'm viewing this correctly, and how much the bookie is getting the wrong end of it giving 10/1.

I think I'll post in the sports betting section also.
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Vegas offers 10/1 odds on correctly picking a 4 - bet parlay. Meaning, if you take the Vikes, Saints, Texans, and 49ers, say, and they each cover, you get a 10/1 return on your dough. ( By the way, aren't the true odds ~16-1? i.e. (.5) (.5) (.5) (.5) = .0625 = 16/1? )

This bookie, however, is offering the same 10/1 odds on 4 bet parlays that include halftime bets. In other words, you can take the Vikes to win the first and second halves of their game, and ditto the Saints, and those are your 4 bets. But of course they are related events ( The Vikes are a lot more likely to cover if they are ahead 22-0 at the half. Etc Etc.)

So instead of 4 unrelated events, the bookie is giving those odds on related events.

The beauty of it is, my friend isn't even bothering picking games any more. He's just using the law of large numbers....so if Vegas says the Colts are -6 in the first half and -12 for the game, he's just gonna flip a coin and take them to win or lose both halves. Then he'll do the same with some other team, and bang, there's his 4- bet parlay.

[jay_shark]

If your probability of success is 50% for each game then you should win 1/2^4 =1/16 . This is the same as odds against you winning of 15:1 . 15 times you lose and 1 time you win which makes sense since you win 1/16 times .

If he's offering you 10:1 then you will lose out in the long run .

1/16*10 -15/16*1 =-0.3125 .

You will profit if your chance of picking the winner is greater than :

10x^4 -(1-x^4)>=0
x>=0.5491 .

[DVO]

Sorry, I wasn't clear.

My friend is being offered 10/1 on the following:

4 - bet parlay of ( as an example)

1) Vikes halftime score ( giving 6, say)
2) Vikings final score ( giving 12, say)
3) Game #2 halftime score
3_ Game #2 final score

so lets say he takes the vikes and gives 6 for his first bet. he would also take the vikes and give 12 for the game ( this is not a second half bet; it is for the whole game).

It looks to me like his true odds are (.5) (.7) (.5) (.7).
assuming he has a 50% shot at getting the first half right, and 70% chance that if he is right in that, he gets the game right - because if the Vikes cover by, say 11 in the first half, they are 70% to cover 12 for the game.

Does this make sense? Am I missing anything?

[T50_Omaha8]

I doin't think jay shark read the whole post.

Very interesting. I don't know much about sports betting, but I believe this works something like this:

Bet 1: Team A wins the game.
Bet 2: Team A wins the second half of the game.
Bet 3: Team B wins the game.
Bet 4: Team B wins the second half of the game.

I would assume that, given team A wins the second half of a game, the probabilty they win the entire game is higher.

Let's say team A has a 50% chance of winning the second half of the game (since the team was chosen randomly).

Now lets consider what happens when team A wins the second half of the game. How often much this team win the whole game to break even?

In order for the bet to break even,

P(A wins 2nd)*P(A wins overall|A wins second)*P(B wins 2nd)*P(B wins overall|B wins second) must be greater than 1/11.

Since we choose randomly, P(A wins second) and P(B wins second) are both 1/2, so we have

P(A wins overall|A wins second*P(B wins overall|B wins second)/4 = 1/11

P(A wins overall|A wins second)*P(B wins overall|B wins second) = 4/11

And since the two are equivalent, also due to the random selection,

P(A wins overall|A wins second) = sqrt(4/11) = 60.3023%

So the question arises:

Throughout sports history, is

P(any random team wins overall | team wins second half) > 60.3%?

If so, you've got a very nice situation on your hands.

edit: okay, so they're covering a spread. I thought these were bets made at halftime, which makes no sense to parlay on second thought. This seems to work more completely to your advantage.

You are going to have to make some normality assumptions or something to get precise odds, however.

[Siegmund]

Do halftime bets really work that way?

I am not a sports bettor, but my read on OP was that the 4-bet parlay was
1) first half of first game
2) second half of first game (NOT final score of first game)
3) first half of second game
4) second half of second game (NOT final score of second game)

such that no one scoring event direct impacts two bets. There would still be SOME relationship between how well a team plays in two halves of the same game, but not nearly weak enough to get you up to 10/1.

[sickofants]

[ QUOTE ]
My friend is being offered 10/1 on the following:

4 - bet parlay of ( as an example)

1) Vikes halftime score ( giving 6, say)
2) Vikings final score ( giving 12, say)
3) Game #2 halftime score
4) Game #2 final score


[/ QUOTE ]
If the bookmaker has the line correct, then the odds of events 1 & 3 are 0.5. For a profitable bet, we need the bet to pay better than 10/1, so we need

0.5*0.5*Pr(events 2 & 4) > 1/11 or
Pr(events 2 & 4) > 0.36

In other words, we need Pr(Wager 2 is good given that Wager 1 was) and Pr(Wager 4 is good given that Wager 3 was) to be better than 60% for the bet to be a good one. I would personally doubt that this is true in general. If the bookies' lines are, on average, good then the half time score will mostly only be out by a little, thus not quite giving you the 60-40 edge for the full time score. If the bookies' lines are bad on average, then I guess you would find easier ways to make some cash from them [img]/images/graemlins/wink.gif[/img].

If the line at full time is always double that of half time, then I guess there may be some good bets to find - a team that often does better in the second half than the first would be a good candidate.

I think it's a long term losing just picking random teams, though.

(Sorry if my terminology is a bit out - I'm not massively familiar with these bets, being from the UK. We like our fractional odds)