The Wolverine
Member
Have been completed. And they all finished 6-2. The commentators just said it was 15 million to 1 odds as a parlay.
All 8 first round matches at the Snooker Masters...
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The Wolverine
Member
I just tried to work it out and came up with this...
$1 on 1st match at 5-1 returns $6
$6 on 2nd match at 5-1 returns $36
$36 on 3rd match at 5-1 returns $216
$216 on 4th match at 5-1 returns $1296
$1296 on 5th match at 5-1 returns $7776
$7776 on 6th match at 5-1 returns $46656
$46656 on 7th match at 5-1 returns $279936
$279936 on 8th match at 5-1 returns $1679616
Have I got it totally wrong? Or the snooker commentator? Or both of us?
$1 on 1st match at 5-1 returns $6
$6 on 2nd match at 5-1 returns $36
$36 on 3rd match at 5-1 returns $216
$216 on 4th match at 5-1 returns $1296
$1296 on 5th match at 5-1 returns $7776
$7776 on 6th match at 5-1 returns $46656
$46656 on 7th match at 5-1 returns $279936
$279936 on 8th match at 5-1 returns $1679616
Have I got it totally wrong? Or the snooker commentator? Or both of us?
You are way off. 6-2 is one of 30 possible outcomes.
The Wolverine
Member
The Wolverine
Member
The match can only end one of those six ways can't it? What am I missing here? What are the other 24 possible outcomes?
So i was thinking of dice but.... scores of 0-6 thru 5-6 also are possible
The Wolverine
Member
Yes, but that is only 6 possible outcomes per match isn't it? Therefore a 5-1 bet? Isn't that correct?
The Wolverine
Member
Don't forget the match just has to finish 6-2. It doesn't matter who won. I think that's a 5-1 bet.
The commentators better stick to commentating.
Using a binomial probability table, one finds that these are the likelihoods that two players of equal skill will play eight racks and that either one of them will win exactly X racks:
x=0 .0078
X=1 .0625
x=2 .2188
x=3 .4375
x=4 .2734
Hence, the chance of eight consecutive matches finishing 6-2 are ,2188 raised to the eight power, or 0.000005252650942, so the odds against it happening are a bit over 190,000 to 1.
Using a binomial probability table, one finds that these are the likelihoods that two players of equal skill will play eight racks and that either one of them will win exactly X racks:
x=0 .0078
X=1 .0625
x=2 .2188
x=3 .4375
x=4 .2734
Hence, the chance of eight consecutive matches finishing 6-2 are ,2188 raised to the eight power, or 0.000005252650942, so the odds against it happening are a bit over 190,000 to 1.
don't care because zhao is flying. 12 seconds per shot. higgins is the ball and chain to his flight though. score 3-2
OverTheNut
Active member
The odds of a correct score (i.e. 6-2) will vary - depending on the odds of the players in the game.
It definitely won't be the same price every time for every player.
Just like 6-0 or 6-5 won't be 5/1 every time.
The commentators probably checked with the bookies what odds 6-2 was at the start of each game for the winning player - and what the combined odds of all those 6-2 games would have paid.
It definitely won't be the same price every time for every player.
Just like 6-0 or 6-5 won't be 5/1 every time.
The commentators probably checked with the bookies what odds 6-2 was at the start of each game for the winning player - and what the combined odds of all those 6-2 games would have paid.
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john higgins, 50, just beat the world champion. absolute grit.
Great match, Higgins got a few huge rolls to get it to double-hill and the last game was like one of those hill/hill 9-ball games where both players get several innings at the table. Cool to see the old guy in the semi-finals.
Agreed. The odds of this occurrence are different if the players are of very different skills. With equal skills, however, the odds of this occurrence are just 190,000 to 1 against.
yea, i'm a fan of zhao's fast playing style but was happy to see the old legend win in the end. the class of '92, they broke the mold when they made them. just incredible
If we assume that the players are of equal ability, we will get the smallest chance that the score will be that lop-sided, but let's go with that to start.
In a single match between two equal players, the chance that Player A will win 6-2 is 2^(-8) * 7*6 /(1*2). Explanation:
The 2 to-the-power-minus-8 is because we have 8 things happening that each has a chance of 1/2
7*6 is from the fact that the two wins by the loser can appear in 7 locations for the first and 6 locations for the second. Neither loss can be the 8th game. Example: WWLWLWWW -- how many different possible strings of W and L are there for 6-2? The answer is 21
The divide by 1, divide by 2 is because the two losses by the winner are indistinguishable.
That gives a chance of Player A winning 6-2 of 21/2^8 or 21/256 or 0.08203125 or a little over 8%
But Player B has the same chance, so the chance that one of them will win at 6-2 is twice or 21/128 = 0.1640625
For that to happen 8 times in a row is that raised to the 8th power or in 1 in 1905133.
If you had to pick the correct winner at 6-2 as opposed to just the correct score, the odds get a lot worse. Like 256 times worse. But those are not the odds that a bookie would offer. I suspect that bookies were offering 7-1 for a 6-2 score by a particular player, which would give the 15 million to one parlay.
It's fairly easy to add in the difference in abilities of the two players. Instead of figuring the chance of a win or loss as 1/2, you insert the estimated chance of the particular player, so you get A^6 and B^2 where A and B are the respective chances for A and B to win a frame.
It turns out that the best chance for a 6-2 score is when the better player is about 75% to win each frame. If he is better than that, he starts to get a lot of 6-0 or 6-1 scores and the odds of a 6-2 decline. The peak is about 40% higher odds of 6-2 than for equal players.
It turns out that the best chance for a 6-2 score is when the better player is about 75% to win each frame. If he is better than that, he starts to get a lot of 6-0 or 6-1 scores and the odds of a 6-2 decline. The peak is about 40% higher odds of 6-2 than for equal players.
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