math question

[Robert Fischer]

Given pool size and the off odds for each horse, how do you calculate total dollars wagered on each horse?

Thanks

Pool Size = $100,000
Takeout = 15%

horse........winOdds
-------------
Country Star 2.00
Tiago 8.00
War Pass 7.80
Grasshopper 1.40
Indian Blessing 7.60

[Greyfox]

Given pool size and the off odds for each horse, how do you calculate total dollars wagered on each horse?

Thanks

Pool Size = $100,000
Takeout = 15%

horse........winOdds
-------------
Country Star 2.00
Tiago 8.00
War Pass 7.80
Grasshopper 1.40
Indian Blessing 7.60

Let me tackle the question. If I'm wrong then someone else can chime in with a better way.
In the example above, the pool was $ 100,000.
15 % take out means that in this example $ 85,000 was left for redistribution.

I think that I can solve the problem by dividing all of the individual odds above, into the odds of the lowest odds runner.
In this instance we have 5 runners.
The lowest odds is Grasshopper at 1.40.

Grasshopper 1.4/1.4 = 1.00
Country Star 1.4/2 = .70
Tiago 1.4/8.0 = .175
War Pass 1.4/7.8 = .179
Indian Blessing .184

Now we add those fractions up.
1.00 +.7 +.175 +.179 +.184 = 2.238

Then we find out the percentage of each of the runners to 2.238.
Grass Hopper 1/2.238 x 100 =44.68 %
Country Star .7/2.238x 100 = 31.28%
Tiago .175/2.238 x 100 = 7.82 %
War .179/2.238 x 100 = 7.99 %
Indian Blessing .184/2.238 x 100 = 8.22%

Now assuming that I haven't made any errors in math, as some of them were calculated by hand, we now know that Grass Hopper's total of the pool is
44.68 % of $ 85, 000 or roughly $ 37,798 or so.
I'll leave it to you to work out the others.

[DRIVEWAY]

Quess:

POOLSIZE - (POOLSIZE / ( ( HORSEODDS) * (100/(100 - TAKEOUT)) ) = HORSEBETAMOUNT

100,000 - (100,000 / ( ( 1.4) * (100/(100 - 15 )) ) = 36087 Approximately

Issues of rounding and breakage will vary

Please post the answer

[ryesteve]

Ignoring breakage, the amount bet, given a 15% take, is .85*Pool / (odds+1)

[Greyfox]

Oops. What I've got above is the moneys that are bet into the 85,000.
The actual money bet on each horse should have been that percentage X 100,000.
Therefore $ 44,680 or so bucks was on Grass Hopper out of the
$100,000. $ 37,798 or so was coming back to the public.

[MakinItHappen]

Robert,

Well, unless I am missing something or hosed something up, the track takeout % of 15% and the payout odds for the horses listed do not seem to jive. One should be able to take 1/(1+payout odds) for each horse and sum these to approx 1.18. I only get 1.09 when I do this based on the pay-off odds you provided. This means that the pay-off odds are too high given the track takeout %, unless a horse is missing.

Therefore, calculating $'s wagered on each horse does not provide an answer that supports the 15% takeout given the data provided, unless I assume a horse is missing and adjust accordingly.

Am I missing something?

Best of Luck Robert and Everyone!

MakinItHappen

[oddsmaven]

makinithappen is correct...the odds do not add up for a 15% takeout..more like 8%...otherwise, ryesteve gave you the right formula to calculate how much is bet on each - the remaining $ after takeout, divided by the odds+1.

[Greyfox]

I took it that the example was posted as "hypothetical" and not to get stuck on discrepancies as to what actually happens at the tracks. The question was what was bet on each horse.

[Robert Fischer]

Horse...........Odds...$$Wagered
Outcome 1 – $2.00 $28,333.33
Outcome 2 – $8.00 $9,444.44
Outcome 3 – $7.80 $9,659.09
Outcome 4 – $1.40 $35,416.67
Outcome 5 – $7.60 $9,883.72

Thanks Ryesteve , Greyfox , and all who participated.

I did fudge the Odds and Pool size because I didn't have the answer. So yes it doesn't add up perfectly , but the method should be sound using the formula that Ryesteve provides
(Pool -Takeout*Pool) / (odds+1)

I am setting up a spreadsheet and will eventually run it on some other samples.

Playing around with an idea I have about using $$$ in Combination with pace and other things....


THANKS GUYS :ThmbUp:

[Greyfox]

Horse...........Odds...$$Wagered
Outcome 1 – $2.00 $28,333.33
Outcome 2 – $8.00 $9,444.44
Outcome 3 – $7.80 $9,659.09
Outcome 4 – $1.40 $35,416.67
Outcome 5 – $7.60 $9,883.72

Thanks Ryesteve , Greyfox , and all who participated.

I did fudge the Odds and Pool size because I didn't have the answer. So yes it doesn't add up perfectly , but the method should be sound using the formula that Ryesteve provides
(Pool -Takeout*Pool) / (odds+1)

I am setting up a spreadsheet and will eventually run it on some other samples.

Playing around with an idea I have about using $$$ in Combination with pace and other things....


THANKS GUYS :ThmbUp:

Not so quick. Forget the takeout for the moment.
The question was how much was bet on each horse?
The bet on each horse does not include take out.
The numbers above should add up to $ 100,000.
But, and maybe it's rounding on my computer, but they don't seem to.

The number ryesteve provided is probably a good one, but I suspect that it's a quick calc way of roughly getting payouts available.
The method that I used above suggests that the amount wagered initially should add up to $100,000 with Grasshopper putting in $ 44,000 plus. Then of course that minus 15 % goes into the pool for payouts. Each runner would subsequently put in money to the take out and pool. But the bets should add to $100,000.

[ryesteve]

The numbers above should add up to $ 100,000.
I think the odds figures in the original post were just a hypothetical

[MakinItHappen]

Not so quick. Forget the takeout for the moment.
The question was how much was bet on each horse?
The bet on each horse does not include take out.
The numbers above should add up to $ 100,000.
But, and maybe it's rounding on my computer, but they don't seem to.

The number ryesteve provided is probably a good one, but I suspect that it's a quick calc way of roughly getting payouts available.

Yes, Greyfox, this is the point I was trying to make in regards to the flawed / hypothetical data. When I did the calcs and the total wagered added up to $92,737 and change instead of something closer to $100k ... I said hmmm... this example is not holding together very well... that is when I checked the odds to make sure they "held together" given the stated 15% takeout.

Nonetheless... it seems like Robert has gotten the information he wanted as the formula Ryesteve provided is correct.

Working through this excercise with complete real #'s will provide a more complete and sound understanding. The breakage #'s never cease to amaze/depress me...

Best of Luck Everyone!

MakinItHappen

[Robert Fischer]

Not so quick. Forget the takeout for the moment.
The question was how much was bet on each horse?
The bet on each horse does not include take out.
The numbers above should add up to $ 100,000.
But, and maybe it's rounding on my computer, but they don't seem to.

The number ryesteve provided is probably a good one, but I suspect that it's a quick calc way of roughly getting payouts available.

Credit should go to Greyfox for getting the correct answer. :ThmbUp:


Good call.
Because I made up the odds and the poolsize, the $$$ only ads up to about $93K. The formula relies on a true relationship between the poolsize and the Odds , which we didn't have here. I will run an actual race in the spreadsheet after I run some actual errands;) .
will post any results / problems

[Greyfox]

Thank you.

By my figs:
Grasshopper 44.68 % $ 44,680 (wagered)
Country star 31.28 $31,280
Tiago 7.82 $ 7,820
War 7.99 % $ 7,990
Indian 8.22 % $ 8,220
Total Wagered $ 100,000 (if not, blame computer rounding).

[Cratos]

Given pool size and the off odds for each horse, how do you calculate total dollars wagered on each horse?

Thanks

Pool Size = $100,000
Takeout = 15%

horse........winOdds
-------------
Country Star 2.00
Tiago 8.00
War Pass 7.80
Grasshopper 1.40
Indian Blessing 7.60

ODDS
Country Star - 2
Tiago - 8.00
War Pass - 7.8
Grasshopper - 1.4
Indian Blessing - 7.6

Inverse
Country Star - 0.333333333
Tiago - 0.111111111
War Pass - 0.113636364
0Grasshopper - 0.416666667
Indian Blessing - 0.11627907
Totals - 1.091026545

Adjusted
Inverse
Country Star - 0.359438425
Tiago - 0.119812808
War Pass - 0.122535827
Grasshopper - 0.449298031
Indian Blessing - 0.125385497
Totals - 1.176470588

Take
Calculated
Wagers
Country Star - $35943.84
Tiago - $11981.28
War Pass - $12253.58
Grasshopper - $44929.80
Indian Blessing - $12538.55
Totals - $117647.06

Actual
Wagers (The answer to your question)
Country Star - $30552.27
Tiago - $10184.09
War Pass - $10415.55
Grasshopper - $38190.33
Indian Blessing - $10657.77
Totals - $100000

This calculation does not reflect the “breakage” and therefore the final payouts to the bettors would be different

[Greyfox]

ODDS
Country Star - 2
Tiago - 8.00
War Pass - 7.8
Grasshopper - 1.4
Indian Blessing - 7.6

Inverse
Country Star - 0.333333333
Tiago - 0.111111111
War Pass - 0.113636364
0Grasshopper - 0.416666667
Indian Blessing - 0.11627907
Totals - 1.091026545

Adjusted
Inverse
Country Star - 0.359438425
Tiago - 0.119812808
War Pass - 0.122535827
Grasshopper - 0.449298031
Indian Blessing - 0.125385497
Totals - 1.176470588

Take
Calculated
Wagers
Country Star - $35943.84
Tiago - $11981.28
War Pass - $12253.58
Grasshopper - $44929.80
Indian Blessing - $12538.55
Totals - $117647.06

Actual
Wagers (The answer to your question)
Country Star - $30552.27
Tiago - $10184.09
War Pass - $10415.55
Grasshopper - $38190.33
Indian Blessing - $10657.77
Totals - $100000

This calculation does not reflect the “breakage” and therefore the final payouts to the bettors would be different

Cratos, I know that you're a Guru at this stuff and probably right, but how did you calculate your first inverse and then the adjusted inverse?

[Greyfox]

The total wagers can only be $ 100,000.:confused:

Your Grasshopper total for $117,000 is suspiciously close to mine for $ 100,000.

[Robert Fischer]

Cratos - Looks good. Would you mind sharing how to calculate the adjusted inverse, take calculated wagers , and actual wagers ?


Using the Formula
(Pool -Takeout*Pool) / (odds+1)

I did an actual race
12/15/2007
Race1 AQUEDUCT
horse Name odds $ bet on horse
Outcome 1 – $2.70 $57,244.28
Outcome 2 – $8.80 $21,612.64
Outcome 3 – $7.80 $24,068.62
Outcome 4 – $1.40 $88,251.60
Outcome 5 – $7.60 $24,628.35
Outcome 6 – $10.80 $17,949.48
Outcome 7 – $33.25 $6,184.05
Outcome 8 – $30.25 $7,973.79
Outcome 9– $57.50 $3,620.58
sum total ...........$251,533.40


actual pool size $248,181

Difference of $2,352.40 :kiss:

[Cratos]

Cratos - Looks good. Would you mind sharing how to calculate the adjusted inverse, take calculated wagers , and actual wagers ?


Using the Formula
(Pool -Takeout*Pool) / (odds+1)

I did an actual race
12/15/2007
Race1 AQUEDUCT
horse Name odds $ bet on horse
Outcome 1 – $2.70 $57,244.28
Outcome 2 – $8.80 $21,612.64
Outcome 3 – $7.80 $24,068.62
Outcome 4 – $1.40 $88,251.60
Outcome 5 – $7.60 $24,628.35
Outcome 6 – $10.80 $17,949.48
Outcome 7 – $33.25 $6,184.05
Outcome 8 – $30.25 $7,973.79
Outcome 9– $57.50 $3,620.58
sum total ...........$251,533.40


actual pool size $248,181

Difference of $2,352.40 :kiss:

The inverse of the odds add to 1.091027, but that is at 85% and the betting must be set to 1 not .85 because the inverses are the theoretical probabilities of winning as set by the wagering. To have a “fair game” the probabilities must equal 1.

Therefore to do that you divide 1/.85 and you get 1.17647 and then you go back and multiply each inverse.

[Greyfox]

Oh. I see . You are still using that Odds + 1 and then inverting it.

So 2-1 beccomes 3, inverted is 1/3 = .333333

But where did you get that formula Odds + 1? It looks like a Dick Mitchell short cut to me.

[Cratos]

Oh. I see . You are still using that Odds + 1 and then inverting it.

So 2-1 beccomes 3, inverted is 1/3 = .333333

But where did you get that formula Odds + 1? It looks like a Dick Mitchell short cut to me.


The formula comes from probability 101. When odds are set to 2-1, it is the same as saying there is a 1 in 3 chance of success or 33%. If the odds were 4-5 it would be 5 in 9 chance of success or 56%. The second number of the odds is always the success number which become the numerator and the adding of the two numbers (e.g. 2 and 1 = 3) becomes the denominator, hence 1/3 = 33%.

[Greyfox]

Thanks Cratos. Well done. :ThmbUp: :ThmbUp:

[Robert Fischer]

Below you will find that I made an error. The Pool Size is the "Mutuel Pool" and not the Win Pool. Which explains a difference.
I have found an easy way to copy/paste direct win pool $$$ for each horse via xpressbet information.
Any other sources of "Win Pool" information would be appreciated.




Using the Formula
(Pool -Takeout*Pool) / (odds+1)

I did an actual race
12/15/2007
Race1 AQUEDUCT
horse Name odds $ bet on horse
Outcome 1 – $2.70 $57,244.28
Outcome 2 – $8.80 $21,612.64
Outcome 3 – $7.80 $24,068.62
Outcome 4 – $1.40 $88,251.60
Outcome 5 – $7.60 $24,628.35
Outcome 6 – $10.80 $17,949.48
Outcome 7 – $33.25 $6,184.05
Outcome 8 – $30.25 $7,973.79
Outcome 9– $57.50 $3,620.58
sum total ...........$251,533.40


actual pool size $248,181

Difference of $2,352.40 :kiss: