probabilities - which formula to apply?

Fibonacci · 2011-06-23 04:41:22

I think you can only generalize the combined WIN and PLACE bet problem by putting the horses into different groups.

Variables
r # of runners
p # of places
h # of hits
bw # horses with a win bet and no place bet
bp # horses with a place bet and no win bet
bb # horses with both a place bet and a win bet

Idea
Treat 1st position separately and combine with probabilities of the remaining positions. This should enable us to use the hypergeometric distribution function again:

Scenarios

WIN and 0 places

WIN and 1 place

no WIN and 0 places

no WIN and 1 place

Last edited by Fibonacci (2011-06-29 06:28:30)

bobbym · 2011-06-23 11:04:49

Hi;

Treat 1st position separately and combine with probabilities of the remaining positions.

That is what I did, but only for the first question. Have you tested your scenarios on a mock problem? Did it check out? If so you are done!

Fibonacci · 2011-06-29 08:13:15

It doesn't add up. Back to the drawing board.

bobbym · 2011-06-29 16:16:39

Hi;

My first part in post #21 works for the first part. Do you want me to contimue or do want to do it for yourself?

Fibonacci · 2011-07-13 23:41:51

Sorry, I' d been away for a while.

I am not quite sure I understand how you arrived at the formula in post #21.

You use the variable bets=3 in the formula, which is the number of bets in the WIN market. (Going back to my question and example in post #18, there are two sets of bets: 3 bets in the WIN market and 2 bets in the PLACE market.)

What I can't see is how we can possibly apply the same formula because it only takes into consideration the number of bets in one market.

bobbym · 2011-07-14 05:20:16

Hi Fibonacci;

I think you are going to have to clarify what you mean by bets.

I looked at it this way. When you bet on 3 horses. Each could win ( 3 in the win market ) and the other 2 can place ( place market ).

All I did there is find out the probability that all 3 of the horses you picked end up in the first 3 positions in a race. If all three of them end up in the first 3 positions then automatically 1 won and the other 2 placed. For that I used the hypergeometric again.

Fibonacci · 2011-07-14 09:02:28

By the way, I saw mentioned somewhere here that you were an Assembler programmer. The good old times ...

Back on topic: From a betting point of view, the bets in the WIN and PLACE markets are completely separate. The bookmaker will treat bets in the two markets independently.

I might bet horse A to WIN and additionally I might place another bet for it to PLACE.
If A comes first, both bets win. If A comes second, the WIN bet loses but the PLACE bet wins.

Continuing with the post #18 example, I placed three WIN bets on horses A, B, C. Additionally I placed PLACE bets on A and B.

Although the markets are independent, the results are not. We know that when A WINs it also PLACEs per definition. I detailed the only possible outcomes for one WIN bet wins + 2 places in post #22.

bobbym · 2011-07-14 10:33:46

Hi;

Used to be, started with the Z80 -> 6809E -> MC68000 -> 80386.

I think you are starting to get into something called expectation. This is totally different from the probability of something occurring.

a WIN bet wins + 2 places (= C wins and A+B place)

I only answered the question of the probability that the 3 horses you picked in the field of 16 ( I think ) all finished in the money. Payoffs are expectation.

Fibonacci · 2011-07-15 04:26:01

bobbym wrote:

started with the Z80 -> 6809E -> MC68000 -> 80386

Started with IBM System/370 -> half a dozen other architectures I don't remember -> 8051

bobbym wrote:

I think you are starting to get into something called expectation. This is totally different from the probability of something occurring.

I am getting a bit out of my depth here. Expectation - is that the same as EV? My limited experience with this is just in relation to Roulette or BlackJack wager requirements. (You determine the EV from the house edge.)

Anyway, I am quite happy to retire this thread now. I have taken a few things from it apart from the hypergeometric distribution function: I even installed GeoGebra, and I am switching my wiki to LaTeX-based MathJAX.

Many thanks for the inspirations.

I shall be back with probability questions about my favourite dice game. No money involved but I'd like to get an edge.

bobbym · 2011-07-15 05:07:30

Hi Fibonacci;

The simplest way to show expectation or expected value or number in action are in games of chance.

You are flipping a fair coin with an idiot. You take heads and do the flipping. He agrees to pay you 1.00 when heads comes up. You agree to pay him .50 when tails comes up. What does the game earn for you? This is the expected value of the game.

On every 2 coin tosses you expect to get 1 head and 1 tail. That means he will give you a dollar once and you will pay him 50 cents once. In short you will be 50 cents up after 2 games. Your expectation is 25 cents for every flip.

Here is the part that separates the professionals from the so called suckers. If you play this game 100 times, you expect to be 25 dollars ahead. It does not matter whether you are 51 dollars ahead or behind by 10 dollars. You still earned 25 dollars for the 100 throws!

Your opponent may walk away with all your money but the fact is he lost 25 cents on every throw and if he continues to play the actual results will get closer and closer to the mathematical expectation. It is hard for your opponent who just won money to understand that he did not win, he lost.

Math Is Fun Forum

#26 2011-06-23 04:41:22

Re: probabilities - which formula to apply?

#27 2011-06-23 11:04:49

Re: probabilities - which formula to apply?

#28 2011-06-29 08:13:15

Re: probabilities - which formula to apply?

#29 2011-06-29 16:16:39

Re: probabilities - which formula to apply?

#30 2011-07-13 23:41:51

Re: probabilities - which formula to apply?

#31 2011-07-14 05:20:16

Re: probabilities - which formula to apply?

#32 2011-07-14 09:02:28

Re: probabilities - which formula to apply?

#33 2011-07-14 10:33:46

Re: probabilities - which formula to apply?

#34 2011-07-15 04:26:01

Re: probabilities - which formula to apply?

#35 2011-07-15 05:07:30

Re: probabilities - which formula to apply?

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