Guys, I need your help.
I know for sure that here are people with deeper knowledge and understating about the matter. I will talk about Tote Betting. In my country there is still a Tote betting with 10 out of 10/12/13 matches type of games with a Jackpot structure. I think it is known as Tote Betting. Here are the rules:
We have 10 predefines matches. If you win them all - you win a Jackpot. I think that sometimes it worth betting on such games, but first I need to figure the combinations/mathematics.
These are the odds for the games.
1 X 2
2.85 3.25 2.6
2.8 3.25 2.6
2.2 3.4 3.3
2.62 3.45 2.62
2.5 3.35 2.85
1.95 3.55 3.95
3 3.2 2.5
5 3.75 1.73
2.5 3.1 3.1
3.35 3.05 2.4
I know for sure how to calculate the total numbers of combinations - it is 10 (number of matches) on 3rd power (3 outcomes for each match). Total 59049 different combinations.
I also know how to calculate the most probable ONE - it is a =PRODUCT(2.5*2.6... etc) in excel choosing the lowest odd for each outcome of each game. In this particular case we get a total odd of 4929 or 1/4929 = 0.00020287 probability of this outcome happens. Same applies for most un-probable (lowest chance of happening)
Here comes my difficulties, because I am not a math expert. NO programing skills as well, but found a friend who could help me with that. How can I find/calculate the 10/100/1000 most probable outcomes of this data set? Is there a formula/function to help me do it?
My idea is as follows. Yes I know Tote?jackpot betting is a different animal and Game Theory should be applied to. But first part should be to calculate the EV of a single bet. Price of a ticket/combination is 1 EUR. If I pay for all combinations I would have to wager 59 049 EUR for a return of say Jackpot of 10 000 EUR AND IF I am the sole winner of the jackpot. It is a stupid Idea. But I do think there are some Combinations which are worth their price because the EV is positive.
One more feature of the game is that I am allowed to place a triple/double bets for a single game. I am allowed to play any match with 1X or X2 or 12 or 1X2 but paying the price for it. So filling combinations is not a problem because I can choose as many as I want on a single ticket. All I have to find are these with skewed payoffs and ONLY THE apply the GAME Theory , and say instead ot play 1.95 on Game 6 (favorite) choose DRAW instead in order to be a Sole winner of a Jackpot in case of Win.
Any ideas or suggestions are welcome,
Thank you!
Tote Betting
- James Ravazzolo
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Re: Tote Betting
in your example, the probability is well above 1/10000, so it would certainly be worth a bet of 1 unit if the payout was 10000. In fact even a payout of 5000 would be worth it. Computing the 50,000 probabilities would be very fast for a program, and then sorting them could be done efficiently. Anything above 1/10000 would be worth a bet .... except for that possibility of multiple winners. Perhaps by investigating past results you could see how common multiple winners is (splitting the 10000 prize).