Betting strategy

[pgrmdave]

Given a tournament with 8 players, where each is ranked with a certain corresponding payout, how would i determine the optimal betting strategy to minimize risk?

 

Example:

Player       Payout
Player 1:   3.45
Player 2:   8.39 
Player 3:   7.76
Player 4:   9.17
Player 5:   9.24
Player 6:   8.74
Player 7:   7.99
Player 8:   8.59

 

So for example, betting $10 on player 1 would result in winning $34.50 if he won, but I'd have to subtract bets I made on everybody else that lost. I've been able to guess and test my way to good numbers, but I'm certain that there must be a formula that could calculate the ideal ratios for betting - any ideas?

[jedaisoul]

Given a tournament with 8 players, where each is ranked with a certain corresponding payout, how would i determine the optimal betting strategy to minimize risk?

I'm not an expert, but I would suggest there are three answers to the question you have asked, and two to the question I think you meant to ask...

• The three answers to the question you have asked (minimise risk) are:
  • Do not bet! This is by far the safest and surest option as you cannot loose, hence the minimum risk. But, if that does not appeal to you...
    
  • Bet on all players in the reverse ratio to their odds (i.e. bet most on the favorite). That should ensure that you will, at best, break even, but will minimise the potential loss, as you are guaranteed to have backed the winner. But, if the certainty of an overall loss does not appeal...
    
  • Bet on the player with the lowest payout ratio (the favorite) as he should be most likely to win (hence the poorer return on the bet). (Player 1 in your example).

  [*] The question I think you meant to ask, is not how to minimise risk, but how to maximise the likelihood and amount of the return (which is a different thing). It is my understanding that the weightings (payout ratios) are set by the bookmaker according to the amount of money bet on the players. He arranges this so that whoever wins, the overall payout is less than the total amount bet. So the bookmaker always takes his cut. So the only ways to optimise your return are:

  • Be the bookmaker.
    
  • Do not bet!

 

Basically, betting is a mug's game. Unless you are the bookmaker, you always loose in the end. It's fixed like that.

[pgrmdave]

That's not true, with those given odds, I can ensure that I earn money, ideally I can find numbers to bet on each player where the returns are nearly the same no matter who wins.

[jedaisoul]

That's not true, with those given odds, I can ensure that I earn money, ideally I can find numbers to bet on each player where the returns are nearly the same no matter who wins.

If that is true, then the example you have given is unrealistic. Bookmakers are business people who make a living out of accepting bets. They don't gamble. They set the odds to ensure that whoever wins, they take their cut. They would not last long in business if they did otherwise.

 

What I think you are talking about is the second option I gave, betting on every player in the inverse of their odds, so that whoever wins, you will receive roughly the same amount back. That is similar to the calculation that the bookmaker makes, except that he shortens the odds to give him a margin. If the bookmaker does his sums correctly, you cannot get back more than you bet using this strategy.

 

Sorry, there is no free lunch in betting. You are betting against professionals. They know their business.

[Qfwfq]

I agree that the professional bookmakers know their stuff so that they're making profit in the long run, however there is no certainty in the matter. The bookmaker might be unlucky on a single given run.

 

In any case, they "probability" is not such a well defined notion for these things, it can only be estimated. I think the bookmakers most of all need experience, both in the trade and in judging players.

 

In order to properly answer Dave's question (in terms fit for a Ph. & M. forum) the table would have to have probabilities as well as payouts. Only by taking these (hypothetically at least) as the actual values does it make sense to discuss the matter as a question of statistics.

[jedaisoul]

I agree that the professional bookmakers know their stuff so that they're making profit in the long run, however there is no certainty in the matter. The bookmaker might be unlucky on a single given run.

 

In any case, they "probability" is not such a well defined notion for these things, it can only be estimated. I think the bookmakers most of all need experience, both in the trade and in judging players.

I agree that I was speaking in general. I'm not familiar with the betting on tournaments, so I don't know how that works. So it is possible that the bookmakers have to estimate the odds, hence may make an error.

 

In order to properly answer Dave's question (in terms fit for a Ph. & M. forum) the table would have to have probabilities as well as payouts. Only by taking these (hypothetically at least) as the actual values does it make sense to discuss the matter as a question of statistics.

I disagree. Probability has nothing to do with what Dave is asking. It's a simple matter of betting on ALL the players in an approriate amount to ensure that WHOEVER wins, the payout is roughly the same. That's a (fairly) simple calculation. The complex bits are:

a) Are the odds fixed when the bet is placed?

B) What happens to your bet(s) if a player pulls out before the game? E.g. If the favorite drops out:

i. What happens to the money you placed on that player?

ii. What happends to the odds on the remaining players, are they shortened?

c) When you win, do you get the individual winning bet back as well as the winnings (as in horse racing)? E.g. If you place $10 at 2.5:1, do you get $25, or $35?

 

Knowing these things I can calculate the amounts to bet on Dave's example, and the expected return.

[jedaisoul]

The easiest way to calculate Dave's example is to:

a) Set a target return ($100).

:) To receive $100 if player 1 wins at 3.45:1, you have to bet $100/3.45 on him i.e. $28.99 (rounded up).

c) Repeat this calculation for the other players.

d) The total you have to bet is $111.16.

 

This is most easily worked out using a spreadsheet, but is simple enough to be done by hand. Note: If you get slightly different figures it is because I've used the ROUNDUP function in Excel.

 

Sorry, no free lunch.

 

Note: This also indicates that the bookmaker's take is 10% of the total bet (less betting tax, if any). Not bad, given that its a certainty whoever wins.

[LaurieAG]

Given a tournament with 8 players, where each is ranked with a certain corresponding payout, how would i determine the optimal betting strategy to minimize risk?

 

Example:

Player       Payout
Player 1:   3.45
Player 2:   8.39 
Player 3:   7.76
Player 4:   9.17
Player 5:   9.24
Player 6:   8.74
Player 7:   7.99
Player 8:   8.59

 

Hi pgrmdave,

 

A couple of years ago I would play a free (written by Germans) horse racing game based on English tracks and the odds were given in a similar way. I'm not sure of its name.

 

The best tactic I found was to work out the best relative payout risk for 1st 2nd and 3rd by picking the one that has the largest payout difference to the next rated 'player' and competitor for the place. In your example no 1 would be preferrable to 3 or 7 because it has a much larger payout difference between the next placed 3 and 7 than they both have with each other or 2.

 

There are several different betting strategies involved with betting on several of the 'players' with amounts determined by the potential payout of a fixed amount, that would cover all bets with a tidy profit.

 

I like to look at betting on the TAB in this sense, when you are the only one playing the game, the maximum you can get back is the prize pool (what you paid) minus government TAX.

[jedaisoul]

There are several different betting strategies involved with betting on several of the 'players' with amounts determined by the potential payout of a fixed amount, that would cover all bets with a tidy profit.

I'd like to see an example that substantiates this claim.

[Qfwfq]

It's a simple matter of betting on ALL the players in an approriate amount to ensure that WHOEVER wins, the payout is roughly the same.

:doh: I forgot about betting on all of them! :hyper:

 

However you have not demonstrated there being no winning strategy, given Dave's figures (and supposing no dropouts). I'll give it a thought but I can't right now. It implies discussing a transformation [imath]{\cal T}:\mathbb{R}^ {+n}\rightarrow\mathbb{R}^{+n}[/imath] with [imath]n[/imath] the number of players, although not a complicated one, and perhaps your strategy is the best case solution but I can't work it out until I have more time.

[jedaisoul]

However you have not demonstrated there being no winning strategy, given Dave's figures (and supposing no dropouts).

Quite true, it's not a formal proof. I believe that it is the optimal strategy as any other would involve an element of risk, but I can't prove that.

 

I'd be interested to see a formal proof...

[pgrmdave]

The easiest way to calculate Dave's example is to:

a) Set a target return ($100).

B) To receive $100 if player 1 wins at 3.45:1, you have to bet $100/3.45 on him i.e. $28.99 (rounded up).

c) Repeat this calculation for the other players.

d) The total you have to bet is $111.16.

 

This is most easily worked out using a spreadsheet, but is simple enough to be done by hand. Note: If you get slightly different figures it is because I've used the ROUNDUP function in Excel.

 

Sorry, no free lunch.

 

Note: This also indicates that the bookmaker's take is 10% of the total bet (less betting tax, if any). Not bad, given that its a certainty whoever wins.

 

You're wrong, because you don't take into account that for every bet you win, you lose all the others. Which means that the formula to calculate your winnings is PAYOUT * AMOUNT BET ON WINNER - SUM(ALL OTHER BETS)

If you increase the amount bet on one player, you decrease the winnings on the others. If I use your strategy in the given example, I lose on the bets of 9.17 and 9.24.

[LaurieAG]

I'd like to see an example that substantiates this claim.

 

Hi jedaisoul,

 

The name for this form of betting is 'Overlay'.

 

Deviant Behavior: Readings in the ... - Google Book Search

[pgrmdave]

Not quite - "overlay" is a term used when the payout is greater than the expected chance of winning. I'm saying that with those numbers, it doesn't matter who wins, I should be able to come out ahead. A simpler example:

Player          Payout
Player 1:      1.5
Player 2:      1.2

 

If I bet $9.99 on player 1 and $11.35 on player 2, I make $3.63 (rounded down) no matter who wins. Either 9.99 * 1.5 - 11.35 or 11.35 * 1.2 - 9.99. My question is how do I come up with those numbers with a formula?

[jedaisoul]

You're wrong, because you don't take into account that for every bet you win, you lose all the others. Which means that the formula to calculate your winnings is PAYOUT * AMOUNT BET ON WINNER - SUM(ALL OTHER BETS)

That's precisely what I DID calculate, but I clearly have not explained the steps well enough. So here goes...

Target Return: $100

Player___Payout_Calculation___Bet
Player 1:__3.45_100/3.45 = $28.99
Player 2:__8.39_100/8.39 = $11.92
Player 3:__7.76_100/7.76 = $12.89
Player 4:__9.17_100/9.17 = $10.91
Player 5:__9.24_100/9.24 = $10.83
Player 6:__8.74_100/8.74 = $11.45
Player 7:__7.99_100/7.99 = $12.52
Player 8:__8.59_100/8.59 = $11.65

Total Bet_________________$111.16

Your return is always $100, whoever wins, but you have to bet $111.16. Note: As already explained, all the bets have been rounded up to nearest cent.

 

I hope that clarifies how you calculate the amount of the individual bets to ensure a chosen return, and hence determine the overall bet required.

If you increase the amount bet on one player, you decrease the winnings on the others.

That depends on what you mean by "winnings". None of the other bets produce "winnings" anyway (in the sense of producing a return greater than the total bet).

 

If I increase the bet on one player:

a) I increase the total bet.

B) I increase the potential return if that player wins.

c) The return on the others (if they win) is unchanged.

d) I introduce an element of probability as all the potential returns are no longer the same.

 

If I use your strategy in the given example, I lose on the bets of 9.17 and 9.24.

That is true, in the sense that you lose whoever wins.

[pgrmdave]

That's precisely what I DID calculate, but I clearly have not explained the steps well enough. So here goes...

 

You seem to miss the point...On your bets, this is the expected returns, calculated as bet * payout - SUM(other bets):

Target Return: $100

Player___Payout_Calculation___Bet______Earnings if won
Player 1:__3.45_100/3.45 = $28.99______17.85
Player 2:__8.39_100/8.39 = $11.92______0.77
Player 3:__7.76_100/7.76 = $12.89______1.76
Player 4:__9.17_100/9.17 = $10.91______-0.21
Player 5:__9.24_100/9.24 = $10.83______-0.26
Player 6:__8.74_100/8.74 = $11.45______0.36
Player 7:__7.99_100/7.99 = $12.52______1.39
Player 8:__8.59_100/8.59 = $11.65______0.56

Total Bet_________________$111.16

 

Here, we have on player 4 if he wins, a payout of 10.91 * 9.17, or 100.04. But we've lost a total of 100.25, so overall we lose.

 

See, I've made some money on most of the bets, and lost on others. I'm proposing that for these numbers, there are bets you can make that will 100% ensure that you win some money, no matter what. On the other hand, if I bet the following way:

 

Player___Payout___Bet______Earnings if won
Player 1:__3.45____$101.07_____$18.20
Player 2:__8.39____$47.90______$18.22
Player 3:__7.76____$51.34______$18.17
Player 4:__9.17____$44.22______$18.15
Player 5:__9.24____$43.92______$18.18
Player 6:__8.74____$46.18______$18.23
Player 7:__7.99____$50.03______$18.20
Player 8:__8.59____$46.90______$18.21

Total Bet_________________$431.56

 

Every single bet wins some money, grouped as tightly as I could get it. It has nothing to do with odds, or a target return. Try those numbers out and you'll see that no matter who wins, I end up about $18 over my original total bet.

[jedaisoul]

Ok, I see what you have done, you've assumed that the winning bet is returned, as well as the winnings. I asked if that was the case, but assumed not as I did not get a reply.

 

IF that is the case then it should be possible to win on ANY bet. I can work out the numbers, but before I do, I'd like confirmation that IS the case. I.e. Not just confirmation that that is what you are assuming, but that it IS the case. I doubt it, because my figures indicate that the bookmaker is taking a nice round 10% on the deal. But that relies on his NOT returning the winning bet with the winnings (or rather, that the "Payout" ratio ALREADY includes the return of the winning bet).

 

At least we understand each other's assumptions now...