Betting strategy

[jedaisoul]

Well, I decided to work the numbers anyway...

 

Taking the return of the winning bet into account, you can win on all cases. The calculation is similar to my original, but you add 1 to the divisor of the bet calculation in each case:

Target Return: $100

Player___Payout_Calculation_____Bet____Net___Gross
Player 1:__3.45_100/(3.45+1) $22.48 $77.55 $100.03
Player 2:__8.39_100/(8.39+1) $10.65 $89.35 $100.00
Player 3:__7.76_100/(7.76+1) $11.42 $88.61 $100.03
Player 4:__9.17_100/(9.17+1) $ 9.84 $90.23 $100.07
Player 5:__9.24_100/(9.24+1) $ 9.77 $90.27 $100.04
Player 6:__8.74_100/(8.74+1) $10.27 $89.75 $100.02
Player 7:__7.99_100/(7.99+1) $11.13 $88.92 $100.05
Player 8:__8.59_100/(8.59+1) $10.43 $89.59 $100.02

Total Bet____________________$95.99

For clarity,I’ve given two figures:

a) “Net”, the winnings on the bet (excluding the return of the bet).

:) “Gross”, the winnings including the return of the bet.

 

The gross return (winnings + winning bet) varies from $100.00 to $100.07, against the total bet of $95.99, so you make $4 whoever wins. Furthermore, you could bet a further $4, split between one or more players, to increase your winnings if one of those player(s) wins, whilst still ensuring that overall you cannot lose.

 

Anyway, I hope that clarifies how you calculate the amount of the individual bets to ensure a chosen return, (assuming that the winning bet is returned with the winnings)...

 

P.S. I'd still be interested to know whether the "Payout" ratio ALREADY includes the return of the winning bet. I think it does, and that would blow a hole through this nice little money making scam...

[LaurieAG]

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.

 

My question is how do I come up with those numbers with a formula?

 

Hi Pgrmdave,

 

The attached code (.txt) and .xls file contain the calcs and data for producing overlay betting sheets on a race meet.

[jedaisoul]

Thanks to LaurieAG for the overlay betting sheets. I'd still suggest caution, because that is based on conventional betting odds where:

a) Winnings = Bet * Odds

:) Payout = Winnings + Bet

 

The figures in your example quote "payout" which I take to mean the payout ratio (overall). So to calculate the conventional odds you need to deduct 1 from each of the payout ratios before you plug the figures in the spreadsheet. I.e.

Target Payout: $100

Player___PayRat__Odds__Calculation_____Bet____Win__Payout
Player 1 __3.45 2.45:1 100/(2.45+1) $28.99 $71.02 $100.01
Player 2 __8.39 7.39:1 100/(7.39+1) $11.92 $88.08 $100.00
Player 3 __7.76 6.76:1 100/(6.76+1) $12.89 $87.13 $100.02
Player 4 __9.17 8.17:1 100/(8.17+1) $10.91 $89.13 $100.04
Player 5 __9.24 8.24:1 100/(8.24+1) $10.83 $89.23 $100.06
Player 6 __8.74 7.74:1 100/(7.74+1) $11.45 $88.62 $100.07
Player 7 __7.99 6.99:1 100/(6.99+1) $12.52 $87.51 $100.03
Player 8 __8.59 7.59:1 100/(7.59+1) $11.65 $88.42 $100.07

Total Bet__________________________$111.16

The above is simply an expanded version of the first figues I gave, but shows the relationship between the payout ratio, odds, winnings and payout. Note: If you treat the payout ratio as being the odds (as in my second example) it will appear that you can make a profit, but I believe that is illusory.

[LaurieAG]

Thanks to LaurieAG for the overlay betting sheets. I'd still suggest caution, because that is based on conventional betting odds where:

a) Winnings = Bet * Odds

:beer: Payout = Winnings + Bet

 

Note: If you treat the payout ratio as being the odds (as in my second example) it will appear that you can make a profit, but I believe that is illusory.

 

Hi jedaisoul,

 

Not Quite, you are forgetting that only 3 or 4 selections are used in the overlay, not the whole field.

 

If you think about the pre result strategy you will see that there are two important components that both have tenuous links with the actual result itself. You can calculate your own ODDS and triangulate the difference between two separate probability systems to potentially arrive with a bet on the winner that will be a guaranteed payout because you have removed the no hopers from your betting strategy.

 

When you create your own rating system you actually use a set of criteria (possibly based on the obvious relationship between the time run the distance travelled and the weight carried and a comparison between the current start and previous starts where the result is known at a minimum) to dermine how your model predicts how the race will end. The results provide feedback over time and, depending on the accuracy of your model, profitable for your selections.

 

But things can go to both extremes. I have seen 1 race meet where a ratings program picked 7 winners from 9 selections in 8 races while I have also seen a race where a horse that placed near to last in its past 5 races at second and third string tracks won with a class record time at a major metropolitan meet. I have also seen many many meets with no results at all.

 

The real benefits of a rating system, especially if you can vary your ratings method(s), is to be able to test historic data (preferrably over at least 2 years or a couple of hundred meets) through your own ratings system and select the best settings that produce the best return, historically, before you outlay one cent on betting system!

[jedaisoul]

Not Quite, you are forgetting that only 3 or 4 selections are used in the overlay, not the whole field.

I was talking about the specific circumstance where you remove all probability by betting on all the players/runners. That will never win because you are essentially doing the same calculation as the bookmaker, only he sets the odds/payout to ensure that he takes his cut whoever wins.

[LaurieAG]

I was talking about the specific circumstance where you remove all probability by betting on all the players/runners. That will never win because you are essentially doing the same calculation as the bookmaker, only he sets the odds/payout to ensure that he takes his cut whoever wins.

 

Hi jedaisoul,

 

If you had the same calculation as the bookmaker your rating order would be the same order as the odds given by the bookmaker, especially if you too factored in a profit. If you just use the bookmakers odds you can still do a dry run of historic data to test your theory, without making any bets.

[jedaisoul]

If you had the same calculation as the bookmaker your rating order would be the same order as the odds given by the bookmaker, especially if you too factored in a profit. If you just use the bookmakers odds you can still do a dry run of historic data to test your theory, without making any bets.

Agreed, but in these circumstances it would be pointless. Unless the bookmaker makes an error, you can never win with this strategy. There has to be an element of probability for you to be able to win. Then you are, effectively, betting against the other punters as to whose strategy is better.

 

So I'm not disagreeing with the idea of trialling a strategy without betting, I did that myself many years ago. I think it is a very good idea, if you are going to bet in the first place. I ran a trial for one year, analysed the results, amended my strategy and trialled for another year. For me, trialling convinced me that that it was not worthwhile, so I abandoned betting as a money making occupation.

 

By the way, I'm not saying that betting can't be worthwhile, but you need a better strategy than other people are using to be able to win overall. I suspect that, retrospectively, you can always find a strategy that would have worked in the test period, but that does not mean that the same strategy will work reliably in practice. I did not find one.

[CraigD]

The worst case for this game would be that the “house” is allowed to see your bets, then determine which player wins (which, to avoid confusion, I’ll can “row the house chooses” from here on).

 

As several people have, I think, pointed out, with the given payouts, assuming the worst case, you can’t win this game (ie: win more than you bet). By my calculations, the house will always win at least about 11.117% of your total bet. In the usual terms of game theory, you’d say this game has an expected value of about -0.11117.

 

Therefore, if you increase the payouts uniformly by more than about 11.117%, it’s possible to make it possible to win the game in the worst case.

 

Regardless of what the payouts are, the strategy to maximize your winnings is to make them the same regardless of which row the house chooses. This can be done by taking any row (assuming all are positive) and calculating the bet for each row by dividing its payout by the selected row’s. Example, rounding to the nearest cent (which slightly breaks the strategy, allowing the house to chose a row that pays the least):

          Payout    Bet    Win
Player 1:   3.45   2.49   8.59
Player 2:   8.39   1.02   8.56
Player 3:   7.76   1.11   8.61
Player 4:   9.17   0.94   8.62
Player 5:   9.24   0.93   8.59
Player 6:   8.74   0.98   8.57
Player 7:   7.99   1.08   8.63
Player 8:   8.59   1.00   8.59
Total bet:         9.55

Here’s an example of this strategy when the payouts are uniformly increased by 1.12, making it possible to win more than you bet

          Payout    Bet    Win
Player 1:   3.86   2.49   9.61
Player 2:   9.40   1.02   9.59
Player 3:   8.69   1.11   9.65
Player 4:  10.27   0.94   9.65
Player 5:  10.35   0.93   9.63
Player 6:   9.79   0.98   9.59
Player 7:   8.95   1.08   9.67
Player 8:   9.62   1.00   9.62
Total bet:         9.55

This game is more interesting if the house is not allowed to know your bet before selecting the row, in which case the game’s payout matrix is 8xN, where N is the number of possible bet distributions available to the player. Such a game can be solved via conventional game theory – I suspect, but haven’t actually verified, that the best strategy for the house is to choose randomly, and the best for the player is the same as the worst case above.

[jedaisoul]

Thanks CraigD. You example is slighty different from the scenario I modelled, but the answer is essentially the same.

[LaurieAG]

This game is more interesting if the house is not allowed to know your bet before selecting the row, in which case the game’s payout matrix is 8xN, where N is the number of possible bet distributions available to the player. Such a game can be solved via conventional game theory – I suspect, but haven’t actually verified, that the best strategy for the house is to choose randomly, and the best for the player is the same as the worst case above.

 

Hi CraigD,

 

In this case the probability for each row will be 1/8 and the payout has no relationship with a rows probability for selection.

 

How are the payout figures calculated in both cases (pre or post selection) because a win bet on any payout greater than 10:1 will return a profit in either case. Are the payouts based on a pool of other people betting on the rows or what, random amounts?

[jedaisoul]

How are the payout figures calculated in both cases (pre or post selection) because a win bet on any payout greater than 10:1 will return a profit in either case. Are the payouts based on a pool of other people betting on the rows or what, random amounts?

I would suggest that the odds are based on the inverse of the total amount bet on a given row, rather than the number of bets. That way, the bookmaker can ensure a profit irrespective of who wins.

[CraigD]

I would suggest that the odds are based on the inverse of the total amount bet on a given row, rather than the number of bets. That way, the bookmaker can ensure a profit irrespective of who wins.

If the house knows with the precise probability of a given row being chosen (ie: “winning”) and sets the payouts proportionally to the inverse of these probabilities, as jedaisoul suggests, a curious thing happens to the optimum strategy of the the player (ie; bettor) strategy: there is none. They player can place his bets in any manner – all on one, the same amount to each, or according to the worst case assumption, as given in post #25.

 

This is because the game’s expected value – the probability of an outcome • its payout – is the same when the probability and the payout are inverses. So any betting strategy has the same expectation.

 

Another interesting case is when the probability of each row is the same (uniform, eg: the row is chose by a few fair coin tosses). In that case, the optimum betting strategy is to bet all of you money on the highest payout – in the given example, “Player 5”. Note that, if the probabilities are uniform, the expected value of this row is [math] 9.24 \cdot \frac18 = 1.115[/math], so betting this way will give you an average gain of 11.5% per play.

How are the payout figures calculated in both cases (pre or post selection) because a win bet on any payout greater than 10:1 will return a profit in either case. Are the payouts based on a pool of other people betting on the rows or what, random amounts?

I believe Laurie is asking questions about how real-life bookmakers – “the house” – determine payouts. As far as I know, this is a complicated subject beyond the domain of simple mathematical game theory alone, touching on tradition and law. I know that in the US state of Nevada, bookmakers are legally permitted to change payouts (odds boards) as they are taking bets. The payout for a bet on a given outcome varies depending on when it is placed. This allows the house to assure that they don’t loose too much if many bettors place bets on a high payout “longshot” outcome that improbably wins.

[jedaisoul]

The payout for a bet on a given outcome varies depending on when it is placed. This allows the house to assure that they don’t loose too much if many bettors place bets on a high payout “longshot” outcome that improbably wins.

That is correct, but I suggest that the bookmaker does not rely on probability. There is a relatively simple strategy that ensures that the house always wins. The bookmaker balances the odds against the total bet on each runner/player so that whoever wins, the payout is less than the total amount bet on all the runners/players.

 

There is a problem with this strategy, but it is not the risk of a "longshot" winning. That can easily be accommodated by shortening the odds on the "longshot" as more bets are taken. The problem is to take enough bets on the less favored players/runners to cover the likely event of the favorite winning. Say there is one player/runner who is recognised as being by far the most likely to win. Just about everyone is going to bet on that one. Which is a problem. If the favorite wins, the bookmaker is going to have to payout all the bets on the favorite, and the winnings. Where is this money to come from? A simplified example:

 

Favorite @ 5:1 on, bets placed $100,000, potential payout $120,000.

No-hoper @ 100:1 against, bets placed $500, potential payout $50,500.

Total bets placed (say) $110,000 (including unspecified other runners/players)...

 

If the no-hoper wins, the bookmaker is very happy, he's made a hansome profit ($110,000 - $50,500).

 

If the favorite wins, not only has he not made a profit, he cannot cover the payout from the bets taken! In this case, the bookmaker has not been able to balance the odds to avoid a loss if the favorite wins, even when the odds on the favorite are as low as 5:1 on. He would have to reduce the odds to 10:1 on, and even then he would only cover the payout. He'd need to reduce the odds on the favorite to 20:1 on (or so) to show a profit if the favorite wins. Then he risks a backlash from the punters, who may feel that they have been cheated.

 

So probability plays little or no part in the bookmaker's strategy. He needs to attract enough bids on the rest of the field to cover the likelihood of the favorite winning. To do that he needs to make the odds attractive enough for people to be prepared to place a bet on an outsider, even though there is little likelihood of winning! That relies more on psycology than probability.

[LaurieAG]

I believe Laurie is asking questions about how real-life bookmakers – “the house” – determine payouts. As far as I know, this is a complicated subject beyond the domain of simple mathematical game theory alone, touching on tradition and law. I know that in the US state of Nevada, bookmakers are legally permitted to change payouts (odds boards) as they are taking bets. The payout for a bet on a given outcome varies depending on when it is placed. This allows the house to assure that they don’t loose too much if many bettors place bets on a high payout “longshot” outcome that improbably wins.

 

There is a difference between how a bookmaker calculates the win/place dividend and how a Tote (house if you like, or TAB, or totalisor) calculates the dividend.

 

A bookie must pay the odds given on their betting slip for a win because it is a form of contract (and may change their payouts/contract amounts as they take bets) while the tote divides the win pool by the number of winning units.

 

So, for the tote, each rows payout is based on the number of betting units in the row (usually $1 units) divided by the total win pool for ALL rows (i.e. all $ bet minus govt tax).

 

I would suggest that the odds are based on the inverse of the total amount bet on a given row, rather than the number of bets. That way, the bookmaker can ensure a profit irrespective of who wins.

 

You describe an amount that can only be calculated AFTER all bets have been placed as per the tote method. The bookies ODDS, however they are calculated, are given AS the bets are placed not after and a win bet is paid at the odds given on your betting slip.

[jedaisoul]

There is a difference between how a bookmaker calculates the win/place dividend and how a Tote (house if you like, or TAB, or totalisor) calculates the dividend.

 

A bookie must pay the odds given on their betting slip for a win because it is a form of contract (and may change their payouts/contract amounts as they take bets) while the tote divides the win pool by the number of winning units.

 

So, for the tote, each rows payout is based on the number of betting units in the row (usually $1 units) divided by the total win pool for ALL rows (i.e. all $ bet minus govt tax).

Agreed.

 

You describe an amount that can only be calculated AFTER all bets have been placed as per the tote method. The bookies ODDS, however they are calculated, are given AS the bets are placed not after and a win bet is paid at the odds given on your betting slip.

I agree that I have simplified the case. I hope that did not confuse anyone. As you say, in reality, the bookie accepts individual bets at fixed odds. So what he must do in practice is change the odds for subsequent bets as the amount bet on a specific runner/player increases. But the overall calculation he is doing is substantially what I said. He attempts to balance the total payout whoever wins againt the total bets received, to leave him with a profit. This does not rely on probability.

 

The problem with that strategy is if there is a very strong favorite, and he is unable to attract sufficient bid on the rest to cover the likely payout if the favorite does indeed win. Then he could actually make a loss. That is where psycology comes in. And, in that case, I suspect the credulity of the average punter works in his (the bookie's) favor.

[ughaibu]

Pgrmdave: This kind of betting is known as "Dutching", the easiest solution is to use a dutching calculator. I think there are some free online, try a search. Presumably you're spreading your bets around several bookmakers, according to who offers the best price(?)

[CHADS]

If you bet on the whole field allocating money to all constituents of the race then you will probably want to put more on the fav to cover the total bet amount with lesser stakes for the decending favoured participants but you will definatly go broke or amazingly break even ..... the bookmakers books are designed so they will make profit .. Even money is in the bookmakers favour becuase they are in the trade for the long term and the fav winning in anything other than a 2 man contest is below 50%.

 

Im a pro Gambler .. if you need me to answer questions just ask!

 

The most important thing in your betting strategy should be the odds not the favourite for every race ... the favourite is what the majority of people have placed their money on and what the bookmakers analysts feel has the best chance .... Usually with horse races for example i will first choose a race for the day usually a race with 12 runners or more in a handicap race.... All ready this is maximizing my potential odds ..... secondly i Analyze all the race/horse data and i can sucessfully remove over half the field .... leaving around 4 or 5 horses to choose from , This takes about 2 hours if you have patience and the presence of mind not to overthink your way out of a good choice..

 

Finally of this last group i list them in the order i believe the data suggests they will finish....

 

Now if you believe a horse will come first then try to find the best odds for that horse , If every bookmaker thinks its favourite then try the horse you believe will come second..... you might find a bookmaker giving 10 - 1 which is great ....

 

With this method i regularly pick 20 - 1 , 33 - 1 winners and everyone in the betting shop ask how ..... Take the time to minimize the chance of failure read all the data and make a choice on odds ...... if i choose a 20 -1 horse it only has to win one time in twenty for a even score .... but if you always pick favs then they must win straight away ...... it takes time but one of the early lessons i found was the big odds put me off .... now i hunt them big odds down .:)