Betting strategy

[jedaisoul]

Originally Posted by Qfwfq

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]

Originally Posted by jedaisoul

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]

Originally Posted by jedaisoul

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]

Originally Posted by pgrmdave

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.

Originally Posted by pgrmdave

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.

Originally Posted by pgrmdave

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]

Originally Posted by jedaisoul

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...

[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).
b) “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]

Originally Posted by 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.

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
b) 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.