Paddy Power 20% accumalator bonus.


Paddy Power Accumulator Promotion Advert
Paddy Power are running a promotion on all top UK Football matches (see right).  They are offering 20% bonus on all 5 Fold+ Accumulators.  At first sight it sounds like a good deal.  But will the bookies "edge" swallow up the potential 20% bonus?

 The first problem is to find an accumulator that has any chance of paying out.  Even if you can find 5 overwhelming favourites at 90% certainty, the chance of all 5 of them coming in is 0.90 x 0.90 x 0.90 x 0.90 x 0.90 = 0.59.  And so although you may feel that you picked absolute bankers you are at only about a 60% chance that you will get a payout. Not even mentioning that dead certs like that are very few and very far between.
 
Calculating Adjusted Probability

The next problem is the bookie's edge.  When a bookie quotes odds for example 5/1 for an event they mean 5 unfavourable outcomes to each 1 favourable which works out as a 1 in 6 chance or a 16.67% chance.  We can convert each outcome (home win/draw/away win) to a probability in the same way.  However when you add the probabilities for all the possible outcomes together you will arrive at something like 106%.  The 6% is the bookie's edge - this is what the bookie stands to make on the event, and consequently what the punters expect to lose.  If you are a frequent casual better, you will find that you win some and you lose some but your over all balance is constantly being chipped away at by this 6%.  For the sake of calculating a realistic probability I am going to spread the 6% edge across all outcomes proportionally (see the Adjusted Probability above calculated by dividing the Implied Probability by 1.06).

 Back to our Accumulator - typically the strongest favourites over the weekend of UK football look something like this: 
Typical Accumulator Picks

 This accumulator would pay out 70c per 10c wagered.  I've done the work and converted the odds to Adjusted Probabilities.  According to the calculations Man City's win probability is 78.70%, Bury have 57.01% chance, Celtic 61.90%, Derby 56.25% and Man Utd 61.22%.  Thus the total probability is 0.787 x 0.5701 x 0.619 x 0.5625 x 0.617 = 0.1031.  So despite picking all the strongest favourites we only have about 10% chance.  I would expect to be losing at least one leg of the accumulator 9 times out of 10.

 This give us an expected payout of 0.1031 * 70c = 7.15c.  Then dont forget to add our 20% bonus to give 8.58c which still leaves us well short of our original 10c stake.

 What Paddy Power have enticed you to do is create a bet that is unlikely to payout and if it does their "edge" will accumulate somewhat like compound interest on each leg of the accumulator to cancel out your 20% bonus.  You end up out of pocket.

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