By now you have been bombarded by yet another tom waterhouse marketing blitz. This time it’s his “amazing” offer for the Melbourne Cup. Just pay $10, pick the first 10 horses in the exact finishing order and $25 million dollars is yours. How he manages to get through the ads without bursting into a Dr Evil laugh is beyond me. You will have also noticed that tom has moved from the old slogan of “What punters want” to “This is betting now” or something stupid along those lines. But he seems to really be going full force with the now bit, meaning that betting now means only allowing mug punters to bet and not even complying with rules that almost all other bookmakers in the country have (NSW racing min bet rules). The William Hill group have made a huge error letting tom lead their business in Australia. Their reputation will be a shambles by the end of his reign and I doubt they will be able to repair the damage he has done.

I asked on twitter if anybody wanted to break down the numbers on this offer for me. Lenny and Matt obliged and sent me both very detailed articles. I have smushed them together to come up with the following post.

The offer

Select the first 10 runners across the line in order for a chance to win up to $25 million. $10 per entry and a maximum of 10 entries per person.

This really works out at odds of $2.5 million per dollar bet. By making each bet cost $10, he can make the final prize seem much bigger. Also I’m amused that he will only allow a maximum of 10 bets, this offer is so impossible that he is pocketing ~100% on every bet, again this is in place to make it seem like the offer is amazing. Let’s look at the real numbers.

The Maths

Lenny: There are a few ways to look at this mathematically – the easiest being to work out the odds if you were to select your top 10 runners in a random draw. Remembering that the selections need to be in order, and assuming we avoid the almost traditional Cup day scratchings, you have a 1 in 24 chance of selecting the winner.  Then a 1 in 23 chance of selecting 2nd (given the same horse can’t finish 1st and 2nd) and so forth – down to a 1 in 15 chance of selecting 10th.

The odds of this – 24 x 23 x 22 etc all the way down to x 15 – are one in 7,117,005,772,800. Or 1 in 7 TRILLION. To put that into some level of perspective: if every single human being alive today in the entire world had 1000 unique guesses, there’d still be no guarantee Tom would have to pay out his $25 million.

But of course, not every horse has an equal chance, so we’ll use a somewhat more complex method to come up with what is close to the correct probability. It’s a little convoluted, sure, but we’ll use last year’s Melbourne Cup odds (normalised to 100%, for accuracy) to work out the approximate chances of the favoured top 10 – i.e. the top 10 favoured horses, in order – actually occurring, based on the odds (sourced from last year’s Sportsbet.com.au sweep).

Fiorente was $7 in a ~124% market; this equates to an 11.445% chance. If you take Fiorente out and re-adjust the odds to again 100%, and assume the market that left is a rough estimate of running 2nd, it shows Mount Athos as an 11.309% chance of running 2nd. You can take Mount Athos out to get 3rd’s percentages etc etc, all the way down to the chance of Seville running 10th being 11.241%.

I’ve run the numbers on this and when you combine all the percentage chances of this top 10 happening in the favoured order – so the odds of any other order are longer – then it is a 1 in 6,905,774,345 chance. That’s one in 6.9 BILLION. Pretty big unders to accept $25 million for a $10 investment with those odds.

Steve: There are always numerous ways to look at a maths problem and Matt takes a different approach. Instead of taking last years top 10, he uses this years top 10 prices from Betfair.

Matt: Let’s assume there are 24 starters. I have taken prices from Betfair for the first 24 runners in market order (prices recorded on Saturday night) and have scaled the market to 100%. This is what it looks like.

1. Admire Ratki – $5.27 = 18.98%
2. Protectionist – $7.94 = 12.60%
3. Lucia Valentina – $8.86 = 11.29%
4. Fawlkner – $14.18 = 7.05%
5. Mutual Regard – $20.37 = 4.91%
6. Who Shot Thebarman – $21.23 = 4.71%
7. Junoob – $23.92 = 4.18%
8. Red Cadaux – $26.60 = 3.76%
9. Cavalry Man – $26.60 = 3.76%
10. Araldo – $31.95 = 3.13%
11. Willing Foe – $31.95 = 3.13%
12. Contributor – $48.54 = 2.06%
13. Van Percy – $48.54 = 2.06%
14. Signoff – $48.54 = 2.06%
15. Brambles – $48.54 = 2.06%
16. Amralah – $48.54 = 2.06%
17. Ambivalent – $57.47 = 1.74%
18. Silent Acheiver – $57.47 = 1.74%
19. Gatewood – $62.11 = 1.61%
20. Dandino – $62.11 = 1.61%
21. Royal Diamond – $62.11 = 1.61%
22. Opinion – $66.23 = 1.51%
23. Sertorius – $79.37 = 1.26%
24. Green Moon – $98.04 = 1.02%

To make this easy, I will be showing the mathematics for the top 10 favourites to finish in that order. Admire Ratki is priced at $5.27 after his impressive Caulfield Cup victory yesterday so he is a 1 in 5.27 or an 18.98% chance to finish first. Easy. Now, how do we work out what Protectionist’s chances of running 2nd and beating the rest of the field are? It’s actually not that difficult. We just need to determine what price Protectionist would be if Admire Ratki wasn’t in the field (as he doesn’t need to beat Admire Ratki). This is determined the same way as a “Without Favourite” market or if Admire Ratki was scratched and a deduction was applied. As the market above is at 100% we can deduct 18.98% from Protectionist’s price of $7.94 which comes to $6.43. We can now say Protectionist would be paying $6.43 to beat the remaining 22 runners.

We do the same thing with Lucia Valentina but deduct Admire Ratki’s 18.98% and Protectionist’s 12.6% from her price of $8.86 bringing it into $6.06. Lucia Valentina is paying $6.06 to beat home the remaining 21 runners.

If we wanted to calculate the chance of the 3 favourites running 1st, 2nd and 3rd in marker order we would multiply $5.27 (Admire Ratki’s winning odds) by $6.43 (Protectionist’s odds of beating the other 22 runners) and by $6.06 (Lucia Valentina’s odds of beating the remaining 21 runners) showing us the trifecta is a $205.35 chance based on the above odds.

I have done the same calculations all the way down to 10th favourite Araldo and this is what it looks like –

18.98% ($5.27) x 15.55% ($6.43) x 16.50% ($6.06) x 12.35% ($8.10) x 9.80% ($10.20) x 10.44% ($9.58) x 10.33% ($9.68) x 10.25% ($9.76) x 11.42% ($8.76) x 10.50% ($9.52)

=

a 1 in 1,280,593,053 chance (that’s a one in one billion two hundred and eighty million five hundred and ninety three thousand and fifty three chance) of the top 10 favorites running in market order in the 2014 Melbourne Cup.

Steve: Matts odds of 1.2 billion is simply the odds of the top 10 finishing in their rated order. I would say we can take Lenny’s numbers from last years results and Matt’s from this years odds and come up with a middling figure of around a 1 in 4 Billion chance.

Conclusion

This offer is a joke and while a bit of fun for the mug punter, it is probably the biggest ripoff in terms of odds I have ever seen. tom could have offered $100 million as the prize money or even $1 billion and it would still be worthless. The funny thing is, even with the odds stacked so heavily in his favour, he has still insured himself against any loss. He has paid an insurance company a small amount (I would guess no more then $50k) and if someone does get lucky then the insurance company will pay out the $25 million. They would spend even more on the marketing of the offer and it will result in many signups of mug punters. So once again a smart marketing move, but again just showing how he thinks of the betting public (as idiots).

The odds of winning OZ lotto are 1 in 45 million and the odds of winning Powerball are 1 in 76 million. By charging $10 per pick, the odds of winning tom’s offer is 1 in 40 Billion. When numbers get this big, people’s eyes glaze over. Let’s put it simply. If tom was a decent guy (bahaha) and wanted to simply break even on this offer, he would need to offer a prize pool of $40 billion dollars, and if you won it you would become the 8th richest person in the world.