3970 – Beating the Bookies by Ruslan
Posted by Listen With Others on 14 Mar 2008
Friday 22nd February, 6pm Print off the first numerical puzzle of the year, a second Listener from Ruslan whose debut, Certificate 18, was well received last May. After my faux pas over Xanthippe’s gender I will not make any assumptions here. My spellchecker suggests changing Ruslan to Russian but I shall stick with the idea that this might be a contraction of Russ Lane.
The theme is betting on a 12 horse race and finding the first three places. Gambling holds no appeal for me, even down to the Lottery, and I have never attended a race meeting so I am grateful that the preamble fully explains the mechanics of each way betting. Is rounding up on payouts normal practice in the industry? It would seem unlikely that bookies would give anything away – even fractions of a penny!
The opening move is quite clear with the three clues involving Iago (14ac, 16ac and 11dn) intersecting but I don’t plan spending any more time on this tonight.
Saturday, 11am So, the three clues involving Iago:
11dn: 120 + 60x + 60x ÷ 4 = 120 + 75x = ?pq?
14ac: 70 + 35x + 35x ÷ 4 = ?p??
16ac: 30 + 15x + 15x ÷ 4 = ??q
From size constraints, 14ac sets the shortest possible odds (x to 1) at 22 to 1 and 16ac the longest at 52 to 1:
My calculator is programmable but I go through 60 calculations on 11dn and 14ac the long way and find four matches for p:
x

11dn

14ac

16ac

28

2220

1295

555

30

2370

1383

593

31

2445

1427

612

33

2595

1514

649

But only 33 to 1 matches q for 16ac, therefore:
Iago 33 to 1, 11dn = 2595, 14ac = 1514, 16ac = 649
Immediately we can see that 14dn must be 140, therefore:
Tyro 6 to 1, 14dn = 140, 3dn = 100
Now, looking at the two clues involving Ciao:
18ac: 25 + 25x ÷ 4 = ?0
1dn: 25 + 25x = ???
Only one fit is found giving:
Ciao 4 to 1, 18ac = 50, 1dn = 125
Moving on to the three clues involving Lido:
6ac: 85 + 85x ÷ 4 = ???0
17ac: 90 + 90x ÷ 4 = ?r??
12dn: 55 + 55x ÷ 4 = ?4r?
The shortest possible odds, 69 to 1, are set by the size of 12dn and all three can accommodate 100 to 1. I don’t think that I want to go through the afternoon doing dozens of repetitive calculations so time to get some computing power on this. I have Excel and BBC Basic but I think that Excel is more suited to this job. It has a ROUNDUP function that I don’t know of directly in Basic. You can round up to any value so for 7654.321 entering 2 rounds up to two places of decimal (7654.33), 0 the integer value (7655) and –2 the hundreds (7700). ROUNDUP and the related ROUNDDOWN can be mimicked in Basic by using INT(x) and multiplication and division by powers of ten. Before Lido, I do a check on Iago using Excel and find no mistakes.
As it happens, only the top three values for 12dn in range have 4 as the second digit so I could have done this quicker by calculator had I but checked:
Lido 100 to 1, 12dn = 1430, 17ac = 2340, 6ac = 2210
With Excel and a calculator I complete the rest of the grid in about 20 minutes and all the odds are known by 1.30pm.
I make a mistake with Olio by reading the Excel Row Header (17) rather than the odds 16 to 1. The mistake was not corrected until a final check was made, and it would not have made any difference to the outcome had it been left, but using odds of 17 to 1 for Olio has an extraordinary effect that I will come to later.
I suffer a panic attack with Sumo at 3ac. I know the odds are 15 to 1 from 2dn but when I enter the values in 3ac find that the result is not an integer:
3ac: 25 + 25 × 15 ÷ 4 = 118.75
By using Excel I had forgotten that we are rounding up fractions!
I use BBC Basic to do the calculations on Ruslan’s bets. X is the odds on each horse, W the payout on a win and P the payout on a place:
10 READ X
20 W=100+50*X+50*X/4
30 IF W>INT THEN W=INT(W)+1
40 P=50+50*X/4
50 IF P>INT(P) THEN P=INT(P)+1
60 PRINT X,W,P
70 GOTO 10
80 DATA 100, 60, 33, 20, 16, 15, 11, 8, 7, 6, 4, 2
So, 50p each way gives the following payouts for a win or place:


Win

Place

Lido

100 to 1

£63.50

£13.00

Mojo

60 to 1

£38.50

£8.00

Iago

33 to 1

£21.63

£4.63

Agio

20 to 1

£13.50

£3.00

Olio

16 to 1

£11.00

£2.50

Sumo

15 to 1

£10.38

£2.38

Nemo

11 to 1

£7.88

£1.88

Filo

8 to 1

£6.00

£1.50

Xeno

7 to 1

£5.38

£1.38

Tyro

6 to 1

£4.75

£1.25

Ciao

4 to 1

£3.50

£1.00

Ergo

2 to 1

£2.25

£0.75

We are asked to find one winner and two places that result in the minimum profit on a £12 outlay – £12.01 plus. Also, the first letters in order spell out how the results may be seen. I am sure that you mathematicians out there have an elegant way of doing this but I am reduced to using trial and error. It is clear that the winner must come from Sumo or below so here are some shots:
· Sumo (£10.38) plus Ciao (£1.00) and Ergo (£0.75) totals £12.13 – fairly minimal and SEC has five entries in Chambers but nothing to do with results as I see them.
· Nemo (£7.88) plus Tyro (£1.25) and Agio (£3.00) also totals £12.13 – but NTA does not stand for the National Turf Association but National Training Award(s).
· Might it be quicker to guess how the results could be seen: on the NET (no – £9.88), by FAX (no – £7.41) or TEL (no – £18.50) – perhaps not.
· Filo (£6.00) plus Iago (£4.63) and Xeno (£1.38) totals £12.01 – FIX or FXI? Aha! The results might be seen as a fix!
Results of the race:
Winner:

Filo at 8 to 1

Second:

Iago at 33 to 1

Third:

Xeno at 7 to 1

Ruslan profits by 1p but wouldn’t one have to pay tax on any winnings, on the full £12.01?
None of the top three favourites are placed – a pretty rare event I would imagine leading to the suspicion that the race was fixed.
All done at 3.30pm.
This is exactly how the puzzle finished for me but it is not a complete account of events. Remember that I had misread the odds for Olio as 17 to 1, which gives £11.63 for a win and £2.63 for a place. Consequently, I found two further combinations that totalled £12.01:
· Nemo (£7.88) plus Olio (£2.63) and Filo (£1.50) totals £12.01 – NOF or NFO.
· Tyro (£4.75) plus Iago (£4.63) and Olio (£2.63) also totals £12.01 – TIO or TOI.
I thought that this was Ruslan being incredibly fiendish and rivalling Elap for numerical wizardry – I was really disappointed to find it incorrect.
Sunday Afternoon – Post Mortem For sheer enjoyment I thought that Homer’s Carte Blanche last week would be hard to beat all year but only a week on and surely Ruslan has done it. There were rather too many repetitive calculations to manage with only a calculator throughout but that may have been due to my method being at fault. Nevertheless, I rather wish now that I had waited a bit longer before turning to Excel – I don’t have it but it is perhaps akin to using TEA for word puzzles – it is something that should only be used as a last resort or I feel that I am missing the point.
Unusual features were: the entry, a refreshing change from the likes of x^{8}, the working in fractions and having all stakes a multiple of 5p. However, the latter may be the reason for the artificial rounding up and also the asymmetric grid. Although easy to spot, the entry was a mini puzzle in its own right – could it have existed anywhere other than in a ‘crossword’ grid?
I thought the naming of the horses a very nice touch and it could have been extended to the entire alphabet, with perhaps the exception of Q. I had a quick look in the index of the Times Atlas and couldn’t see any appropriate place name ending in O but there were quite a few with vowel endings: Qena, Qaxi, etc.
I considered the stakes used in clues ridiculously low but this very weekend, by a happy coincidence, a punter won a million pounds on an eightrace accumulator for a stake of just 50p. However, the Ladbrokes Web site says that there is a £2 minimum stake for tote betting, whatever that is.
The scenario may have been a touch unrealistic but I would find it difficult to believe that there was a solver who did not rejoice in this gem of a puzzle.
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