Analysis of Rule4 for arbitrage betting
When looking into racing arbitrage I came across one condition that worried me in which bookmakers will decimate the odds.
Tattersalls Rule 4 (c) to give it it's full title is applied when a horse is removed from the race after bets have been placed and ensures the bookies are still in pocket after refunding everyone who backed the non-runner. So how does this affect someone who backed all of the outcomes? I don't see a quick way of doing this and I couldn't find any tools online so I'm going to have to analyse a lot of horse races.
For the first example I will use today's 14:50 @ Wincanton, we are betting on all outcomes with a total stake of £100, here are the best odds for the race today and the required stakes to get the same 95.24% (£4.76 loss) return regardless of the outcome:
| Odds | Stake(£) |
| 3.5 | 27.21 |
| 4 | 23.81 |
| 4.33 | 22 |
| 5 | 19.05 |
| 12 | 7.94 |
Using
this chart from Ladbrokes in which we are given the deductions with the odds in decimals I've written a script that is available on
Github to create tables showing all of the resultant odds. The top row holds the odds of the horse which has dropped out and the left column holds the odds for the horses still running.
| Odds | 3.5 | 4 | 4.33 | 5 | 12 |
|---|
| 3.5 | X | 2.875 | 3 | 3 | 3.375 |
|---|
| 4 | 3.25 | X | 3.4 | 3.4 | 3.85 |
|---|
| 4.33 | 3.4975 | 3.4975 | X | 3.664 | 4.1635 |
|---|
| 5 | 4 | 4 | 4.2 | X | 4.8 |
|---|
| 12 | 9.25 | 9.25 | 9.8 | 9.8 | X |
|---|
It will take far too long to work out every possible outcome by manually multiplying each of the resultant odds with it's original stake and adding the stake of the non-runner, so I then changed the script to work this out and print the highest possible return, the lowest possible return and the mean of all possible outcomes:
Difference in return || Actual return | Race
Worstcase| Mean |Bestcase||Worstcase| Mean | Normal |Bestcase
1.587 | 5.587 | 9.354 || 96.826 | 100.825 | 95.239 | 104.592 https://www.oddschecker.com/horse-racing/wincanton/15:25/winner non runner
To clarify what this table means, the worst possible outcome with a single non runner and applying rule4 to this race is an increase in returns by 1.587% to 96.826% and the best case the return goes up 9.354% to 104.592%, and the mean is a 5.587% increase upto 100.825%.
This is looking good, but we need more data to be sure. So I've scraped Oddschecker for all of the days races to analyse..
Difference in return || Actual return | Race
Worstcase|Mean|Bestcase |Worstcase| Mean | Normal |Bestcase
0.420 | 3.389 | 11.848 || 90.509 | 93.478 | 90.089 | 101.937 https://www.oddschecker.com/horse-racing/ante-post-racing/national-hunt/punchestown-champion-chase/winner
0.383 | 1.646 | 7.080 || 39.682 | 40.945 | 39.299 | 46.379 https://www.oddschecker.com/horse-racing/ante-post-racing/national-hunt/punchestown-champion-hurdle/winner
0.124 | 1.944 | 5.012 || 62.773 | 64.593 | 62.649 | 67.661 https://www.oddschecker.com/horse-racing/ante-post-racing/national-hunt/champion-stayers-hurdle/winner
1.315 | 4.194 | 13.562 || 89.421 | 92.300 | 88.106 | 101.668 https://www.oddschecker.com/horse-racing/ante-post-racing/national-hunt/punchestown-gold-cup/winner
0.505 | 1.754 | 3.630 || 76.730 | 77.980 | 76.225 | 79.855 https://www.oddschecker.com/grand-national/winner
15.987| 16.084| 16.181 || 111.456| 111.553| 95.469 | 111.650 https://www.oddschecker.com/horse-racing/wincanton/13:50/winner
3.341 | 7.217 | 14.232 || 100.695| 104.572| 97.355 | 111.587 https://www.oddschecker.com/horse-racing/wincanton/14:20/winner
1.341 | 6.491 | 14.403 || 101.891| 107.041| 100.550| 114.954 https://www.oddschecker.com/horse-racing/wincanton/14:50/winner
1.587 | 5.587 | 9.354 || 96.826 | 100.825| 95.239 | 104.592 https://www.oddschecker.com/horse-racing/wincanton/15:25/winner
1.398 | 4.247 | 8.516 || 95.070 | 97.919 | 93.672 | 102.187 https://www.oddschecker.com/horse-racing/wincanton/16:00/winner
4.643 | 7.835 | 12.808 || 97.510 | 100.702| 92.867 | 105.675 https://www.oddschecker.com/horse-racing/wincanton/16:30/winner
1.623 | 9.015 | 22.792 || 100.974| 108.366| 99.351 | 122.143 https://www.oddschecker.com/horse-racing/wincanton/17:00/winner
0.358 | 3.719 | 5.988 || 90.180 | 93.541 | 89.822 | 95.810 https://www.oddschecker.com/horse-racing/stratford/14:00/winner
0.514 | 4.566 | 12.507 || 105.460| 109.511| 104.946| 117.453 https://www.oddschecker.com/horse-racing/stratford/14:30/winner
0.577 | 4.917 | 13.126 || 97.292 | 101.631| 96.714 | 109.840 https://www.oddschecker.com/horse-racing/stratford/15:00/winner
0.856 | 5.491 | 13.493 || 95.051 | 99.686 | 94.195 | 107.688 https://www.oddschecker.com/horse-racing/stratford/15:35/winner
0.272 | 3.060 | 6.590 || 91.514 | 94.302 | 91.242 | 97.831 https://www.oddschecker.com/horse-racing/stratford/16:10/winner
0.941 | 5.697 | 11.092 || 98.808 | 103.564| 97.867 | 108.959 https://www.oddschecker.com/horse-racing/stratford/16:40/winner
0.174 | 2.775 | 6.808 || 88.980 | 91.581 | 88.806 | 95.614 https://www.oddschecker.com/horse-racing/stratford/17:10/winner
0.248 | 2.735 | 5.898 || 100.508| 102.996| 100.261 | 106.158 https://www.oddschecker.com/horse-racing/wetherby/14:10/winner
3.389 | 8.403 | 18.806 || 102.423| 107.437| 99.033 | 117.840 https://www.oddschecker.com/horse-racing/wetherby/14:40/winner
0.581 | 3.361 | 12.945 || 88.275 | 91.056 | 87.695 | 100.640 https://www.oddschecker.com/horse-racing/wetherby/15:10/winner
5.939 | 7.494 | 9.729 || 100.962| 102.517| 95.023 | 104.751 https://www.oddschecker.com/horse-racing/wetherby/15:45/winner
0.392 | 2.479 | 10.070 || 98.750 | 100.837| 98.358 | 108.428 https://www.oddschecker.com/horse-racing/wetherby/16:20/winner
0.270 | 4.151 | 9.187 || 92.139 | 96.019 | 91.869 | 101.056 https://www.oddschecker.com/horse-racing/wetherby/16:50/winner
1.219 | 3.274 | 5.857 || 94.447 | 96.502 | 93.229 | 99.085 https://www.oddschecker.com/horse-racing/wetherby/17:20/winner
0.176 | 3.086 | 5.584 || 89.016 | 91.926 | 88.840 | 94.424 https://www.oddschecker.com/horse-racing/navan/14:15/winner
1.001 | 2.877 | 4.504 || 77.569 | 79.445 | 76.568 | 81.072 https://www.oddschecker.com/horse-racing/navan/14:45/winner
0.769 | 2.427 | 6.307 || 78.471 | 80.129 | 77.702 | 84.009 https://www.oddschecker.com/horse-racing/navan/15:20/winner
0.439 | 3.170 | 5.652 || 90.356 | 93.087 | 89.917 | 95.569 https://www.oddschecker.com/horse-racing/navan/15:55/winner
0.271 | 3.492 | 11.208 || 90.979 | 94.200 | 90.708 | 101.916 https://www.oddschecker.com/horse-racing/navan/16:25/winner
0.603 | 3.368 | 5.498 || 88.070 | 90.834 | 87.466 | 92.964 https://www.oddschecker.com/horse-racing/navan/16:55/winner
0.314 | 2.494 | 5.029 || 80.319 | 82.499 | 80.005 | 85.034 https://www.oddschecker.com/horse-racing/navan/17:25/winner
0.157 | 2.612 | 5.778 || 80.156 | 82.612 | 79.999 | 85.777 https://www.oddschecker.com/horse-racing/philadelphia-park/21:04/winner
2.030 | 4.058 | 7.589 || 101.015| 103.043| 98.985 | 106.574 https://www.oddschecker.com/horse-racing/keeneland/21:24/winner
0.260 | 2.362 | 5.816 || 87.505 | 89.607 | 87.244 | 93.061 https://www.oddschecker.com/horse-racing/keeneland/21:57/winner
0.357 | 3.080 | 5.659 || 91.297 | 94.020 | 90.941 | 96.599 https://www.oddschecker.com/horse-racing/keeneland/22:30/winner
6.111 | 6.111 | 6.111 || 28.333 | 28.333 | 22.222 | 28.333 https://www.oddschecker.com/horse-racing/aqueduct/21:11/winner
2.037 | 4.155 | 9.437 || 95.299 | 97.418 | 93.262 | 102.700 https://www.oddschecker.com/horse-racing/gulfstream/21:13/winner
1.040 | 3.853 | 8.255 || 89.483 | 92.296 | 88.442 | 96.697 https://www.oddschecker.com/horse-racing/gulfstream/21:46/winner
0.174 | 3.713 | 12.030 || 88.819 | 92.358 | 88.645 | 100.675 https://www.oddschecker.com/horse-racing/gulfstream/22:19/winner
1.903 | 4.214 | 10.118 || 103.082| 105.393| 101.179| 111.297 https://www.oddschecker.com/horse-racing/gulfstream/22:54/winner
2.378 | 5.543 | 12.018 || 104.949| 108.114| 102.571| 114.589 https://www.oddschecker.com/horse-racing/golden-gate-fields/21:15/winner
1.614 | 3.697 | 6.894 || 83.923 | 86.006 | 82.309 | 89.204 https://www.oddschecker.com/horse-racing/golden-gate-fields/21:45/winner
0.334 | 4.576 | 14.724 || 87.099 | 91.342 | 86.766 | 101.489 https://www.oddschecker.com/horse-racing/golden-gate-fields/22:15/winner
1.782 | 4.036 | 6.569 || 84.709 | 86.962 | 82.926 | 89.496 https://www.oddschecker.com/horse-racing/golden-gate-fields/22:45/winner
0.910 | 3.614 | 8.879 || 88.703 | 91.406 | 87.793 | 96.672 https://www.oddschecker.com/horse-racing/golden-gate-fields/23:15/winner
1.145 | 4.360 | 6.543 || 105.296| 108.512| 104.152| 110.695 https://www.oddschecker.com/horse-racing/golden-gate-fields/23:45/winner
0.781 | 2.766 | 9.008 || 81.973 | 83.958 | 81.192 | 90.200 https://www.oddschecker.com/horse-racing/turf-paradise/21:25/winner
1.061 | 3.362 | 5.305 || 91.247 | 93.548 | 90.186 | 95.491 https://www.oddschecker.com/horse-racing/turf-paradise/21:56/winner
1.146 | 4.271 | 17.626 || 94.000 | 97.124 | 92.854 | 110.480 https://www.oddschecker.com/horse-racing/turf-paradise/22:26/winner
1.743 | 3.870 | 9.727 || 97.871 | 99.997 | 96.127 | 105.854 https://www.oddschecker.com/horse-racing/turf-paradise/22:58/winner
0.516 | 3.249 | 7.000 || 85.169 | 87.902 | 84.653 | 91.653 https://www.oddschecker.com/horse-racing/turf-paradise/23:30/winner
0.555 | 3.067 | 5.444 || 80.984 | 83.496 | 80.430 | 85.874 https://www.oddschecker.com/horse-racing/turf-paradise/00:01/winner
1.484 | 3.515 | 10.749 || 81.332 | 83.363 | 79.848 | 90.597 https://www.oddschecker.com/horse-racing/turf-paradise/00:32/winner
0.578 | 3.425 | 11.097 || 79.170 | 82.017 | 78.592 | 89.690 https://www.oddschecker.com/horse-racing/turf-paradise/01:03/winner
0.188 | 2.876 | 9.591 || 96.101 | 98.789 | 95.913 | 105.505 https://www.oddschecker.com/horse-racing/santa-anita/21:30/winner
3.643 | 6.268 | 10.892 || 99.279 | 101.903| 95.636 | 106.528 https://www.oddschecker.com/horse-racing/santa-anita/22:00/winner
0.657 | 3.463 | 9.045 || 99.164 | 101.970| 98.507 | 107.552 https://www.oddschecker.com/horse-racing/santa-anita/22:30/winner
1.560 | 4.547 | 8.232 || 99.843 | 102.831| 98.283 | 106.516 https://www.oddschecker.com/horse-racing/santa-anita/23:00/winner
0.720 | 3.367 | 8.092 || 98.576 | 101.223| 97.857 | 105.949 https://www.oddschecker.com/horse-racing/santa-anita/23:30/winner
0.514 | 3.450 | 7.552 || 87.960 | 90.896 | 87.446 | 94.998 https://www.oddschecker.com/horse-racing/tampa-bay/21:31/winner
0.955 | 4.065 | 6.027 || 87.903 | 91.013 | 86.948 | 92.975 https://www.oddschecker.com/horse-racing/tampa-bay/22:04/winner
1.926 | 4.986 | 12.225 || 99.224 | 102.284| 97.298 | 109.523 https://www.oddschecker.com/horse-racing/emerald-downs/22:15/winner
1.438 | 4.406 | 12.364 || 97.573 | 100.541| 96.135 | 108.499 https://www.oddschecker.com/horse-racing/emerald-downs/22:47/winner
0.893 | 3.438 | 9.290 || 93.797 | 96.342| 92.904 | 102.194 https://www.oddschecker.com/horse-racing/emerald-downs/23:19/winner
0.792 | 4.954 | 11.170 ||103.807 | 107.969|103.015 | 114.185 https://www.oddschecker.com/horse-racing/emerald-downs/23:52/winner
1.615 | 4.984 | 12.997 || 86.380 | 89.749| 84.765 | 97.762 https://www.oddschecker.com/horse-racing/emerald-downs/00:24/winner
0.747 | 3.582 | 5.914 || 79.189 | 82.024| 78.442 | 84.356 https://www.oddschecker.com/horse-racing/emerald-downs/00:56/winner
0.627 | 4.064 | 8.828 || 82.116 | 85.554| 81.489 | 90.318 https://www.oddschecker.com/horse-racing/emerald-downs/01:27/winner
0.776 | 3.870 | 8.738 || 81.438 | 84.532| 80.662 | 89.401 https://www.oddschecker.com/horse-racing/emerald-downs/01:54/winner
1.419 | 3.038 | 8.350 || 76.762 | 78.380| 75.343 | 83.693 https://www.oddschecker.com/horse-racing/maronas/21:25/winner
0.337 | 2.641 | 8.255 || 71.196 | 73.499| 70.858 | 79.114 https://www.oddschecker.com/horse-racing/maronas/21:50/winner
0.439 | 2.456 | 4.990 || 72.428 | 74.445| 71.989 | 76.979 https://www.oddschecker.com/horse-racing/maronas/22:15/winner
0.646 | 2.758 | 5.412 || 75.577 | 77.689| 74.931 | 80.342 https://www.oddschecker.com/horse-racing/maronas/22:40/winner
0.869 | 2.625 | 7.910 || 73.883 | 75.639| 73.014 | 80.924 https://www.oddschecker.com/horse-racing/maronas/23:05/winner
That is 76 races, obviously we can't count anything antepost because the stake wouldn't be returned, and it's worth noting that this is calculated from the best odds, and we cannot possibly know the odds of a horse at the time it drops out so it will be a bit out. However if we are to use this data as a rough guide it appears rare that rule4 negatively impacts returns when
dutching but it's not something worth hunting for.
To conclude it appears to me the most lucrative and sure-fire way to profit from this is to bet on all outcomes of horse races for arbitrage, and to rake in the various offers bookmakers have such as: money back for second place, money back if your horse falls, and best odds guaranteed.