jonrob.net


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(£)
3.527.21
423.81
4.3322
519.05
127.94

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.

Odds3.544.33512
3.5X2.875333.375
43.25X3.43.43.85
4.333.49753.4975X3.6644.1635
5444.2X4.8
129.259.259.89.8X

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.