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Effects of Box Wagering in a Trifecta Pool

Listed below is a 7 Horse field with each horse’s theoretical chance to win, place and show.

Horse Win Place Show Total
1 0.55556 0.22778 0.07889 0.86223
2 0.22222 0.32999 0.22222 0.77443
3 0.11111 0.22222 0.27333 0.60666
4 0.04762 0.08624 0.16295 0.29681
5 0.0303 0.06722 0.11668 0.2142
6 0.02299 0.04615 0.09911 0.16825
7 0.0102 0.0204 0.04682 0.07742
Total 1.00000 1.00000 1.00000 3.00000

If each horse were to be wagered on in exact proportions to it’s assigned chance of finishing first, second or third, a near perfect distribution of money wagered on each combination would look as follows:

Note: Place and Show Odds on all horses were re-normalized to reflect each combination’s correct money distribution. Distribution based on a $10,000 pool.

 

1-2-3 0.55556 0.42733 0.39109 0.09285 $928.48
1-2-4 0.55556 0.42723 0.23316 0.05535 $553.54
1-2-5 0.55556 0.42733 0.16695 0.03964 $396.35
1-2-6 0.55556 0.42723 0.14181 0.03367 $336.67
1-2-7 0.55556 0.42733 0.06699 0.0159 $159.04
Total

1.00000 0.23741 $2,374.08






1-3-2 0.55556 0.28777 0.34305 0.05484 $548.45
1-3-4 0.55556 0.28777 0.25155 0.04022 $402.16
1-3-5 0.55556 0.28777 0.18012 0.18012 $287.96
1-3-6 0.55556 0.28777 0.153 0.02446 $244.61
1-3-7 0.55556 0.28777 0.07228 0.01156 $115.56
Total

1.00000 0.3112 $1,598.74






1-4-2 0.55556 0.11168 0.2931 0.01819 $181.85
1-4-3 0.55556 0.11168 0.36052 0.02237 $223.68
1-4-5 0.55556 0.11168 0.1539 0.00955 $95.49
1-4-6 0.55556 0.11168 0.13072 0.00811 $81.11
1-4-7 0.55556 0.11168 0.06175 0.00383 $38.31
Total

0.99999 0.06205 $620.44






1-5-2 0.55556 0.08705 0.27624 0.01336 $133.59
1-5-3 0.55556 0.08705 0.33978 0.01643 $164.32
1-5-4 0.55556 0.08705 0.20257 0.0098 $97.96
1-5-6 0.55556 0.08705 0.12321 0.00596 $59.58
1-5-7 0.55556 0.08705 0.0582 0.00281 $28.15
Total

1.00000 0.04836 $483.60












1-6-2 0.55556 0.05976 0.27034 0.00898 $89.75
1-6-3 0.55556 0.05976 0.33252 0.01104 $110.40
1-6-4 0.55556 0.05976 0.19824 0.00658 $65.82
1-6-5 0.55556 0.05976 0.14195 0.00471 $47.13
1-6-7 0.55556 0.05976 0.05696 0.00189 $18.91
Total

1.00001 0.0332 $332.01






1-7-2 0.55556 0.02642 0.25417 0.00373 $37.31
1-7-3 0.55556 0.02642 0.31263 0.00459 $45.89
1-7-4 0.55556 0.02642 0.18638 0.00274 $27.38
1-7-5 0.55556 0.02624 0.13346 0.00196 $19.59
1-7-6 0.55556 0.02642 0.11336 0.00166 $16.64
Total

1.00000 0.01468 $146.79






2-1-3 0.22222 0.33997 0.39109 0.02955 $295.46
2-1-4 0.22222 0.33997 0.23316 0.01761 $176.15
2-1-5 0.22222 0.33997 0.16695 0.01261 $126.13
2-1-6 0.22222 0.33997 0.14181 0.01071 $107.13
2-1-7 0.22222 0.33997 0.06699 0.00506 $50.61
Total

1.00000 0.07554 $755.48






2-3-1 0.22222 0.33167 156.39 0.01153 $115.27
2-3-4 0.22222 0.33167 0.32303 0.02381 $238.09
2-3-5 0.22222 0.33167 0.2313 0.01705 $170.48
2-3-6 0.22222 0.33167 0.19647 0.01448 $144.81
2-3-7 0.22222 0.33167 0.09281 0.00684 $68.40
Total

1.00000 0.07371 $737.05






2-4-1 0.22222 0.12871 0.12831 0.00367 $36.70
2-4-3 0.22222 0.12871 0.44456 0.01272 $127.15
2-4-5 0.22222 0.12871 0.18978 0.00543 $54.28
2-4-6 0.22222 0.12871 0.1612 0.00461 $46.11
2-4-7 0.22222 0.12871 0.07615 0.00218 $21.78
Total

1.00000 0.02861 $286.02






2-5-1 0.22222 0.10033 0.11933 0.00266 $26.61
2-5-3 0.22222 0.10033 0.41344 0.00922 $92.18
2-5-4 0.22222 0.10033 0.24648 0.0055 $54.95
2-5-6 0.22222 0.10033 0.14992 0.00334 $33.43
2-5-7 0.22222 0.10033 0.07082 0.00158 $15.79
Total

0.99999 0.0223 $222.96






2-6-1 0.22222 0.06888 0.11624 0.00178 $17.79
2-6-3 0.22222 0.06888 0.40274 0.00616 $61.65
2-6-4 0.22222 0.06888 0.2401 0.00368 $36.75
2-6-5 0.22222 0.06888 0.17192 0.00263 $26.31
2-6-7 0.22222 0.06888 0.06899 0.00106 $10.56
Total

0.99999 0.01531 $153.06






2-7-1 0.22222 0.03045 0.10793 0.00073 $7.30
2-7-3 0.22222 0.03045 0.37393 0.00253 $25.30
2-7-4 0.22222 0.03045 0.22293 0.00151 $15.08
2-7-5 0.22222 0.03045 0.15963 0.00108 $10.80
2-7-6 0.22222 0.03045 0.13559 0.00092 $9.17
Total

1.00001 0.0677 $67.65






3-1-2 0.11111 0.29286 0.34305 0.01116 $111.63
3-1-4 0.11111 0.29286 0.25155 0.00819 $81.85
3-1-5 0.11111 0.29286 0.18012 0.00586 $58.61
3-1-6 0.11111 0.29286 0.153 0.00498 $49.79
3-1-7 0.11111 0.29286 0.07228 0.00235 $23.52
Total

1.00000 0.03254 $325.40






3-2-1 0.11111 0.42427 0.15639 0.00737 $73.72
3-2-4 0.11111 0.42427 0.32303 0.01523 $152.28
3-2-5 0.11111 0.42427 0.2313 0.0109 $109.04
3-2-6 0.11111 0.42427 0.19647 0.00926 $92.62
3-2-7 0.11111 0.42427 0.09281 0.00438 $43.75
Total

1.00000 0.04714 $471.41






3-4-1 0.11111 0.11088 0.13994 0.00172 $17.24
3-4-2 0.11111 0.11088 0.3942 0.00486 $48.57
3-4-5 0.11111 0.11088 0.20698 0.00255 $25.50
3-4-6 0.11111 0.11088 0.17581 0.00217 $21.66
3-4-7 0.11111 0.11088 0.08306 0.00102 $10.23
Total

0.99999 0.01232 $123.20






3-5-1 0.11111 0.08643 0.12933 0.00124 $12.42
3-5-2 0.11111 0.08643 0.3643 0.0035 $34.98
3-5-4 0.11111 0.08643 0.26714 0.00257 $25.65
3-5-6 0.11111 0.08643 0.16248 0.00156 $15.60
3-5-7 0.11111 0.08643 0.07676 0.00074 $7.37
Total

1.00001 0.00961 $96.02






3-6-1 0.11111 0.05934 0.12571 0.00083 $8.29
3-6-2 0.11111 0.05934 0.3541 0.00233 $23.35
3-6-4 0.11111 0.05934 0.25966 0.00171 $17.12
3-6-5 0.11111 0.05934 0.18593 0.00123 $12.26
3-6-7 0.11111 0.05934 0.07461 0.00049 $4.92
Total
1.00001 0.00659 $65.94






3-7-1 0.11111 0.02623 0.11604 0.00034 $3.38
3-7-2 0.11111 0.02623 0.32687 0.00095 $9.52
3-7-4 0.11111 0.02623 0.23969 0.0007 $6.98
3-7-5 0.11111 0.02623 0.17163 0.0005 $5.00
3-7-6 0.11111 0.02623 0.14578 0.00042 $4.25
Total

1.00001 0.00291 $29.13






4-1-2 0.04762 0.24928 0.2931 0.00348 $34.79
4-1-3 0.04762 0.24928 0.36052 0.00428 $42.80
4-1-5 0.04762 0.24928 0.1539 0.00183 $18.27
4-1-6 0.04762 0.24928 0.13072 0.00155 $15.52
4-1-7 0.04762 0.24928 0.06175 0.00073 $7.33
Total

0.99999 0.01187 $118.71






4-2-1 0.04762 0.36113 0.12831 0.00221 $22.07
4-2-3 0.04762 0.36113 0.44456 0.00765 $76.45
4-2-5 0.04762 0.36113 0.18978 0.00326 $32.64
4-2-6 0.04762 0.36113 0.1612 0.00277 $27.72
4-2-7 0.04762 0.36113 0.07615 0.00131 $13.10
Total

1.00000 0.0172 $171.98






4-3-1 0.04762 0.24319 0.13994 0.00162 $16.21
4-3-2 0.04762 0.24319 0.3942 0.00457 $45.65
4-3-5 0.04762 0.24319 0.20698 0.0024 $23.97
4-3-6 0.04762 0.24319 0.17581 0.00204 $20.36
4-3-7 0.04762 0.24319 0.08306 0.00096 $9.62
Total

0.99999 0.01159 $115.81






4-5-1 0.04762 0.07356 0.10951 0.00038 $3.84
4-5-2 0.04762 0.07356 0.30848 0.00108 $10.81
4-5-3 0.04762 0.07356 0.37943 0.00133 $13.29
4-5-6 0.04762 0.07356 0.13758 0.00048 $4.82
4-5-7 0.04762 0.07356 0.06499 0.00023 $2.28
Total

0.99999 0.0035 $35.04






4-6-1 0.04762 0.05051 0.10691 0.00025 $2.57
4-6-2 0.04762 0.05051 0.30114 0.00072 $7.24
4-6-3 0.04762 0.05051 0.3704 0.00089 $8.91
4-6-5 0.04762 0.05051 0.15812 0.00038 $3.80
4-6-7 0.04762 0.05051 0.06345 0.00015 $1.52
Total

1.00002 0.00024 $24.04






4-7-1 0.04762 0.02233 0.09983 0.00011 $1.06
4-7-2 0.04762 0.02233 0.28121 0.0003 $2.99
4-7-3 0.04762 0.02233 0.34589 0.00037 $3.68
4-7-5 0.04762 0.02233 0.14765 0.00016 $1.57
4-7-6 0.04762 0.02233 0.12542 0.00013 $1.33
Total

1.00000 0.00107 $10.63






5-1-2 0.0303 0.24419 0.27624 0.00204 $20.44
5-1-3 0.0303 0.24419 0.33978 0.00251 $25.14
5-1-4 0.0303 0.24419 0.20257 0.0015 $14.99
5-1-6 0.0303 0.24419 0.12321 0.00091 $9.12
5-1-7 0.0303 0.24419 0.0582 0.00043 $4.31
Total

1.00000 0.00739 $74.00






5-2-1 0.0303 0.35377 0.11933 0.00128 $12.79
5-2-3 0.0303 0.35377 0.41344 0.00443 $44.32
5-2-4 0.0303 0.35377 0.24648 0.00264 $26.42
5-2-6 0.0303 0.35377 0.14992 0.00161 $16.07
5-2-7 0.0303 0.35377 0.07082 0.00076 $7.59
Total

0.99999 0.01072 $107.19






5-3-1 0.0303 0.23823 0.12933 0.00092 $9.24
5-3-2 0.0303 0.23823 0.3643 0.00263 $26.30
5-3-4 0.0303 0.23823 0.26714 0.00193 $19.28
5-3-6 0.0303 0.23823 0.16248 0.00117 $11.73
5-3-7 0.0303 0.23823 0.07676 0.00055 $5.54
Total

1.00001 0.0072 $72.09






5-4-1 0.0303 0.09245 0.10951 0.00031 $3.07
5-4-2 0.0303 0.09245 0.30848 0.00086 $8.64
5-4-3 0.0303 0.09245 0.37943 0.00106 $10.63
5-4-6 0.0303 0.09245 0.13758 0.00039 $3.85
5-4-7 0.0303 0.09245 0.06499 0.00018 $1.82
Total

0.99999 0.0028 $28.01






5-6-1 0.0303 0.04948 0.1006 0.00015 $1.51
5-6-2 0.0303 0.04948 0.28337 0.00042 $4.25
5-6-3 0.0303 0.04948 0.34855 0.00052 $5.22
5-6-4 0.0303 0.04948 0.20779 0.00031 $3.11
5-6-7 0.0303 0.04948 0.0597 0.00009 $0.89
Total

1.00001 0.00149 $14.98






5-7-1 0.0303 0.02187 0.09431 0.00006 $0.62
5-7-2 0.0303 0.02187 0.26565 0.00018 $1.76
5-7-3 0.0303 0.02187 0.32675 0.00022 $2.16
5-7-4 0.0303 0.02187 0.1948 0.00013 $1.29
5-7-6 0.0303 0.02187 0.11848 0.00008 $0.79
Total

0.99999 0.00067 $6.62






6-1-2 0.02299 0.23879 0.27034 0.00148 $14.84
6-1-3 0.02299 0.23879 0.33252 0.00183 $18.26
6-1-4 0.02299 0.23879 0.19824 0.00109 $10.88
6-1-5 0.02299 0.23879 0.14195 0.00078 $7.79
6-1-7 0.02299 0.23879 0.05696 0.00031 $3.13
Total

1.00001 0.00549 $54.90






6-2-1 0.02299 0.34594 0.11624 0.00092 $9.24
6-2-3 0.02299 0.34594 0.40274 0.0032 $32.03
6-2-4 0.02299 0.34594 0.2401 0.00191 $19.10
6-2-5 0.02299 0.34594 0.17192 0.00137 $13.67
6-2-7 0.02299 0.34594 0.06899 0.00055 $5.49
Total

0.99999 0.00795 $79.53






6-3-1 0.02299 0.23296 0.12571 0.00067 $6.73
6-3-2 0.02299 0.23296 0.3541 0.0019 $18.97
6-3-4 0.02299 0.23296 0.25966 0.00139 $13.91
6-3-5 0.02299 0.23296 0.18593 0.001 $9.96
6-3-7 0.02299 0.23296 0.07461 0.0004 $4.00
Total

1.00001 0.00536 $53.57






6-4-1 0.02299 0.09041 0.10691 0.00022 $2.22
6-4-2 0.02299 0.09041 0.30114 0.00063 $6.26
6-4-3 0.02299 0.09041 0.3704 0.00077 $7.70
6-4-5 0.02299 0.09041 0.15812 0.00033 $3.29
6-4-7 0.02299 0.09041 0.06345 0.00013 $1.32
Total

1.00002 0.00208 $20.79






6-5-1 0.02299 0.07047 0.1006 0.00016 $1.63
6-5-2 0.02299 0.07047 0.28337 0.00046 $4.59
6-5-3 0.02299 0.07047 0.34855 0.00056 $5.65
6-5-4 0.02299 0.07047 0.20779 0.00034 $3.37
6-5-7 0.02299 0.07047 0.0597 0.0001 $0.97
Total

1.00001 0.00162 $16.21






6-7-1 0.02299 0.02139 0.09237 0.00005 $0.45
6-7-2 0.02299 0.02139 0.26019 0.00013 $1.28
6-7-3 0.02299 0.02139 0.32003 0.00016 $1.57
6-7-4 0.02299 0.02139 0.19079 0.00009 $0.94
6-7-5 0.02299 0.02139 0.13662 0.00007 $0.67
Total

1.00000 0.0005 $4.91






7-1-2 0.0102 0.23252 0.25417 0.0006 $6.03
7-1-3 0.0102 0.23252 0.31263 0.00074 $7.42
7-1-4 0.0102 0.23252 0.18638 0.00044 $4.42
7-1-5 0.0102 0.23252 0.13346 0.00032 $3.17
7-1-7 0.0102 0.23252 0.11336 0.00027 $2.69
Total

1.00000 0.00237 $23.70






7-2-1 0.0102 0.33686 0.10793 0.00037 $3.71
7-2-3 0.0102 0.33686 0.37393 0.00128 $12.85
7-2-4 0.0102 0.33686 0.22293 0.00077 $7.66
7-2-5 0.0102 0.33686 0.15963 0.00055 $5.48
7-2-6 0.0102 0.33686 0.13559 0.00047 $4.66
Total

1.00001 0.00344 $34.36






7-3-1 0.0102 0.22685 0.11604 0.00027 $2.69
7-3-2 0.0102 0.22685 0.32687 0.00076 $7.56
7-3-4 0.0102 0.22685 0.23969 0.00055 $5.55
7-3-5 0.0102 0.22685 0.17163 0.0004 $3.97
7-3-7 0.0102 0.22685 0.14578 0.00034 $3.37
Total

1.00001 0.00232 $23.14






7-4-1 0.0102 0.08804 0.09983 0.00009 $0.90
7-4-2 0.0102 0.08804 0.28121 0.00025 $2.53
7-4-3 0.0102 0.08804 0.34589 0.00031 $3.11
7-4-5 0.0102 0.08804 0.14765 0.00013 $1.33
7-4-6 0.0102 0.08804 0.12542 0.00011 $1.13
Total

1.00000 0.00089 $9.00






7-5-1 0.0102 0.06862 0.09431 0.00007 $0.66
7-5-2 0.0102 0.06862 0.26565 0.00019 $1.86
7-5-3 0.0102 0.06862 0.32675 0.00023 $2.29
7-5-4 0.0102 0.06862 0.1948 0.00014 $1.36
7-5-6 0.0102 0.06862 0.11848 0.00008 $0.83
Total

0.99999 0.00071 $7.00






7-6-1 0.0102 0.04711 0.09237 0.00004 $0.44
7-6-2 0.0102 0.04711 0.26019 0.00013 $1.25
7-6-3 0.0102 0.04711 0.32003 0.00015 $1.54
7-6-4 0.0102 0.04711 0.19079 0.00009 $0.92
7-6-5 0.0102 0.04711 0.13662 0.00007 $0.66
Total

1.00000 0.00048 $4.81

True Chance*: This is the true chance of a particular combination coming in using the probabilities that were assigned to each horse.

Distribution**: This is the amount of money that would be wagered on each combination based upon its true chance probabilities. The distribution above was calculated using a $10,000 trifecta pool. The distributions used can be adjusted using simple multiplication for any size pool. Example: A $200.000 pool is 20 times larger than the ($10,000) pool we used, so a distribution of $4.00 in our chart would equal an $80.00 distribution in a $200.000 pool.

Number Of Four Horse Box Combinations ($200,000 pool)

Combinations Highest Distribution Lowest Distribution
1-2-3-4 1-2-3 = $18,570 4-3-1 = $324
1-2-3-5 1-2-3 = $18,570 5-3-1 = $189
1-2-3-6 1-2-3 = $18,570 6-3-1 = $135
1-2-3-7 1-2-3 = $18,570 7-3-1 = $54
1-2-4-5 1-2-4 = $11,071 5-4-1 = $61
1-2-4-6 1-2-4 = $11,071 6-4-1 = $44
1-2-4-7 1-2-4 = $11,071 7-4-1 = $18
1-3-4-5 1-3-4 = $8,043 5-4-1 = $61
1-3-4-6 1-3-4 = $8,043 6-4-1 = $44
1-3-4-7 1-3-4 = $8,043 7-4-1 = $18
1-4-5-6 1-4-5 = $1,910 6-5-1 = $33
1-4-5-7 1-4-5 = $1,910 7-4-1 = $18
1-4-6-7 1-4-6 = $1,622 7-6-1 = $9
1-5-6-7 1-5-6 = $1.192 7-6-1 = $9
2-3-4-5 2-3-4 = $4,762 5-4-2 = $173
2-3-4-6 2-3-4 = $4,762 6-4-2 = $125
2-3-4-7 2-3-4 = $4,762 7-4-2 = $51
2-4-5-6 2-4-5 = $1,086 6-5-4 = $67
2-4-5-7 2-4-5 = $1,086 7-5-4 = $27
2-5-6-7 2-5-6 = $669 7-6-5 = $13
3-4-5-6 3-4-5 = $510 6-5-4 = $67
3-4-5-7 3-4-5 = $510 7-5-4 = $27
3-5-6-7 3-5-6 = $312 7-6-5 = $13
4-5-6-7 4-5-6 = $96 7-6-5 = $13

Looking at the 1-2-3-7 trifecta box the 1-2-3 combination would have $18,570 while the 7-3-1
combination would only have $54. What pari– mutual manager would not welcome a $20 trifecta box wagered into a $200,000 pool? Listed below are some facts surrounding a $20 trifecta box wager.

Prices of the highest and lowest trifecta dirived from the 1-2-3-7 box combination.

Takeout % Remaining Pool Combo Odds* $2 Payoff





0 $200,000 1-2-3 9.7-1 $21.40
20 $160,000 1-2-3 7.6-1 $17.20
25 $150,000 1-2-3 7.0-1 $16.00
30 $140,000 1-2-3 6.5-1 $15.00
35 $130,000 1-2-3 6.0-1 $14.00





0 $200,000 7-3-1 3702.7-1 $7,407.40
20 $160,000 7-3-1 2961.9-1 $5,927.80
25 $150,000 7-3-1 2776.7-1 $5,557.40
30 $140,000 7-3-1 2591.5-1 $5,185.00
35 $130,000 7-3-1 2406.4-1 $4,814.80

Effect Of A $20 1-2-3-7 Trifecta Box

Takeout % Remaining Pool Combo Odds* $2 Payoff Return
0 $200,240 1-2-3 9.7-1 $21.40 100%
20 $160,192 1-2-3 7.6-1 $17.20 100%
25 $150,180 1-2-3 7.0-1 $16.00 100%
30 $140,168 1-2-3 6.5-1 $15.00 100%
35 $130,156 1-2-3 6.0-1 $14.00 100%






0 $200,240 7-3-1 2704.9-1 $5,411.80 73.00%
20 $160,192 7-3-1 2163.7-1 $4,329.40 73.00%
25 $150,180 7-3-1 2028.4-1 $4,058.80 73.00%
30 $140,168 7-3-1 1893.1-1 $3,788.20 73.00%
35 $130,156 7-3-1 1757.8-1 $3,517.60 73.00%
Takeout % Remaining Pool Combo Odds* $2 Payoff Return
0 $100,240 1-2-3 9.7-1 $21.40 100%
20 $80,192 1-2-3 7.6-1 $17.20 100%
25 $75,180 1-2-3 7.0-1 $16.00 100%
30 $70,168 1-2-3 6.5-1 $15.00 100%
35 $65,156 1-2-3 5.9-1 $13.80 98.60%






0 $100,240 7-3-1 2131.7-1 $4,265.40 57.60%
20 $80,192 7-3-1 1705.2-1 $3,412.40 57.60%
25 $75,180 7-3-1 1598.5-1 $3,199.00 57.60%
30 $70,168 7-3-1 1491.9-1 $2,985.80 57.60%
35 $65,156 7-3-1 1385.2-1 $2,772.40 57.60%

Odds*: After breakage.

Box wagering is batch wagering. The wager made above was a $20 wager on 24 different trifecta combinations. The patron boxed the 3 favorites with the long shot into a medium size pool (by US standards) yet affected the long shot combination dramatically. A mere $20 reduced payouts by 42.4% and lowered the $2 payoff by as much as $3,142.00. When professionals batch wager they would never affect payoffs as dramatically as amateurs do by using boxes and wheels.