header-photo

Number of wagering combinations depending on field size

Field Size Win Quinella Exacta Trifecta Superfecta






3 3 3 6 6 X
4 4 6 12 24 24
5 5 10 20 60 120
6 6 15 30 120 360
7 7 21 42 210 840
8 8 28 56 336 1680
9 9 36 72 504 3024
10 10 45 90 720 5040
11 11 55 110 990 7,920
12 12 66 132 1,320 11,880
13 13 78 156 1,716 17,160
14 14 91 182 2,184 24,024
20 20 190 380 6,840 116,280

Number of wagering combinations for average field size

Ave. Field Size Double Pick 3 Pick4 Pick5 Pick6






6 36 216 1,296 7,776 46,656
7 49 343 2,401 16,807 117,649
8 64 512 4096 32,768 262,144
9 81 729 6,561 59,049 531,441
10 100 1,000 10,000 100,000 1,000,000
11 121 1,331 14,641 161,051 1,771,561
12 144 1,728 20,736 248,832 2,985,984

Morning Line

A morning line is someone’s estimate of what each horse’s closing odds will be. It also could be someone’s opinion of what they think each horse’s chances should be. I’m never quite sure which one the author of a morning line is trying to convey. I do know that many morning lines are mathematically incorrect. There is a correct way to make a morning line and hopefully this will help in making a more mathematically correct morning line.

The first thing to do is take the number 100 and add to it the track takeout for win. If the track takeout were 18% our starting number would be 100 + 18 = 118 or 118%. The odds assigned each horse, when converted to a % and added up must = 118%. I don’t believe being a point or two off is the end of the world, but being 5 or more points off is a disservice to the racetrack patron who looks at a morning line for guidance.

To convert odds to percentages you add the divisor to the dividend and divide that number into the divisor. Example: (dividend/divisor) say the odds of a horse are 3/1. Add the 1 (the divisor) to the 3 (the dividend) = 4 and then divide 4 into 1 = .25%. When someone makes a horse 3/1 they are saying that the horse has a 25/118 or will win once every 4.72 attempts. If there were zero takeout, then the horse would win (25/100 = 4) once in every 4 attempts if this line were accurate.

Listed below are the correct percentages when converting odds to percentages.

Tote Odds Formula
Percent Tote Odds Formula
Percent
1/9* 1+10 = 11 10/11 .909 7/1 7+1 = 8 1/8 .125
1/5 1+5 = 6 5/6 .833 8/1 8+1 = 9 1/9 .111
2/5 2+5 = 7 5/7 .714 9/1 9+1 = 10 1/10 .100
½ 1+2 = 3 2/3 .667 10/1 10+1 = 11 1/11 .091
3/5 3+5 = 8 5/8 .625 11/1 11+1 = 12 1/12 .083
4/5 4+5 = 9 5/9 .556 12/1 12+1 = 13 1/13 .077
1 1+1 = 2 ½ .500 13/1 13+1 = 14 1/14 .071
6/5 6+5 = 11 5/11 .455 14/1 14+1 = 15 1/15 .067
7/5 7+5 = 12 5/12 .417 15/1 15+1 = 16 1/16 .063
3/2 3+2 = 5 2/5 .400 20/1 20+1 = 21 1/21 .048
8/5 8+5 = 13 5/13 .385 25/1 25+1 = 26 1/26 .038
9/5 9+5 = 14 5/14 .357 30/1 30+1 = 31 1/31 .032
2/1 2+1 = 3 1/3 .333 35/1 35+1 = 36 1/36 .028
5/2 5+2 = 7 2/7 .286 40/1 40+1 = 41 1/41 .024
3/1 3+1 = 4 ¼ .250 45/1 45+1 = 46 1/46 .022
7/2 7+2 = 9 2/9 .222 50/1 50+1 = 51 1/51 .020
4/1 4+1 = 5 1/5 .200 60/1 60+1 = 61 1/61 .016
9/2 9+2 = 11 2/11 .182 70/1 70+1 = 71 1/71 .014
5/1 5+1 = 6 1/6 .167 80/1 80+1 = 81 1/81 .012
6/1 6+1 = 7 1/7 .143 90/1 90+1 = 91 1/91 .011

* The tote board will display odds of 1/9 but it should correctly be displayed at 1/10.

How I make a morning line is give every horse a % chance of winning and list it in decimal form. The chances of every horse must add up to 1 or 100% (.55 is the same as 55%). Once I have my “chance of winning” I need to multiply by (the takeout + 1). If the takeout is 14% or .14 then the multiplier is 1.14. Looking at row #1 the true “chance of winning” for horse #1 is .55556. If the takeout is 14% then .55556 x 1.14 = .633338

Now that we know how to convert odds to percentages we can construct a morning line that is mathematically correct. An example of making a morning line is listed below.

Horse # Chance of Winning 14% Takeout 24% Takeout




1 .55556 .633338 .688894
2 .22222 .253331 .275553
3 .11111 .126665 .137776
4 .04762 .054287 .059049
5 .03030 .034542 .037572
6 .02299 .026209 .028508
7 .01020 .011628 .012648




Total 1.0000 1.140000 1.240000

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.

Win Pool with a 20% Takeout and Dime Breakage

New wager Pool size Pool after take Amt on winner Odds $1 Payout $2 Payout Breakage %Loss on new wager Profit
0 100,000 80,000 5,000 15.00-1 16 32 0 0 0
1000 101,000 80,800 6,000 12.47-1 13.4 26.8 400 16.25% 12,400
2000 102,000 81,600 7,000 10.66-1 11.6 23.2 400 27.50% 21,200
3000 103,000 82,400 8,000 9.30-1 10.3 20.6 0 35.63% 27,900
4000 104,000 83,200 9,000 8.24-1 9.2 18.4 400 42.50% 32,800
5000 105,000 84,000 10,000 7.40-1 8.4 16.8 0 47.50% 37,000
6000 106,000 84,800 11,000 6.71-1 7.7 15.4 100 51.88% 40,200
7000 107,000 85,600 12,000 6.13-1 7.1 14.2 400 55.63% 42,700
8000 108,000 86,400 13,000 5.65-1 6.6 13.2 600 58.75% 44,800
9000 109,000 87,200 14,000 5.23-1 6.2 12.4 400 61.25% 46,800
10000 110,000 88,000 15,000 4.87-1 5.8 11.6 1000 63.75% 48,000
11000 111,000 88,800 16,000 4.55-1 5.5 11 800 65.63% 49,500
12000 112,000 89,600 17,000 4.27-1 5.2 10.4 1200 67.50% 50,400
13000 113,000 90,400 18,000 4.02-1 5 10 400 68.75% 52,000
14000 114,000 91,200 19,000 3.80-1 4.8 9.6 0 70.00% 53,200
15000 115,000 92,000 20,000 3.60-1 4.6 9.2 0 71.25% 54,000
16000 116,000 92,800 21,000 3.42-1 4.4 8.8 400 72.50% 54,400
17000 117,000 93,600 22,000 3.25-1 4.2 8.4 800 73.75% 54,400
18000 118,000 94,400 23,000 3.10-1 4.1 8.2 100 74.38% 55,800
19000 119,000 95,200 24,000 2.97-1 3.9 7.8 1600 75.63% 55,100
20000 120,000 96,000 25,000 2.84-1 3.8 7.6 1000 76.25% 56,000
25000 125,000 100,000 30,000 2.33-1 3.3 6.6 1000 79.38% 57,500
30000 130,000 104,000 35,000 1.97-1 2.9 5.8 2500 81.87% 57,000

The chart above is an illustration of the effects of a win wager and the breakage associated with the wager. This also demonstrates the negative effects a bettor can have on his own return. Because of exorbanent takeouts and breakage that ractracks and governments charge, this is the single biggest barrier to increasing handle.

Chance of winning the pick 6

Real Win Odds Chance of Coming In Tickets Hit/Billion Odds
1-1 .015625 15,625,000 63-1
2-1 .001371742 1,371,742 728-1
3-1 .000244141 244,141 4095-1
4-1 .000064 64,000 15,624-1
5-1 .000021433 21,433 46,656-1
6-1 .0000085 8,500 117,646-1
7-1 .000003815 3,815 262,122-1
8-1 .000001882 1,882 531,349-1
9-1 .000001 1,000 999,999-1
10-1 .000000564 564 1,773,049-1
15-1 .00000006 60 16,666,666-1
20-1 .000000012 12 83,333,332-1
25-1 .000000003 3 333,333,332-1
30-1 .000000001 1 999,999,999-1
35-1 .0000000005 .5 1,999,999,999-1
40-1 .0000000002 .2 4,999,999,999-1
50-1 .00000000006 .06 16,666,666,666-1
60-1 .00000000002 .02 49,999,999,999-1
70-1 .0000000000078 .0078 128,205,128,204-1
80-1 .00000000000354 .00354 282,485,875,705-1
90-1 .00000000000176 .00176 568,181,818,181-1
100-1 .000000000000942 .000942 1,061,571,125,264-1

Tote Board

TOTE BOARD

One thing that a racetrack could do to make things easier for its patrons is change the way we present the odds. Currently we display odds in an antiquated fashion displaying odds like 3:2, 4:5, 1:9 (which really mean 1:10 or even 1:20). This is confusing to the new fan and at the same time it is not as accurate as converting odds to a decimal display. When the tote board displays odds of 5 or 5:1 is the horse currently 5:1 or 5.9:1? The difference in return is $12.00 verses $13.80. For those that may argue that changing to a decimal display may confuse the current customer. We already display closing odds in the charts and DRF using the decimal form. Another thing that most racetracks do is display odds in increments such as 35:1, 40:1, 45:1, 50:1, 60:1, 70:1 and so on and when they get to 99:1 it stops. If a horse is 39.3:1 why can’t we display the accurate odds?

Listed below is an example of how the odds would look in the decimal form.

Current Display Decimal Display
1/9       .05 or .1
1/5 .2 or .3
2/5   .4
½   .5
3/5  .6 or .7
4/5 .8 or .9
1 1  1.1
6/5  1.2 or 1.3
7/5 1.4
3/2  1.5
8/5  1.6 or 1.7
9/5    1.8 or 1.9
2 2  2.1, 2.2, 2.3 or 2.4
5/2  2.5, 2.6, 2.7, 2.8, or 2.9
3 3,  3.1, 3.2, 3.3, or 3.4
7/2  3.5, 3.6, 3.7, 3.8, or 3.9

 

Years ago I visited Roosevelt Raceway and was impressed with one of the features that their tote board offered. It displayed the range of place and show prices each horse would pay. I don’t recall seeing this features before or since but I believe this would be helpful to racetrack patrons and possibly encourage higher handle for these pools.