# Winning Trifectas or Winning Football Teams Come Predominantly from Inside FFG Median Bell

## By Ion Saliu, Founder of Gambling Mathematics

Written on December 13, 2003 — and later.

BellCurveGenerator version 12, October 16, 2007.

The following report shows the distribution of random team combinations based on their lexicographic indexes. Every week, I have chosen randomly five games played in the National Football League (NFL) of the United States. The football played in the U.S. would be more correctly named touchball, not to be confused with soccer or real football (played by foot). The games have a betting line: the favorite is expected to win by, at least, a number of points.

I applied the strategy to five games. There are two outcomes in rapport to the betting line. Total possible football combinations is therefore 25 = 32. The Fundamental Formula of Gambling (FFG) demonstrates that in a majority of cases the winning combinations will be from the FFG median zone. The FFG median zone and the normal (Gauss) bell share a large percentage of elements, but the areas are not identical.

Only the first column of the report is of interest here. It represents the lexicographical index of the winning team combination. If the combination failed to fall inside the FFG median bell, it is asterisked. The last column shows the winning teams of the five randomly selected NFL games.

~ Percentage of 25 combinations within the FFG median bell: 38%
* represents a no-hit.

I get the NFL schedule from the official site of the National Football League (nfl.com — official is good sometimes). The bookies use different ordering of the games. For example, at the beginning of the 2003 NFL season, the week 14 was listed this way (or the way I saw it):

NFL Week 14: Sunday, Dec. 7        4  5  7  8  11
1) Bears at Packers, 1:00 pm    21-34
2) Bengals at Ravens, 1:00 pm   13-31
3) Cowboys at Eagles, 1:00 pm   10-36
4) Texans at Jaguars, 1:00 pm    0-27
5) Colts at Titans, 1:00 pm     29-27
6) Raiders at Steelers, 1:00 pm  7-27
7) Chargers at Lions, 1:00 pm   14-7
8) Seahawks at Vikings, 1:00 pm  7-34
9) Bucs at Saints, 1:00 pm      14-7
10) Redskins at Giants, 1:00 pm  20-7
11) Cardinals at 49ers, 4:05 pm  14-50
12) Chiefs at Broncos, 4:15 pm   21-45
13) Dolphins at Patriots, 4:15 pm   0-12
14) Jets at Bills, 4:15 pm       7-16
15) Panthers at Falcons, 8:30 pm   14-20
16) Rams at Browns, 9:00 pm (Dec. 8)   26-20

I ran PermuteCombine, the Combinations option for 15 numbers, 5 numbers per combination. Total combinations to generate: 22 (the median calculated by the Fundamental Formula of Gambling for a probability equal to 1/32). The combination #22 for that particular run was:
4 5 7 8 11.
You can see what games they represented in that week's schedule. The winning combination was:
JAGUARS, COLTS, CHARGERS, VIKINGS, 49ERS
or lexicographical index 20.

Let's face the unknown now: Week 15, December 14, 2003. The schedule:

NFL Week 15: Sunday, Dec. 14       3  4  5  7  13
1) Falcons at Colts, 1:00 pm
2) Bills at Titans, 1:00 pm
3) Cowboys at Redskins, 1:00 pm
4) Lions at Chiefs, 1:00 pm
5) Texans at Bucs, 1:00 pm
6) Jaguars at Patriots, 1:00 pm
7) Vikings at Bears, 1:00 pm
8) Steelers at Jets, 1:00 pm
9) Seahawks at Rams, 1:00 pm
10) 49ers at Bengals, 1:00 pm
11) Ravens at Raiders, 4:05 pm
12) Browns at Broncos, 4:05 pm
13) Panthers at Cardinals, 4:15 pm
14) Packers at Chargers, 4:15 pm
15) Giants at Saints, 8:30 pm
16) Eagles at Dolphins, 9:00 pm (Dec. 15)

The combination #22 by one run of PermuteCombine was: 3 4 5 7 13
The games was written to a text file GAMES.5 with the following content:

Cowboys, Redskins
Lions, Chiefs
Texans, Bucs
Vikings, Bears
Panthers, Cardinals

December 15, 2003. The winning combination in NFL Week 15 was:
COWBOYS, CHIEFS, BUCS, BEARS, CARDINALS
or lexicographical index 16 (right in the middle!)
The Arizona Cardinals lost the game by 3 points. The Panthers, however, were expected to win by 6 points. If the straight up winners had been considered (Panthers instead of Cardinals), the winning combination would have had index #15.

We do not know the results at the time of this writing. Nor do we know the results of NFL Week 16. The combination #22 by one run of PermuteCombine is: 1 3 8 13 15
The schedule for week 16 is:

NFL Week 16: Sunday, Dec. 21

1) Falcons at Bucs, 1:30 pm (Dec. 20)
2) Chiefs at Vikings, 5:00 pm (Dec. 20)
3) Patriots at Jets, 8:30 pm (Dec. 20)
4) Ravens at Browns, 1:00 pm
5) Bengals at Rams, 1:00 pm
6) Lions at Panthers, 1:00 pm
7) Dolphins at Bills, 1:00 pm
8) Saints at Jaguars, 1:00 pm
9) Giants at Cowboys, 1:00 pm
10) Titans at Texans, 1:00 pm
11) Redskins at Bears, 1:00 pm
12) Chargers at Steelers, 4:05 pm
13) Cardinals at Seahawks, 4:15 pm
14) 49ers at Eagles, 4:15 pm
15) Broncos at Colts, 8:30 pm
16) Packers at Raiders, 9:00 pm (Dec. 22)

The games would be written to a text file GAMES.5 with the following content:

Falcons, Bucs
Patriots, Jets
Saints, Jaguars
Cardinals, Seahawks
Broncos, Colts

December 22, 2003. The winning combination in NFL Week 16 was:
FALCONS, PATRIOTS, SAINTS, SEAHAWKS, BRONCOS
or lexicographical index 3 (no hit).

How much did I win? I really appreciate the concept of the rule of law. The legality of sports betting in the United States is tricky. The only legally well-defined betting games in the United States are the state-run lotteries and horse racing.

In October of 2003 I had the most expensive drink in my life. It was beer, of all elixirs! It was soon after I had released BellCurveGenerator. I went to an off-track wagering parlor. My main goal was to play two trifectas generated by BellCurveGenerator. Also, the combinations were no hits in the last 500 races or so. Both combinations contained either number 9 or number 10. I disregard races with fewer horses.

I played some other strategies just to blend in, like a normal player. The first BellCurveGenerator trifecta on my list had already hit before I entered the off-track wagering facility. It wasn't much money — if under a thousand dollars is not that much?! The second trifecta had not been a winner for the past 20+ races. It was a good time to think of playing. The trifecta containing number 10 was ripe to hit within the next 3 races with 10 or more horses.

I looked up the TV monitors and only one race met my restrictions. It was only one race. Usually the hits occur when several races meet the restrictions simultaneously. First, I decided I would play for double the minimum bet (\$4). Then, I thought I'd better wait for the situation when more than one race would meet the restrictions simultaneously. I only had beer. Just one beer waiting for the future.

The FFG median bell trifecta hit that very next race. It was within next three alright! The trifecta yielded almost \$5000 for \$2. Granted, if I had played the payout would have been about \$3,000 (perhaps more than that). In any event, that plastic glass full of beer has been the most expensive drink in my whole life. It's not too bad, if you think about it cold-headedly. I've read of idiots who paid over a million dollars for a bottle of wine! Now, that's stupid, because they don't even drink the content!

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