CRAM Math probability series practicals

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Problem: Construct a mathematical model to produce the following output.

Parameters: Input from any reliable sources available by HTTP; output at least 5 picks per week

long-run hypotheses:

  • if (scoresum/scorediff) = 1, then blowout
  • if (scoresum/scorediff) > (scoresum/scorediff)/(3.5), then close win (FG or less)

hometeam score, hometeam score (scoresum/scorediff)

Projected Week 1

Probable Action:

  • $20 Three-Team Parlay USC, Florida, TCU
  • $10 Five-Team Teaser Rutgers, Ohio State, BYU, Rice, Texas
  • $10 Five-Team Teaser LSU, TCU, USC, Florida, Penn State
  • Various $2 and $5 Three-Team Teasers for laffs

Total action: < $50


Rutgers 35, Buffalo 6 (41/29)

LSU 38, Mississippi State 21 (59/27)


TCU 24, Baylor 6 (30/18)

Florida 31, Western Kentucky 10 (41/21)

Ohio State 28, Youngstown State 6 (34/22)

BYU 21, Arizona 17 (38/4)

USC 42, Idaho 13 (55/29)

Rice 24, Nichols State 6 (30/18)

West Virginia 38, Western Michigan 17 (55/21)

Virginia Tech 35, East Carolina 12 (47/23)

Texas 45, Arkansas State 3 (48/42)

Penn State 35, Florida International 3 (38/32)

Projected Week 2


Oregon State 28, Cincinnati 15 (42/13)


West Virginia 42, Marshall 9 (51/33)

Florida 39, Troy 15 (54/24)

Clemson 38, La-Monroe 17 (55/21)

Miami 33, Oklahoma 32 (65/1)

Alabama 24, Vanderbilt 13 (37/11)

Iowa 21, Syracuse 12 (33/9)

Ohio State 35, Akron 9 (44/26)

Bringham Young 27, UCLA 24 (51/3)

Northern Iowa 31, Iowa State 28 (59/3)

Projected Week 3


TCU 31, Air Force 17 (48/14)

West Virginia 38, Maryland 21 (59/17)


Auburn 28, Mississippi State 10 (38/18)

Florida 28, Tennessee 17 (45/11)

Northwestern 21, Duke 12 (33/9)

USC 38, Nebraska 14 (52/24)

Projected Week 4

Clemson 24, NC State 17 (41/7)

Ohio State 35, Northwestern 17 (52/18)

Texas 45, Rice 10 (55/35)

LSU 28, South Carolina 14 (42/14)

USC 31, Washington State 24 (55/7)

No Further Projections

The problem of making further projections beyond Week 4 is the absence of a reliable model for predicting injuries/replacements on teams a month into the season--something else to work on.

Making it work

See Agua Caliente, Tijuana, Baja California, Mexico.

The United States has pushed the deadline back to summer 2008 for requiring a passport to re-enter the country at land border crossings for US citizens.

A parlay bet is three or more games played on the weekly parlay card as a single wager.

A teaser bet is three or more games played on the weekly 6-point teaser card as a single wager. The "teaser" pays out much less than the parlay card for the same number of games but has a much higher probability of paying out, with six points spotted to the projected losers (and off the projected winners as well) when compared to the parlay card.

A hedge is a wager made against your main bet as a form of self-insurance.

The idea in making a wager is not to make just one wager.
A 6/1 payout on a single 3-team parlay wager means that the house is betting you will lose 5 times out of 6 in the long run, definitely stacked against you.
The same 6/1 3-teamer looks a lot better with rotated losers on three other 3-teamers, so that the projected payout is 6/4 - not as dramatic as 6/1 winnings, but better than 50% of winning for the week and not losing. Decent probability of a 50% increase of your assets on the week at 6/4 is a heck of a lot better than 3%-5% interest per year on a certificate of deposit... but you already knew that or you wouldn't be reading this.
WWW (main wager)
LWW (hedge, 1st game to loser)
WLW (hedge, 2nd game to loser)
WWL (hedge, 3rd game to loser)
If your information is that the games will be close, you can self-insure with a single teaser wager on your parlay.
WWW parlay pays out 6/1
WWW teaser hedges at 5/2

The takeback is usually a few cents on the dollar, shaving a little off the winnings but not an untolerable play tax.


Minimum wager is $2 on parlay and teaser cards. Maximim wager varies depending on the number of teams on the teaser/parlay card wager. Straight wagers not encouraged (insufficient payout to justify risk).

3-team parlay/teaser max is $300.

3 for 3 parlay pays out 6/1 less any takeback by the sports book.
3 for 3 teaser pays out 5/2 less any takeback by the sports book.

4/5-team parlay/teaser max is $150.

4 for 4 parlay pays out 10/1 less any takeback by the sports book.
4 for 4 teaser pays out 7/2 less any takeback by the sports book.
5 for 5 parlay pays out 20/1 less any takeback by the sports book.
5 for 5 teaser pays out 5/1 less any takeback by the sports book.

6/7/8-team parlay/teaser max is $125 (usually not recommended because of the increasingly long odds).

Consolation parlay 0 for 15 pays 200/1 (15 for 15 pays 7500/1), but this is so rare that you are only throwing your money away on this wager.


Good hedges stop you from being a loser, or at least limit your damage. Brilliant hedging means you come out ahead most of the time, being a loser less than 25% of the time.

On making a single parlay wager, back it up with the same as a teaser, so that if you wager $10 on the parlay, back it up with a $10 teaser hedge.
On making a 4-team wager, also bet the 3-team teaser combinations of that wager as well for added payout/hedging.

If you expect to walk out of Tijuana, never bet your shoes.


Last year, everything went superbly during weeks 1, 2, and 3. Reached for the moon and lost everything on close games during weeks 4 and 5; retired for the season. This web page exists to provide written record of the continuing probability experiment as of 2007.

More on Making It Work

Consider a team playing in a game where you think it will cover 7 out of 10 games played against its scheduled opponent for the week. To cover, the team must win by points plus the spread (usually a negative number for the projected winner).

Let us say team X is a -7 projected winner at the sports book, so that its opponent team Y is a +7 loser. If the final score is 15 to 7 in team X's favor, then team X beats the spread and wins the bet, but if the same team X wins by a score of say 12 to 7, the "team X to win" bet loses because the difference between 12 (team X winner score) and 7 (team Y loser score) is only -5, not enough to cover the -7 spread.

If a team has a 7/10 best-estimate probability of covering the spread on the bet, then it has a 70% chance of covering. Now, imagine that you have found three teams that are 70% on covering bets as individual teams against their respective opponent teams. What does this mean?

70% coverage, single 3-team parlay wager

Assuming each team has an estimated 70% of covering that week's spread against its opponent, then a 3-team parlay has the following odds of paying off:

\frac 7 {10} \times \frac 7 {10} \times \frac 7 {10} = \frac {343} {1000} = 34.3%

Obviously, the house is favored by well over 55%. For you to have an even or better chance of winning this bet, your teams need to be around 90% coverers.

Same with rotated loser hedge wagers

For your three projected winners, you get the same odds as above:

WWW: 34.3%

For the wager with the first team losing, you have the following odds:

LWW: \frac 3 {10} \times \frac 7 {10} \times \frac 7 {10} = \frac {147} {1000} = 14.7%

For the wager with the second team losing, you have the following odds:

WLW: \frac 7 {10} \times \frac 3 {10} \times \frac 7 {10} = \frac {147} {1000} = 14.7%

For the wager with the third team losing, you have the following odds:

WWL: \frac 7 {10} \times \frac 7 {10} \times \frac 3 {10} = \frac {147} {1000} = 14.7%

The total probability of winning on the WWW/LWW/WLW/WWL wagers is the sum of the four probabilities, or better than 78%, not a sure thing, but definitely weighted in your favor. If all of the bets are $10 each, then you play $40 with an expected payout of $60, $20 in your favor. If all of the bets are $100 each, then you have $400 in play to pay out $600, $200 in your favor.

Even if your three winners are only 50% coverers, this system of wagers givers you 50% probability of winning, which is a lot better than the 12.5% probability of winning on a single 3-team parlay wager at 50% individual team coverage of the spread.
One of the earliest known hedge betting systems was described in Griffith's translation of Sun Wu Tzu's classic The Art of War dating back to around 350 BC or so.

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