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Probability of a Perfect Bracket
Introduction
A question I get a lot in March is, "What is the probability of filling out a March Madness bracket completely perfectly?" A frequently quoted statistic in the media is 1 in 9,223,372,036,854,780,000. This quotation is based on guessing randomly, which nobody does, and makes the hair on the back of my neck stand up. Here I will give a basic strategy you can follow, knowing nothing about basketball, and an estimate of your probability of success with said strategy.
Rules
Following are the rules of the tournament. If you already know them, you can skip this part.
For most intents and purposes, the tournament is single elimination, starting with 64 teams. To satisfy my perfectionist readers, there are actually 68 teams, where eight of them are matched up in four games. The winners of those four games, and 60 other teams, result in 64 teams, which is when the bracket picking typically begins.
The 64 teams are divided into four different conferences, North, South, West, and East, of 16 teams each. Each team in each conference will have a "seed," from 1 to 16, which is meant to be a ranking of their ability, although it is an imperfect method. Next the following will happen:
- The four 1 seeds will play the four 16 seeds.
- The four 8 seeds will play the four 9 seeds.
- The four 5 seeds will play the four 12 seeds.
- The four 4 seeds will play the four 13 seeds.
- The four 6 seeds will play the four 11 seeds.
- The four 3 seeds will play the four 14 seeds.
- The four 2 seeds will play the four 15 seeds.
- The four 7 seeds will play the four 10 seeds.
- After the games in steps 1 to 8, the 64 teams will be narrowed down to 32.
- The winners from rule 1 will play the winners from rule 2.
- The winners from rule 3 will play the winners from rule 4.
- The winners from rule 5 will play the winners from rule 6.
- The winners from rule 7 will play the winners from rule 8.
- After the games in steps 10 to 13, the 32 remaining teams will be narrowed down to 16.
- The winners from rule 10 will play the winners from rule 11.
- The winners from rule 12 will play the winners from rule 13.
- After the games in steps 15 and 16, the 16 remaining teams will be narrowed down to eight.
- The winners from rule 15 will play the winners from rule 16.
- After the games in step 18, the eight remaining teams will be narrowed down to 4. This will establish a winner from each of the four divisions.
- The winner of the regional that had the #1 overall team as determined by the NCAA basketball committee when selecting the tournament teams plays the winner of the regional that had the #4 overall team; with the winner advancing.
- The winners of the two regions, not mentioned in rule 20, play each other, with the winner advancing.
- The winners of steps 20 and 21 will play, the winner winning the tournament.
Once it gets to 64 teams, there are 32+16+8+4+2+1=63 games in the tournament.
Basic Strategy
Always pick the team with the higher-ranking seed, or lower number. For example, in the four games where a number 1 seed plays a number 16 seed, pick the number 1 seed. Of the 136 times a 1 seed has played a 16 seed, the number one seed won 135 times. 2018 saw the first number one seed lose to a 16 seed when UMBC (which has a great chess team) beat the University of Virginia.
When you get down to a number one seed winning each of the four divisions, pick the remaining three games randomly.
Matchups
The following table shows many face-offs there have been among all unbalanced match-ups have that happened at least once. This does not include games where teams of equal seed played against each other. The right column shows the probability the higher ranked team won.
Unbalanced Matchup Results
| Higher Seed | Lower Seed | Games Played | Higher Seed Wins | Probability |
|---|---|---|---|---|
| 1 | 2 | 67 | 36 | 0.537313 |
| 1 | 3 | 36 | 22 | 0.611111 |
| 1 | 4 | 64 | 47 | 0.734375 |
| 1 | 5 | 48 | 40 | 0.833333 |
| 1 | 6 | 13 | 10 | 0.769231 |
| 1 | 7 | 7 | 6 | 0.857143 |
| 1 | 8 | 75 | 60 | 0.800000 |
| 1 | 9 | 71 | 65 | 0.915493 |
| 1 | 10 | 6 | 5 | 0.833333 |
| 1 | 11 | 8 | 4 | 0.500000 |
| 1 | 12 | 20 | 20 | 1.000000 |
| 1 | 13 | 4 | 4 | 1.000000 |
| 1 | 16 | 144 | 143 | 0.993056 |
| 2 | 3 | 56 | 34 | 0.607143 |
| 2 | 4 | 7 | 3 | 0.428571 |
| 2 | 5 | 5 | 0 | 0.000000 |
| 2 | 6 | 30 | 23 | 0.766667 |
| 2 | 7 | 82 | 57 | 0.695122 |
| 2 | 8 | 7 | 2 | 0.285714 |
| 2 | 9 | 1 | 0 | 0.000000 |
| 2 | 10 | 52 | 34 | 0.653846 |
| 2 | 11 | 18 | 15 | 0.833333 |
| 2 | 12 | 2 | 2 | 1.000000 |
| 2 | 15 | 144 | 134 | 0.930556 |
| 3 | 4 | 7 | 4 | 0.571429 |
| 3 | 5 | 4 | 2 | 0.500000 |
| 3 | 6 | 75 | 45 | 0.600000 |
| 3 | 7 | 15 | 9 | 0.600000 |
| 3 | 8 | 2 | 2 | 1.000000 |
| 3 | 9 | 2 | 2 | 1.000000 |
| 3 | 10 | 12 | 8 | 0.666667 |
| 3 | 11 | 49 | 32 | 0.653061 |
| 3 | 14 | 144 | 122 | 0.847222 |
| 3 | 15 | 2 | 2 | 1.000000 |
| 4 | 5 | 75 | 42 | 0.560000 |
| 4 | 6 | 4 | 2 | 0.500000 |
| 4 | 7 | 5 | 2 | 0.400000 |
| 4 | 8 | 9 | 4 | 0.444444 |
| 4 | 9 | 3 | 2 | 0.666667 |
| 4 | 10 | 2 | 2 | 1.000000 |
| 4 | 12 | 39 | 26 | 0.666667 |
| 4 | 13 | 144 | 113 | 0.784722 |
| 5 | 6 | 1 | 1 | 1.000000 |
| 5 | 8 | 3 | 1 | 0.333333 |
| 5 | 9 | 3 | 1 | 0.333333 |
| 5 | 10 | 1 | 1 | 1.000000 |
| 5 | 12 | 144 | 93 | 0.645833 |
| 5 | 13 | 19 | 16 | 0.842105 |
| 6 | 7 | 9 | 6 | 0.666667 |
| 6 | 8 | 1 | 0 | 0.000000 |
| 6 | 10 | 7 | 4 | 0.571429 |
| 6 | 11 | 144 | 90 | 0.625000 |
| 6 | 14 | 15 | 13 | 0.866667 |
| 7 | 8 | 2 | 1 | 0.500000 |
| 7 | 10 | 144 | 87 | 0.604167 |
| 7 | 11 | 3 | 0 | 0.000000 |
| 7 | 14 | 1 | 1 | 1.000000 |
| 7 | 15 | 5 | 3 | 0.600000 |
| 8 | 9 | 144 | 74 | 0.513889 |
| 8 | 11 | 1 | 1 | 1.000000 |
| 8 | 12 | 2 | 0 | 0.000000 |
| 8 | 13 | 1 | 1 | 1.000000 |
| 8 | 16 | 1 | 0 | 0.000000 |
| 9 | 11 | 1 | 0 | 0.000000 |
| 9 | 13 | 1 | 1 | 1.000000 |
| 10 | 11 | 3 | 1 | 0.333333 |
| 10 | 14 | 1 | 1 | 1.000000 |
| 10 | 15 | 5 | 5 | 1.000000 |
| 11 | 14 | 7 | 6 | 0.857143 |
| 12 | 13 | 12 | 9 | 0.750000 |
Analysis
The way I used to analyze the probability of a perfect bracket was to look at historical experience of any one seed beating another seed. For example, the probability of a 4 seed beating a 5 seed. At the time of this writing, with 36 years of data from 1985 to 2021, such a matchup has happened 75 times, with the 4 seed winning 42 of them, for a probability of 56%. This is a decent method, but suffers from a small sample size problem. I think a better way to get at the probability of the higher seeded team winning any given game, according to the two seed numbers, is to look at all 2,268 tournament games played in the 36 years between 1985 and 2021. Doing so gave me the opportunity to smooth out the ups and down in the data and make for a better estimate. I get into how I did more more deeply in my page on March Madness.
The following table shows the probability of the higher seeded team winning any possible matchup necessary to win if the player picked the higher seeded team every game. In the case of a 1 seed playing a 1 seed, I assume a 50% chance of winining any given game. The "old method" probability looks at the exact probability, based on historical experience. The "new method" is based on my method of smoothing out the data to get a more accurate picture of the strength of any given seed.
Probability Favorite Wins
| Round | Event | Games Played | Probability Old Method |
Probability New Method |
|---|---|---|---|---|
| 1 | 1 beats 16 | 4 | 0.993056 | 0.993049 |
| 1 | 2 beats 15 | 4 | 0.930556 | 0.933458 |
| 1 | 3 beats 14 | 4 | 0.847222 | 0.887485 |
| 1 | 4 beats 13 | 4 | 0.784722 | 0.832170 |
| 1 | 5 beats 12 | 4 | 0.645833 | 0.768372 |
| 1 | 6 beats 11 | 4 | 0.625000 | 0.697340 |
| 1 | 7 beats 10 | 4 | 0.604167 | 0.620749 |
| 1 | 8 beats 9 | 4 | 0.513889 | 0.540650 |
| 2 | 1 beats 8 | 4 | 0.800000 | 0.792047 |
| 2 | 4 beats 5 | 4 | 0.560000 | 0.540873 |
| 2 | 3 beats 6 | 4 | 0.600000 | 0.622246 |
| 2 | 2 beats 7 | 4 | 0.695122 | 0.702952 |
| 3 | 1 beats 4 | 4 | 0.734375 | 0.668944 |
| 3 | 2 beats 3 | 4 | 0.607143 | 0.551538 |
| 4 | 1 beats 2 | 4 | 0.537313 | 0.578959 |
| 5 | 1 beats 1 | 2 | 0.500000 | 0.500000 |
| 6 | 1 beats 1 | 1 | 0.500000 | 0.500000 |
Before going on, let me use the notation of pr(x) = probability of event x happening. For example, pr(rolling a total of 7 with two dice) = 1/6.
Remember that there are four divisions in the tournament, so for the first four rounds, the player will have to win any given matchup four times.
The probability of winning all 32 games in the first round and advancing to round 2 is: [pr(1 seed beats 16 seed)*pr(2 seed beats 15 seed)*pr(3 seed beats 14 seed)*pr(4 seed beats 13 seed)*pr(5 seed beats 12 seed)*pr(6 seed beats 11 seed)*pr(7 seed beats 10 seed)*pr(8 seed beats 9 seed)]^4.
Under the new method, this probability of surviving to round 2 is 1 in 4,354.
In round 2, the player will have 16 games to win. Assuming he survives round 1, the probability of surviving round 2 will be [pr(1 seed beats 8 seed)*pr(2 seed beats 7 seed)*pr(3 seed beats 6 seed)*pr(4 seed beats 5 seed)]^4. This probability, using the new method is 1 in 811. The probability of surviving both rounds 1 and 2 is 1 in 3,531,138.
In round 3, the player will have 8 games to win. Assuming he survives rounds 1 and 2, the probability of surviving round 3 will be [pr(1 seed beats 4 seed)*pr(2 seed beats 3 seed)]^4. This probability, using the new method is 1 in 54. The probability of surviving to this point, from the beginning, is about 1 in 190 million.
In round 4, the player will have 4 games to win. These will all be 1 seed vs. 1 seed games. Let's assume a 50% chance of winning each game. The probability of winning all four games is (1/2)^4 = 1 in 16. The probability of surviving to this point, from the beginning, is about 1 in 1.7 billion.
In round 5, the player will have 2 games to win. These will all be 1 seed vs. 1 seed games. Again, let's assume a 50% chance of winning each game. The probability of winning both games is (1/2)^2 = 1 in 4. The probability of surviving to this point, from the beginning, is about 1 in 6.8 billion.
The player will still have one more game to win, the championship game. If he survived this far, it will be another 1 seed vs. 1 seed. Let's again assume a 50% chance of winning. That brings the probability of survival through the championship game, for a perfect bracket, to about 1 in 13.6 billion.
By the way, using the old method results in a probability of a perfect bracket of 1 in 56.7 billion.
Warren Buffett Prize
Warren Buffett has offered $1,000,000 per year, for life, to any employee of his who can fill out a perfect bracket. Warren has about 377,000 employees (source). Assuming each one followed the strategy above, and lived 60 more years, the expected value per employee is 0.4 cents and the expected cost to Mr. Buffet over all his employees is $1,667.
If you don't want to risk sharing the glory of a perfect bracket with someone else following my strategy, I'd suggest picking one or two 9 seeds to beat an 8 seed. The probability of the nine seed beating an eight seed is 47.8%, so a small sacrifice to increase your chances at hogging the glory of a perfect bracket to yourself.
Compare Online NBA Odds
Basketball : Basketball Euroleague
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
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Tue Jan 14th 2pm
ASVEL Lyon Villeurbanne KK Partizan NIS |
ASVEL Lyon Villeurbanne faces KK Partizan NIS. ASVEL's home advantage is crucial, while Partizan's defense could be key. Expect a tightly contested game with potential for big plays. | |||
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Tue Jan 14th 2pm
Saski Baskonia Olympiacos |
Saski Baskonia vs. Olympiacos clash expects a tight game. Consider Olympiacos' strong form, but Baskonia's home advantage could offset. Defensive strategies will likely dictate the game's flow. | |||
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Tue Jan 14th 2pm
Paris Basketball Anadolu Efes |
Consider Anadolu Efes’s strong performance this season. Their key players bring experience and depth. Paris Basketball needs a strategic defense to counter Efes’s aggressive offense. Look for underdog bets. | |||
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Tue Jan 14th 2pm
Pallacanestro Olimpia Milano ALBA Berlin |
Olimpia Milano, strong at home, has a better roster. ALBA Berlin's defense struggles in away games; expect high pace. Favor Milano with their impressive 3-point shooting. | |||
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Tue Jan 14th 2pm
Real Madrid Maccabi Tel Aviv |
Consider Real Madrid's strong home court advantage and past performance. Maccabi Tel Aviv may struggle defensively, though their fast-paced offense could surprise. | |||
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Wed Jan 15th 1pm
Žalgiris Virtus Segafredo Bologna |
Žalgiris enjoys strong home court advantage. Virtus relies on defense and 3-point shooting. Key players for Žalgiris are crucial for rebounds. Close match expected; slight edge to Žalgiris. | |||
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Wed Jan 15th 2pm
KK Crvena zvezda Fenerbahce SK |
Expect a close game between KK Crvena zvezda and Fenerbahce SK. Consider betting on under points, as defense prevails. Watch for home court advantage favoring Crvena zvezda. | |||
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Wed Jan 15th 2pm
FC Bayern München AS Monaco |
Bayern München vs. AS Monaco: Tight defense and strategic plays determine outcomes in this basketball showdown. Expect careful scoring, tenacity, and possible surprises on both sides. | |||
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Wed Jan 15th 2pm
FC Barcelona Bàsquet Panathinaikos |
Barcelona's strong home record gives them an edge, but Panathinaikos' recent form can't be ignored. Expect a close contest with potential for a high-scoring game. Watch key players. |
Basketball : NBA
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Mon Jan 13th 7pm
Washington Wizards Minnesota Timberwolves |
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⇗5.00 |
⇗5.00 |
Consider Timberwolves' strong defense and Wizards' dynamic offense. Watch key players like Edwards and Beal. Recent performance trends suggest a close and competitive matchup. |
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Mon Jan 13th 7pm
Toronto Raptors Golden State Warriors |
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Toronto's defense faces a challenge against Golden State's three-point shooting. Watch for Curry’s impact and Siakam’s response. Warriors favored, but Raptors can surprise. |
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Mon Jan 13th 7pm
New York Knicks Detroit Pistons |
⇗10.00 |
⇗10.00 |
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Knicks possess strong home advantage; Pistons' defense is weak. Knicks' offense can exploit gaps. Betting tip: Consider Knicks with a point spread for better value. |
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Mon Jan 13th 8pm
Houston Rockets Memphis Grizzlies |
-135
⇗5.00 |
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Rockets may struggle against the Grizzlies' defense. Grizzlies have strong recent performance. Key players to watch: Morant for Grizzlies, Green for Rockets. Grizzlies favored at home. |
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Mon Jan 13th 10pm
Los Angeles Lakers San Antonio Spurs |
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⇗3.00 |
Lakers have stronger lineup, relying on star power. Spurs focus on team play, young talents. Lakers favored to win but watch for Spurs' aggressive tactics. |
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Mon Jan 13th 10pm
Los Angeles Clippers Miami Heat |
⇘10.00 |
⇗5.00 |
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Consider Clippers' strong defense and Miami's recent form. Check player injuries and head-to-head stats. Home court advantage may influence the outcome. |
Basketball : NBA Championship Winner
| Sat May 31st 6pm | Competitor/Team | Quote |
|---|---|---|
| Boston Celtics |
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| Oklahoma City Thunder |
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| Cleveland Cavaliers |
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| New York Knicks |
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| Denver Nuggets |
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| Dallas Mavericks |
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| Milwaukee Bucks |
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| Memphis Grizzlies |
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| Golden State Warriors |
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| Minnesota Timberwolves |
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| Los Angeles Lakers |
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| Los Angeles Clippers |
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| Houston Rockets |
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| Philadelphia 76ers |
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| Phoenix Suns |
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| Orlando Magic |
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| Sacramento Kings |
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| Miami Heat |
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| Indiana Pacers |
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| Atlanta Hawks |
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| San Antonio Spurs |
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| New Orleans Pelicans |
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| Chicago Bulls |
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| Utah Jazz |
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| Brooklyn Nets |
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| Charlotte Hornets |
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| Detroit Pistons |
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| Toronto Raptors |
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| Portland Trail Blazers |
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| Washington Wizards |
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Basketball : NCAAB
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Mon Jan 13th 6pm
Arkansas-Pine Bluff Golden Lions Prairie View Panthers |
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Arkansas-Pine Bluff struggles in away games. Prairie View is stronger at home. Expect Prairie View to cover the spread due to their offensive edge and Pine Bluff's inconsistent performance. |
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Mon Jan 13th 6pm
Maryland Terrapins Minnesota Golden Gophers |
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Maryland Terrapins have a strong lineup this season. Minnesota Golden Gophers' defense is critical for their success. Key players' performance will determine the outcome. |
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Mon Jan 13th 6pm
Rutgers Scarlet Knights UCLA Bruins |
⇗10.00 |
⇗5.00 |
⇗5.00 |
UCLA Bruins are favored against Rutgers Scarlet Knights. Consider UCLA's strong defense and home advantage. Rutgers' inconsistent form is a risk. Analyze team stats for informed betting. |
| Upcoming matches | Money Line | Spread | Total | Featured Insight |
|---|---|---|---|---|
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Mon Jan 13th 7pm
Notre Dame Fighting Irish Boston College Eagles |
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Notre Dame's defense is strong, but Boston College has a competitive offense. Expect a close game with a tight scoreline. Monitor key player performances closely. |
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Mon Jan 13th 7pm
Furman Paladins Wofford Terriers |
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Furman Paladins show strong defensive play, while Wofford Terriers excel in three-point shooting. Consider Furman's defensive edge and Wofford's offensive strength when planning your bets. |
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Mon Jan 13th 7pm
Alcorn St Braves Alabama St Hornets |
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Alcorn St Braves have a strong defense, while Alabama St Hornets excel at home games. Key player injuries could impact performance. Consider trends and statistics for better insight. |
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Mon Jan 13th 7pm
Miss Valley St Delta Devils Texas Southern Tigers |
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Texas Southern Tigers have a strong home advantage. Miss Valley St Delta Devils struggle on defense. Consider betting on Texas Southern for a possible win. |
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Mon Jan 13th 7pm
Loyola (MD) Greyhounds American Eagles |
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⇗220.00 |
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Bet on American Eagles for a close match, considering Loyola’s defense weaknesses. Expect a tight game with low scoring. |
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Mon Jan 13th 7pm
Morgan St Bears Norfolk St Spartans |
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⇗5.00 |
Morgan St Bears face Norfolk St Spartans; expect tight defense and a close score. Key players' performance crucial. Consider underdog potential and recent form for bets. |
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Mon Jan 13th 7pm
UT Rio Grande Valley Vaqueros Texas A&M-Commerce Lions |
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Analyze team performance, previous encounters, and injury reports. Assess home advantage and player stats to make informed betting decisions. Consider recent form and point spread trends for both teams. |
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Mon Jan 13th 7pm
Incarnate Word Cardinals Nicholls St Colonels |
⇗5.00 |
⇗210.00 |
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Analyze team stats, form, and injuries before betting. Check head-to-head results, home/away performance, and player performance. Consider betting odds and expert predictions for informed decision. |
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Mon Jan 13th 7pm
Stephen F. Austin Lumberjacks SE Louisiana Lions |
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Consider the Lumberjacks' strong defense and the Lions' offensive power. Recent matchups show close scores, suggesting a tight game. Watch for key player performances to sway outcome. |
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Mon Jan 13th 7pm
North Carolina Central Eagles Delaware St Hornets |
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North Carolina Central Eagles have a strong defense, dominating recent matchups. Delaware St Hornets struggle offensively. Eagles likely favored. Consider point spread betting for Eagles’ strong performance. |
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Mon Jan 13th 7pm
Grambling St Tigers Florida A&M Rattlers |
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Grambling St Tigers and Florida A&M Rattlers face off in an intense match. Grambling's defense and Rattlers' speed are key factors. Consider injuries and home-court advantage. |
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Mon Jan 13th 7pm
South Carolina St Bulldogs Maryland-Eastern Shore Hawks |
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Consider the Hawks' recent strong performances. Bulldogs struggle with defense. Monitor player injuries for both teams. Betting tip: Favor the Hawks but watch for potential upset. |
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Mon Jan 13th 7pm
Howard Bison Coppin St Eagles |
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Howard Bison has strong defense but struggles in away games. Coppin St Eagles capitalize on turnovers. Key players' performance will be critical. Expect a close match with fluctuating momentum. |
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Mon Jan 13th 7pm
Southern Jaguars Bethune-Cookman Wildcats |
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Evaluate team stats before wagering on Southern Jaguars vs. Bethune-Cookman Wildcats. Consider form, injury reports, and head-to-head records. Home court advantage may play a crucial role. |
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Mon Jan 13th 8pm
Jackson St Tigers Alabama A&M Bulldogs |
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Consider current form, player stats, and injury reports for Jackson St Tigers vs. Alabama A&M Bulldogs. Home court advantage and recent head-to-head history may also impact the outcome. |
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Mon Jan 13th 8pm
Houston Christian Huskies McNeese Cowboys |
⇗50.00 |
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Houston Christian Huskies vs. McNeese Cowboys: Consider trends, player form, and past matchups. Key players impact outcome. Monitor injury updates and betting odds for smart decisions. |
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Mon Jan 13th 8pm
Lamar Cardinals New Orleans Privateers |
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Lamar Cardinals vs. New Orleans Privateers: Analyze past performances, current roster strength, and recent trends. Home advantage and defensive stats could sway outcomes. Consider player injuries and head-to-head records. |
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Mon Jan 13th 8pm
Texas A&M-CC Islanders Northwestern St Demons |
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Texas A&M-CC Islanders vs Northwestern St Demons: Islanders' strong defense meets Demons' potent offense. Slight edge to Islanders. Key Players: Islanders' Taylor, Demons' Johnson. |
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Mon Jan 13th 9pm
Elon Phoenix Campbell Fighting Camels |
-345
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Focus on Elon’s home performance and Campbell's road defense. Bet on total points scored. Consider recent player form and injury updates before placing your bets. |
External Links
Discussion about this page in my forum at Wizard of Vegas.