During his career he faced most of the best masters in the country at one time or another and was considered to be the best player in New England for a number of years. As late as 1891 he was able to give Pillsbury odds of Pawn and move. Writing in Wonders and Curiosities of Chess, Irving Chernev claimed that Burille once solved 62 chess problems in one hour.
Burille was a member of a group of Boston chess players and theoreticians who formed a chess association they called the Mandarins of the Yellow Buttons. In order to join, a prospective member must have been an amateur chess player and must have beaten a recognized master, i.e. a professional international champion, in an even game of chess.
The club met on Saturday afternoon for chess and spent the evening dining together and discussing chess. The members included Franklin K. Young, F. H. Harlow, Dr. E.M. Harris, C. F. Howard, Major O.E. Michaelis, General W. C. Paine, Dr. Horace Richardson, Charles B. Snow, Henry Nathan Stone and Preston Ware. Members later formed the Deschapelles Club of Boston where chess and whist was played. The club's most prominent member was the 18-year old Pillsbury.
Burille finished 15th at New York City 1889 (the 6th American Chess Congress won by Mikhail Chigorin and Max Weiss). He beat F.K. Young (13.5–1.5) in a match in 1888, and lost to Harry N. Pillsbury (3–7) in 1892 (Burille gave odds of pawn and move). He also played in cable chess matches New York vs. London in 1896 (won a game against Henry Bird) and 1897 (lost a game to Henry Atkins).
Burille, also a checkers master, spent time as one of the operators of Ajeeb, a chess-playing automaton and during that time he played over 900 games of chess, losing only three and he never lost a single checkers game.
A skilled telegraph operator, Burille once used telegaphy to pull a joke on Pillsbury who was playing a game against an opponent to whom he had given Rook odds. Pillsbury's opponent was also a telegraph operator and Burille quietly tapped out suggested moves. As a result, Pillsbury lost several games and when he finally called it a night and observed that his opponent had never played that well before that's when he discovered he had actually been playing Burille at Rook odds.
A noted tacticain, Franklin K. Young gave a number of games by Burille in his book The Grand Tactics of Chess.
Although he only finished 15eth (out of 20) in the double-round 6th American Chess Congress with a score of 15-23, he scored wins over Chigorin and Gunsberg.
The sixth American Chess Congress was held in New York in 1889 and was a 20-man double round-robin tournament making it one of the longest tournaments in history.
The event was won by Mikhail Chigorin and Max Weiss. Both finished with a score of 29, but Chigorin defeated Weiss in their individual game and drew one...sort of.
The time limit was 15 moves per hour and an unusual feature was that if the second game was drawn, it didn't count and a third game was required with colors determined by lot. There were 48 draws in the second half of the tournament, so 48 additional games had to be played.
In the two regular games played betweem Chigorin and Weiss, both games were drawn, meaning they had to play a third game which was won by Chigorin. As a result, the tournament crosstable shows a draw and a win for Chigorin.
In order to determine a winner, Chigorin and Weiss played a match that was tied after four games. At that point both players stated they didn't want to continue the match, they just wanted to go home. The organizers reluctantly agreed and split the prize money.
The tournament was financed through the sale of 500 tournament books with subscribers paying $10 in advance and the money would be used for cash prizes and to pay Steinitz for annotating the games. In order to make sure subscribers got their money's worth, after the 500 books were printed the plates were destroyed which would make the books collector's items. It also meant the tournament was not so well known.
As a result of Lipschutz' sixth place finish, which was the best for an American player, his supporters in the Eastern US tried to push his claim to being US Champion but his claim was not accepted and George H. MacKenzie was still regarded as the US champion.
After MacKenzie's death there was some dispute as to who the US champion was. Mackenzie died in April 1891 and, later that year, Max Judd proposed he, Jackson Showalter and Lipschutz contest a triangular match for the championship. Lipschutz withdrew so Judd and Showalter played a match which was won by Judd.
A claim by Walter Penn Shipley that Lipschutz became US Champion as a result of being the top-scoring American at the Sixth American Chess Congress is refuted in a biography of Lipschutz.
Lipschutz was not officially recognized as US Champion until 1892 when he decisively defeated Jackson W. Showalter in a match +7 -1 =1.
Showalter played two other matches which apparently were not for the US Championship. In 1894 he defeated Albert Hodges in match play and then lost another match to Hodges in 1895. Some consider this to have been a single match with a break while others consider it to have been two separate matches. Overall, Hodges scored +11 -10 =5. In 1895 Showalter defeated Lipschutz in a return match, scoring +7 -4 =3.
In 1897 Showalter lost the title to Pillsbury who held it until his death in 1906. After Pillsbury's death Frank Marshall, who was acknowledged to be the best US player, was generally regarded as champion, but in 1909 there arose considerable debate over the issue.
In 1908 Marshal had played a match with Capablanca and got wiped out, scoring one win and losing eight. As a result, Capablanca proclaimed himself to be American champion!
Marshall countered that because Capa wasn't an American citizen he could not be the champion and so Marshall himself was the Champ. At this point Walter Penn Shipley put forth the argument that neither Capa nor Marshall was the US Champion...it was Showalter.
His reasoning was that since Showalter had held the title he had never declined a challenge and until he did so, nobody could claim the championship. Shipley pointed out that while Marshall was the best US player and Capa defeated him, it was self-evident that a non-citizen could not be champion.
Additionally, since Hodges had challenged and defeated Showalter, Hodges gained the title, but when Showalter issued a challenge for a rematch, Hodges declined and let the title revert back to Showalter.
Pillsbury then challenged and defeated Showalter to gain the title and upon Pillsbury's death, the title reverted back to Showalter. And, because the championship could not be decided in any way except through match play, Marshall had never challenged Showalter. Hence, Marshall was never champion and so Capa's claim to be th US champion was spurious.
The result of the debate was that Marshall challenged Showalter to a match that took place in late 1909. Marshall won by a score of +7 -2 =3 and became the US Champion.
As for the Sixth American Congress, Wikipedia says that under rules that reigning World Champion Wilhelm Steinitz helped to develop, the winner was to be regarded as World Champion for the time being, but must be prepared to face a challenge from the second- or third-placed competitor within a month. I think the article means "World Champion Challenger," not Champion.
Weiss, who was hardly World Champion material, was not interested. But, in 1889 Steinitz defeated Chigorin in a match in Havana and in 1891, he defeated Gunsberg in New York City and Chigorin again, also in Havana, in 1892.
1-2) Weiss and Chigorin 29 – 9
3) Gunsberg 28½- 9½
4) Blackburne 27-11
5) Burn 26 -12
6) Lipschuetz 25.5-12.5
7) Mason 22 -16
8) Judd 20 -18
9) Delmar 18 -20
10) Showalter 18 -20
11) Pollock 17.5-20.5
12) Bird 17 -21
13) Taubenhaus 17 -21
14) David Baird 16 -22
15) Burille 15 -23
16) Hanham 14 -24
17-18) Gossip and Martinez 13.5-25.5
19) John Baird 7 -31
20) MacLeod 6.5-31.5