SQL Server 2017

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CREATE TABLE dbo.Matches(DateField DATE,HomeTeam varchar(100),AwayTeam varchar(100));
INSERT INTO dbo.Matches
VALUES

('2018-08-10',   'Man United',    'Leicester'),
('2018-08-11',   'Bournemouth',   'Cardiff'),
('2018-08-11',   'Fulham',       'Crystal Palace'),
('2018-08-11',   'Huddersfield',   'Chelsea'),
('2018-08-11',   'Newcastle',    'Tottenham'),
('2018-08-11',   'Watford',     'Brighton'),
('2018-08-11',   'Wolves',      'Everton'),
('2018-08-12',   'Arsenal',      'Man City'),
('2018-08-12',   'Liverpool',     'West Ham'),
('2018-08-12',   'Southampton',    'Burnley'),
('2018-08-18',   'Cardiff',         'Newcastle'),
('2018-08-18',   'Chelsea',       'Arsenal'),
('2018-08-18',   'Everton',       'Southampton'),
('2018-08-25',   'Round3Example_1',       'Round3Example_2')

14 rows affected

;WITH CTE AS
(
SELECT	DateField,
		CASE WHEN DATEDIFF(day,LAG(DateField) OVER(ORDER BY DateField),DateField) > 3 THEN 1 ELSE 0 END as newround,
		Hometeam,
		AwayTeam
FROM dbo.Matches

)
SELECT Datefield, HomeTeam,AwayTeam, SUM(newround) OVER(ORDER BY DateField) + 1
FROM CTE;


Datefield
HomeTeam
AwayTeam
(No column name)


10/08/2018 00:00:00
Man United
Leicester
1

11/08/2018 00:00:00
Bournemouth
Cardiff
1

11/08/2018 00:00:00
Fulham
Crystal Palace
1

11/08/2018 00:00:00
Huddersfield
Chelsea
1

11/08/2018 00:00:00
Newcastle
Tottenham
1

11/08/2018 00:00:00
Watford
Brighton
1

11/08/2018 00:00:00
Wolves
Everton
1

12/08/2018 00:00:00
Arsenal
Man City
1

12/08/2018 00:00:00
Liverpool
West Ham
1

12/08/2018 00:00:00
Southampton
Burnley
1

18/08/2018 00:00:00
Cardiff
Newcastle
2

18/08/2018 00:00:00
Chelsea
Arsenal
2

18/08/2018 00:00:00
Everton
Southampton
2

25/08/2018 00:00:00
Round3Example_1
Round3Example_2
3

Datefield	HomeTeam	AwayTeam	(No column name)
10/08/2018 00:00:00	Man United	Leicester	1
11/08/2018 00:00:00	Bournemouth	Cardiff	1
11/08/2018 00:00:00	Fulham	Crystal Palace	1
11/08/2018 00:00:00	Huddersfield	Chelsea	1
11/08/2018 00:00:00	Newcastle	Tottenham	1
11/08/2018 00:00:00	Watford	Brighton	1
11/08/2018 00:00:00	Wolves	Everton	1
12/08/2018 00:00:00	Arsenal	Man City	1
12/08/2018 00:00:00	Liverpool	West Ham	1
12/08/2018 00:00:00	Southampton	Burnley	1
18/08/2018 00:00:00	Cardiff	Newcastle	2
18/08/2018 00:00:00	Chelsea	Arsenal	2
18/08/2018 00:00:00	Everton	Southampton	2
25/08/2018 00:00:00	Round3Example_1	Round3Example_2	3