Sql-server – Deadlocks in SQL Server – how to avoid

As per the code mentioned below, I am trying to understand how 'Deadlock' can be avoided with the help of a table and a single row. Could someone help me understand how this technic can help avoid deadlock situations.?

Disclaimer:
I found this from an answer to a different but relevant question in this forum but I could not add a comment on that thread.. Hence thought to raise it as a question by itself..

The idea is to – Instead of invoking sp_getapplock, we can use the following table to avoid deadlocks

CREATE TABLE dbo.DeadlockTestMutex(
ID INT NOT NULL,
CONSTRAINT PK_DeadlockTestMutex PRIMARY KEY(ID),
Toggle INT NOT NULL);
GO

INSERT INTO dbo.DeadlockTestMutex(ID, Toggle)
VALUES(1,0); 

Once the above table is ready and populated with the data as shown above, use this statement inside your stored procedures

UPDATE dbo.DeadlockTestMutex SET Toggle = 1 - Toggle WHERE ID = 1; 

Such that, the stored procedures are as follows:

ALTER PROCEDURE dbo.UpdateCounter1 @Key1 INT
AS
SET NOCOUNT ON ;
SET XACT_ABORT ON;
SET TRANSACTION ISOLATION LEVEL REPEATABLE READ;
BEGIN TRANSACTION ;

----------
UPDATE dbo.DeadlockTestMutex SET Toggle = 1 - Toggle WHERE ID = 1;
----------

UPDATE dbo.DeadlockTest SET Counter1=Counter1+1 WHERE Key1=@Key1;
SET @Key1=@Key1-10000;
UPDATE dbo.DeadlockTest SET Counter1=Counter1+1 WHERE Key1=@Key1;
COMMIT;
GO

ALTER PROCEDURE dbo.UpdateCounter2 @Key2 INT
AS
SET NOCOUNT ON ;
SET XACT_ABORT ON;
SET TRANSACTION ISOLATION LEVEL REPEATABLE READ;
BEGIN TRANSACTION ;

----------
UPDATE dbo.DeadlockTestMutex SET Toggle = 1 - Toggle WHERE ID = 1;
----------    

SET @Key2=@Key2-10000;
UPDATE dbo.DeadlockTest SET Counter2=Counter2+1 WHERE Key2=@Key2;
SET @Key2=@Key2+10000;
UPDATE dbo.DeadlockTest SET Counter2=Counter2+1 WHERE Key2=@Key2;
COMMIT;
GO 

So, how does adding this one liner can avoid deadlocks?

Here is the code for the table used by the stored procedures..

CREATE TABLE dbo.Numbers(n INT NOT NULL PRIMARY KEY); 
GO 

INSERT INTO dbo.Numbers 
    ( n ) 
        VALUES  ( 1 ); 
GO 
DECLARE @i INT; 
    SET @i=0; 
WHILE @i<21  
    BEGIN 
    INSERT INTO dbo.Numbers 
        ( n ) 
        SELECT n + POWER(2, @i) 
        FROM dbo.Numbers; 
    SET @i = @i + 1; 
    END;  
GO

SELECT n AS ID, n AS Key1, n AS Key2, 0 AS Counter1, 0 AS Counter2
INTO dbo.DeadlockTest FROM dbo.Numbers
GO

ALTER TABLE dbo.DeadlockTest ADD CONSTRAINT PK_DeadlockTest PRIMARY KEY(ID);
GO

CREATE INDEX DeadlockTestKey1 ON dbo.DeadlockTest(Key1);
GO

CREATE INDEX DeadlockTestKey2 ON dbo.DeadlockTest(Key2);
GO