How does a Tiebreak Work?

Hello Chess Friends!

As i know many of you may do not know or getting curious and some dont mind it just by looking the scores then their we go!.  But how does a tiebreak work in tournaments created on chess.com?

There are different type of tie break that can be use depending the tournament's director on your specific areas. But chess.com uses the  (Neustadtl score method). Named after Hermann Neustadtl, who proposed it in a letter published in Chess Monthly in 1882.

Neustadtl score method is calculated by adding the sum of the conventional scores of the players he/she has defeated to half the sum of the conventional scores of those he/she has drawn against.

The main point is to give more value for a win/draw against a player ranked high, than for a win/draw against a player ranked low in the tournament.

Since players may share the same Neustadtl score, further means of breaking ties may be required.

Below is a simplified example of how the tie breaking system works :

Bob won one game against Mary and two games against John. So Bob gets 1x1.5 points from Mary and 2 x 1.5 points from John, which sums up to 4.5 tie break points.

Mary won one game against Bob and drew one game against John. So Mary gets 1x3.0 points from Bob and 0.5x1.5 points from John, which sums up to 3.75 tie break points.

John won one game and drew one game against Mary. So John gets 1.5x1.5 points from Mary, which sums up to 2.25 tie break points.

       For your Math clarification :
      

    Bob won 1 game against Mary so lets say a variable (a=1).

   And Mary with a total score of 1.5 say a variable of (b=1.5)

   Hence,

              a*b = 1*1.5 = 1.5 Therefore, Bob gets 1.5 tiebreak-score from Mary.

             and soon .

If two players have the same score and the same Tie Break score, both will advance in the tournament.

All Credits to Chess.com.

More About tie-break scores ?

https://www.youtube.com/watch?v=hfwm-6nkFaI&t=162s