Hypothetical situation; in a chess tournament, player A. has 4 victories, but player B also has 4 victories. How is a tie break used to determine the first place winner between the two?
Thanks in advance. 
For a USCF-rules Swiss event, if not otherwise specified it is assumed to be modified median then Solkoff then cumulative then opponentsâ cumulative. If the scores are 4-0 instead of non-perfect 4-1, 4-2, 4-3, etc. then a blitz playoff is an endorsed option.
If accelerated pairings are used then some organizers will opt to replace cumulative with something else (such as Sonnenborn-Berger).
Some organizers feel that a short tournament should have Solkoff before modified median.
Round Robins generally use Sonnenborn-Berger first, and donât use any form of cumulative at all.
Please remember that all tie-break systems are unfair, and the ones used are designed to be unfair in a blindly unbiased manner.
Thank you for your response. However, I have no clue as to what a, âModified medianâ, or a, âSolkoffâ, etc., is.
How does a competitor know if the TD is awarding the first place cash prize fairly or not?
The tie-break systems are in the USCF rulebook (Rule 34). In âModified Medianâ, the total of a playerâs opponents final scores is summed, after first discarding the highest and lowest. âSolkoffâ is the same, but without discarding any of the scores. It is usually not too hard to compute these by hand for all the people tied for first. (Generally, TDâs have computer software to pair tournaments, and that does the calculation.) If the final wall chart is not posted, you could ask the TD to let you have a print-out from the pairing program.
Isnât the final wall chart at a U.S.C.F. rated event supposed to be posted? Without doing this, how is a competitor supposed to know the actual final standings? I would think if a T.D. doesnât post the final wall chart, this would seem to open the door wide for the T.D. to proclaim whomâever they want as the winner and also pay out, (or not), any amount of money they wish if the cash prizes are based on say 20 entries and 20 entries are not reached. Without posting the final wall chart, the opportunity for corruption here seems to be very large.
Speaking from practical experience, by the time the final wall chart could be posted at the site, most of the players have gone home. Iâve printed out copies of the wall charts for players to take with them many times, I think most TDs would do the same.
We do post the information on MSA, but not tie breaks, because we donât know what tie breaks were used.
Also, there are some tie breaks that cannot be computed from the rating report. There are also some unusual circumstances where the rating report would not compute the same tie breaks as were done on site, though both are computed properly based on the information given to compute them.
You never tie-break cash prizes. Tie-breaks are only used for indivisible prizes like trophies, tournament qualificiations, scholarships, etc.
In that case you add up the prizes the players tied for (no more prizes in the pool than there are players) and divide by the number of players. If only some of the players are eligible for some of the prizes then you also need to check to see whether or not awarding those prizes seperately would be better for the affected players, and if so then you do that. You use the most valuable prizes that a player is eligible for
Example:
Overall prizes of $500 for first, $250 for second $150 for third, $75 for fourth, $100 for top expert, $100 for top A, $100 for top B.
A master scores 5-0
Two masters and an expert score 4.5-0.5
An expert, two A players and a B player score 4-1
The top master takes the $500 prize.
The other masters and the top expert split the sum of the $250, $150 and $100 prizes (the $100 top expert prize is brought in instead of the $75 fourth prize since $100 is more valuable) and thus each get $166.67.
The other expert, two A-players and the B-player bring in the $75 (4th), $100 (top A) and $100 (top B) for $275 split four ways resulting in each getting $68.75. However, the B-player gets $100 for just that prize, so the B-player gets that $100 and the other three players do a three-way split of $175 for $58.33 each (which is more than the $50 each that the two A-players would get for splitting only the A-prize, so the $58.33 each split stands).
Thatâs actually Median tiebreaks. For Modified Median, those with plus scores discard only the bottom opponent score, those even do as above, and those with minus scores discard only the top opponent score. Longer tournaments discard more opponent scores
âNeverâ is too strong. Rule 32A requires only that the distribution method be announced beforehand if it varies from the standard rules. You describe the standard rules.
In my opinion, pooling and dividing cash prizes between tied players, as you describe, is one of the main reasons for the last round âGM Drawâ situation with Swiss System tournaments.
If the players involved in the tie are high scorers (e.g., 4-1) the round in which they lost (or average of the rounds they drew) will give the same results as cumulative, higher is better. Someone who recovers from a first round upset will have faced weaker opposition than someone who lost to the champion in the last round.
You underestimate the extent to which competitors, especially the top ones in contention for prizes, are intimately aware of the situation, tiebreaks, etc. If the TD tries to pull a fast one, heâs likely to get some probing questions. We used to calculate our own post-tournament ratings too, back when that formula was something you could do by hand.
If thatâs what the GMs want in a Swiss System tournament, said tournament is fairly likely to continue to give it to them. 
If you use a computer, the best and most fair tiebreak is âperformance of the oppositionâ. Unlike the other systems which attempt a rough hack at calculating the playing strength of the opponents a player faced, âperformance of the oppositionâ gives a percise actual calculation of the playing stength a player faced.
An additional bonus is that it is the only tie-break system you need to use because it gives each players an individual tie-break number (âratingâ) that is is almost never duplicated by another oppontent. With other tie-break systems, the same tie-break number is often returned for multiple players and then you have to cascade down the tie-break system order until you generate a unique result for each tied player.
FWIW, most GMs arenât too interested in the first place trophy for the â4th Annual Cowtown Championshipâ.
I donât really like Strength of Opposition because I feel people who take byes (donât play games) should receieve lower tie-breaks. For that reason I prefer modified median.
In Adult (open) tournaments, cash prizes are usually split between tied players, so the only time tie-breaks matter is for individual prizes (trophies, qualifying spots for invitational tourneys, and sometimes titles)
Since there are lots of trophies in scholastic tournaments, thatâs usually where the tie-breaks matter. It can be the difference between getting a 3rd place trophy and a 6th place trophy (or no trophy if just top 5). Although there are fewer byes in scholastic events than adul ones, I still like modified median because it institutes a small level of comradery among opponents. Two kids play in the first round, and whatever the outcome, they want the other to do well in the rest of the tournament, because that will improve their tie-breaks at the end. I felt this as a scholastic player some years ago, and I encouraged it whenever I directed a scholastic event.
But the question which interests me is why organizers and tournament directors would be interested in giving GMâs what they want. Without the typical Swiss â a few rounds of slaughter, followed by a couple of rounds of somewhat hard games, followed by last round quick draws and checks being handed out â maybe the GMâs and would-be GMâs would not be so interested in the tournament and would stay home and pursue their other hobbies and/or vices.
But so what? What motivates organizers to stage such tournaments? If they are organizing the tournaments for the love of chess, what about the GMâs preferred payday scenario is inspiring? If they are organizing tournaments for profit, how does this scenario contribute to their bottom line? Is it so important to the finances of the tournaments to have the GMâs dropping by to pick up their checks?
If you were a basketball fan, would you want to play a game with an NBA player? Sure heâd embarrass you on the court, and you might not learn anything, but then again you might.
I think some of that is going on. People are paying to be in the presence of GMs and maybe play against one. Itâs mutually agreeable, a thrill for one guy, a paycheck for the other. In basketball you canât really get that, but in chess you can.
Those who donât like that can play in other tournaments that donât attract GMs.
Maybe if you played in a few such events, or directed them, or organized them, or had in depth discussions with local players as part of deciding the format of a major event, then you could answer your own question.
Some players want the chance to sit down at the board against the GM. Some would rather have a more locally focused event with players of comparable ability. We organize events and prize structures in such a way so that our main player base will show up and play. They vote with their entry fees if in no other way.
This is a good example of a tie break method that cannot be reproduced from the crosstable of an event on MSA. Why? Because we donât know (for sure) what ratings were used when computing the performance of the opposition on site.
Youâd at least have a chance of knowing in an unrated section, so maybe it could be used there. Oh, wait. Oops.