What merit is there to the so-called "Swiss gambit?" The "Swiss gambit" refers to the idea of intentionally lowering one's performance at the beginning of a Swiss-system tournament, to one degree or another, in order to have an easier path through the later stages of the tournament. E.g. a highly-rated player in a field could take a half-point bye in the first round (instead of a likely win) in order to likely be paired against weaker competition for the next few rounds than would have happened otherwise.

It certainly shouldn't be the case that it's always a good idea, or Swiss-system tournaments would be very poorly conceived. But depending on where a given player sits ratings-wise in the field, and the exact distribution of the ratings of players in the tournament, it is not inconceivable that such a Swiss gambit could increase a player's expected final score. Of course, intentionally giving points away at any point could obviously decrease the expected score as well. This is all I am asking for here:


  Has any serious research been done concerning scenarios in which a Swiss gambit is/isn't effective, probabilistically speaking, in the sense of raising/lowering the gambiteer's expected tournament score?


Pointers to any legitimately mathematical (and mathematically legitimate) discussions of the matter would be most appreciated, as would the creation of such in an answer of course.
I tried writing a crude pairings/results simulator, to see whether taking a bye could increase a top player's score.  When generating pairings, the program ignored pairing history and color (which I realize can matter, but I didn't want to have to program it to go back and redo pairings if there was a conflict - this is a crude simulator, not an actual pairings engine!)  But it was able to handle pairing people in a scoring category with the usual top half/bottom half method, as well as the all-important "pairing up" of the top person from the lower category with the bottom person from the higher category if there was an odd number of players in the higher score category.  

I assumed a uniform ratings distribution through whatever ratings range I selected.  I used the "Standard winning expectancy" formula at the bottom of page 11 in this document.  I did not account for fatigue.  I assumed a draw probability of half of the probability that the higher-rated player would lose (for example, if the expected score was 0.75 according to the formula, I assumed a win would happen 70%, a draw 10%, and a loss 20%.  For even matches with 0.5 expected score it would be 40% - 20% - 40%.)  I set the program to run 100000 tournaments at a time, to get a good average. 

The Swiss gambit pretty much always decreased a high-rated player's overall score regardless of the number of players, rounds, or rating spread (unless I set the draw probability parameter to zero, which is unrealistic.)  At best it had only a small negative effect on the final score.  Although the player's performance in later rounds was indeed better due to weaker opponents, that performance did not quite overcome the nearly half-point lost.  The top players were better off playing in all the rounds.

For example, in a simulation of an 8 round 200 player tournament, with player ratings ranging from 200 to 2000, the 2000-rated player had an average score of about 6.35 if they did not take a bye.  If they took a first-round bye, the average was only about 6.24.

However, for some small tournaments with large point spreads and a certain number of players, although the average score dropped, the probability of placing first actually increased.  For example, in a 5 round 32 player tournament with players rated from 200 to 2000, taking a first round bye decreased the average score from 4.23 to 3.95, but increased the probability of taking clear first from 33.2% to 34.7%.  I'm not sure if these are artifacts of an imperfect pairing engine, though; the exact pairings matter more in such situations.  In most of my simulations the decrease in score corresponded with a lower probability of taking first (and the decrease was somewhat larger than the increase shown here.)

Interestingly, although it also wasn't effective compared to playing all the rounds, it seems that taking a half-point in the second or even third round often gave a slightly better score than taking one in the first round, especially when the ratings spread was large (in the 8 round 200 player example, they scored about 6.26 by taking the bye in the second or third round, as opposed to 6.24 by taking it in the first round.)  The first round has a top half player against an easy opponent; why skip a game you'll almost certainly win, instead of skipping the next one where your opponent may have something of a chance?

So, overall:  The average score decreases when using the Swiss gambit.  The odds of winning the tournament might go up in certain specific scenarios, but I'd need a better program to say for sure, and if there is any such effect it's sensitive to the exact number of players.