Mad777 wrote:Since my goal is always to improve what I offer as TO and by listening from you who play my tournament, I went ahead and revised the GA medal award rules (refer OP), the new rule to be for each player who win 2 consecutive round by 11-0 or wining 3 rounds throughout the whole tournament by 11-0 (with the exception if the round has been win from a deadbeat opponent).
I also researched the entire games set from Round 1 to Round 10 included, I then compiled a list at the bottom of the OP.
I hope this will make more sense and adhere to your vision

Happy to hear that you took another look at it! The probability calculations involved were at the top (or maybe above) my level of comprehension, so it would take me quite a while to figure out what the odds are for the new set-up, but obviously you've taken it in the right direction. The whole thing only caught my eye because people tend to seriously miscalculate probabilities when you have things like consecutive events (e.g. overestimating the chances of a team going undefeated or winless) or when large numbers are involved (e.g. lotteries). Here, I can see how someone would look at 100 players playing hundreds of games each and thinking, "someone could easily get X wins in a row."
I doubt I'll have time to try to figure out the math involved in the current set-up. But I do have some guesses from what I remember from plugging in the numbers from before. I think that if anyone worked out the probabilities, you'd still find them uncomfortably low. However, you're probably in or close to a spot where the medal is realistically achievable because of certain realities that are obscured by the averages that are plugged in to the probability calculations. For example, let's say you have a pretty good player with a 60% win rate. Let's say that player's win rate goes up to 80% when he faces an opponent that misses a turn. Since we play 11 games at a time against a single opponent, that's a huge jump when it comes to going undefeated for a round. The probability of going undefeated in that round jumps from 0.4% to 8.6%.
Of course, for our 60% player, going undefeated for a round isn't impossible, just very low. That 0.4% isn't 0%, and missed turns aren't the only thing that could significantly raise expected win percentage over a round of simultaneous games against a single opponent. The player could face an opponent that is substantially weaker than who he usually plays. The opponent might be travelling and have to rush turns.
It will be interesting to see what the actual results of this experiment are over this tournament and future tournaments.
Finally, one interesting (to me, at least) finding while typing this up: Let's say you have a player/scenario with an 80% expected win rate (e.g. good player v. bad player) and another with a 60% win rate (e.g. good player v. average player). What is more likely to happen:
a) 80% player undefeated for 2 consecutive rounds (22 games);
b) 60% player undefeated in 1 round (11 games); or
c) neither--chances of (a) and (b) are about the same
[spoiler=Answer]I would've guessed (b) but the answer is actually (a). If a player can expect to win 80% of his games, his probability of winning 22 straight is actually twice as high as the 60% player winning 11 straight (0.8% v 0.4%).[/spoiler]