Thanks Limequat. Great observations. Yes, I've experienced this as well, when there are others ahead of me, I easily win my battles even with lower percentage dragons. I did what I did as an experiment to see what would happen with the battling as the task was not critical towards my maximum Bingo points. I have spent the last 3 weeks that I was playing Bingo consistently either first or second on the Leaderboard (i.e. Gold, default to drop down a league, Silver, Gold League), and this is what I have experienced; so to help others. During this time, I've had plenty of battling tasks, definitely more than 10. Each time, I used a dragon with 75% or greater chance of winning (as I have plenty of high-level dragons at level 189). In fact, at the moment, TL decided to start a 22 round tournament (no doubt to spur people to spend more gold as it currently costs 30 gold to Ultimate out rather than the normal 12) which I thought might be an advantage; but alas it is somewhat not - i.e. please refer to my comments 2 paragraphs below after my side comment paragraph.
As a BIG aside, because I want to collect my last 50 tickets, I decided to forego the tournament and save my battles for a greater chance of winning against the low-level dragons in the early rounds of the tournament; and for us more experienced players, who really cares about earning a ho-hum triple color super rare (or even worse, only a rare one a few tournaments back; it has been ages since a Champion dragon was the tournament prize; at the moment, I'm only playing the tournaments to quickly advance if trying to earn items for the monthly battle arena dragon or if it is in the way of another event that I might be playing, i.e. Tales). I know it has been said in this forum plenty of times by others, but I'll say it again as feedback to TeamLava: having multiple events on at the same time week after week serves to really ANNOY your loyal players. With this and your gold traps that have never been fixed, this is the reason that many players refuse to spend money on buying gold. Many of my neighbors have told me this. Please take a lesson from this if you want your company to grow. Do not upset your customer base like this! Take a lesson from your last Leaderboard event where I applaud you for making the 10 milestones achievable for the average player without having to spend gold. In my group, I observed many people spending gold to actually win the Grand Prize dragon even well beyond the 10th milestone whereas in others, there was a distinct lack of interest, and I did so myself. Give a little to get more back!
Anyway, getting back on topic, let's just call it 10 times at the top of the league where I started a battling task. Each time, I used a 75% or greater dragon and always lost the first battle. In fact, in the last 3 battle tasks, with the tournament going against levels 1 to 6 dragons, I lost using dragons with 90% chance of winning; and then generally I won easily in the next round. I also observed each time (as a veteran of the Battle Arena), for the lost rounds, the damages dealt each time for each 3 blows were exactly the same! It would be a brave person to tell me that this is not rigged!
Anyway, to be helpful to others, I have gotten around this issue by calculating ahead of time that you will always lose the first battle, so just make sure you have another high-level dragon (or use a lower level one for the first), then if playing on iOS, use the free gift to watch a video or use 4 gold to advance immediately to re-battle).
Hope everyone can use the notes and advice. Good luck.
Note: Please see my reply below to katali119 regarding percentages and statistics.