you can get a distribution that shows the percent chance of losing x number of times in a row.
In other words something that gives:
"you will lose 9 times in a row at least x number of times for every 1000 wagers at a win rate of 55%."
"you will lose 10 times...."
etc.
That is what I had in my files until they were destroyed. I found this format more relevant than "there is a x% chance of losing 9 in a row" since I look at it from the standpoint that I WILL make 1000 wagers from today onward.
There is a big flaw in one of the contingencies of this distribution, IMO. The contingency that every wager has exactly the same (55%) chance of winning simply b/c you choose it, is not true. This gets complicated, but the way I see it there are 'right sides' and 'wrong sides' from a value standpoint on numerous events. At some points you are really seeing the off-numbers and choosing 60% winners, and then maybe the next week you make mistakes and during some of those stretches you may be a 40% handicapper. So the chances of losing a certain number in a row is constantly changing, just as some events hold more value than others due to public misconception etc, etc.
This is one of those topics that is difficult to put into words. The above example is a good example to illustrate random streaks. But be very careful using static, raw statistics to apply to this market. Backfitting is a huge error when trying to predict future events. If you won 55% of your last 10,000 wagers are you a 55% handicapper? Maybe. All those 10,000 wagers show is that you WERE a 55% handicapper. And the next 10,000 events may offer less value or maybe more as the game changes, players become more athletic and/or injury prone,etc. For a lot of 'human nature' reasons the math gurus usually don't do well with their computer models betting on sporting events.
I could go on and on about my opinion, but I think what you are getting at is trying to figure out how much you can risk without going broke on each wager given probable streaks. Maybe some sort of Kelly system which I would stay away from. The way I look at it is this: the more wagers that I make the more probable I will lose 100 in a row at some point. Although it is almost statistically impossible, if I live long enough it will happen. It might take a trillion wagers to lose 100 in a row, but never count on losing 10 in a row as impossible or even improbable given a 55% historical win rate. It will happen it's just a matter of time, and you never know when--it's usually after a really good streak, for me.