While trying to get my daily x5 today, I managed to achieve a streak of 19 consecutive losses in randoms. That got me thinking: How likely is that?
Let's start with an expected winrate of 0.5 to keep the math simple. The probability of losing 19 times in a row, if you play exactly 19 matches each session, is 0.519 = 0.0000019073486328125. Meaning it is a 1 in 524,288 chance, so it happens on average once every 19*524,288=9,961,472 games.
Usually, I my WR is about 50%, but what if I didn't play my A game and was playing on par with 40% WR player? My chance of losing each game is now 0.6, so 0.619 =0.0000609359740010496. Still rather unlikely.
Even dropping me to AFK bot level of 30% WR yields a probability of 0.719 =0,0011398895185373143 or 1 in 877 sessions.
However, I didn't always play sessions of 19 games and stop. In fact, even today I played 29 matches (and ended with 7 wins, 22 losses). How long would you have to play to get a loss streak of 19 losses in a row, if you kept playing till you had 19 losses back-to-back?
We need to calculate the runs probability now. On average, you'd need to play (1-0.519 )/(0.519*0.5) = 1,048,574. Still a session of 1 million matches in a row. For a WR of 40%, it drops to 41,024.
That is still not the actual probability, because I never count my losses across sessions. So "interrupted" runs don't count. The actual probability is somewhere inbetween the 10 million games result from above and the 1 million games result here.
TL,DR: A 19 games loss streak is rather unlikely