Winning and Losing Streaks Formula
The longest expected losing streak (or winning streak) can be calculated using the following formula:
n = number of trials (i.e. total number of bets)
ln = natural logarithm1
P = probability2
| .. | = absolute value or ‘modulus’
1 - Suffice to say, explaining what natural logarithm is would be worthy of a series of articles. For the time being, use Excel to calculate this for you.
2 - For winning streak calculations use the positive value (i.e. the probability of winning). For losing streak calculations use the negative probability value. For example, if the probability to win the bet is 33% then the probability that the bet loses (negative probability) is 67%.
If you want a formula for Excel or Google Sheets it would be:
"p" = needs to be expressed as percentage value between 0-1, so (percentage / 100). ie. 60% = 0.60, 5% = 0.05
You can see it in action here: https://docs.google.com/spreadsheets/d/1T7k5KVUwB606rfyrCrfZNTs8xyVyF7C-0PLlIPzaU8o