I still make a chart or table to establish some kind of pattern for my formulas or equations.
consider consecutive losses
first bet = 3
total losses = 3
second bet = 6
total losses = 9
third bet = 12
total losses = 9+12 = 21
looks like a geometric series where
a = 3, r = 2 and we want to know Sum(n) < 300
Sum(n) = a(rn - 1)/(r - 1)
300 = 3(2^n - 1)/(2-1)
2^n - 1 = 100
2^n = 101
n = log 101/log2 = 6.65
So after 6 losses she lost 3(2^6 - 1)/2-1) = 189
after 7 losses she lost 3(2^7 - 1)/2-1) = 381
she can play 6 times in a row, expecting to lose each time , running out on the 7th turn.
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