Case analysis: the arithmetic of retail option buying

A trader buys near-expiry options. Model each trade in R units (1R = premium paid): win $+2.47R$ with probability 0.25, lose $-1.03R$ with probability 0.75 (costs of $0.03R$ are included). The trader risks 5% of capital per trade. (a) Compute the expectancy and the growth rate per trade. How many trades halve the median trader's capital? (b) What is the probability that the trader is ahead after 50 trades? After 200? (c) Relate (a)–(b) to the SEBI FY26 findings in 3.10.4: high loss rates, higher losses with higher turnover relative to capital, and persistence of losses.