Bankroll Tracker and Analytics

The Bankroll Tracker and Analytics page is a two-output ledger: ROI and average P&L per session. Three inputs: Starting Bankroll (default $1000), Current Bankroll (default $1150), Sessions (default 20). ROI = (current − start) / start × 100 = 150/1000 = 15.00%. Avg per Session = (current − start) / sessions = 150/20 = $7.50. That is the entire model: a percent on starting capital and a per-session mean of the same $150 delta.

The $1150 current versus $1000 start is a +15% stretch. It does not know whether you deposited $200 in the middle (which would make true ROI lower on a time-weighted basis) or withdrew $50 (which would make the $1150 an understatement of performance). There is no cash-flow field. Type a start and current that live on the same funding basis, or the 15.00% is a vanity percent.

Sessions = 20 turns $150 into $7.50 a session. If a “session” is a night, that is $7.50 a night on a $1000 roll — 0.75% of start per session. If a session is a month, it is a different story. The denominator is whatever you counted. Raising sessions to 50 without changing the delta drops the average to $3.00; the ROI stays 15.00% because ROI does not use sessions. That split is useful: ROI is the total trip, average is the pace.

Negative current: start $1000, current $850, 20 sessions → ROI −15.00%, avg −$7.50. Zero sessions is blocked (min 1). Start is min 0.01 to avoid a divide by zero on ROI. Current can be 0: ROI −100%, avg = −1000/sessions.

This is not a time-weighted return, not an IRR, not a Sharpe ratio, not a max-drawdown. It will not replace a spreadsheet of daily marks. It will convert two bankroll snapshots and a session count into the 15.00% and $7.50 the defaults advertise, so a “I’m up” claim has a denominator.

Bankroll tracking is bookkeeping before it is analytics. Professional players keep a ledger: date, game, start, end, notes. ROI (return on investment) in this toy is the simplest definition, (W_T − W_0)/W_0, the total return on the opening pile. Fund managers would demand time-weighted returns so that a mid-period deposit does not look like skill. SorteCalc’s three-field form cannot do that. It exists for a snapshot: I started at $1000, I now have $1150, I did that over 20 sessions, what percent and what average?

The $7.50 average is not a robust location statistic. One $200 night and nineteen $−2.63 nights still average $7.50 if the total is $150. Median session, standard deviation, and max drawdown are the numbers that tell you if the 15% was a smooth grind or a spike. They need a series. This page has two points and a count. Mason Malmuth’s bankroll chapters and every poker-site graphing tool assume a series. Use those when you have the CSV.

Why include it among calculators? Because people quote “I’m up 15%” without saying from what, and “I win $7.50 a session” without saying how many sessions and whether the last one was a $400 outlier. Putting both outputs on one screen forces the division. The 20-session default is a month of weekend play, a common recreational window — short for inference, long enough to feel like a track record.

Limits: two wealth points, equal session weights, no deposits/withdrawals, no risk adjustment, no game mix. A 15% ROI on 20 sessions of $10 slots is not comparable to 15% on 20 sessions of $1000/hand baccarat; the tracker never sees the unit size. Pair with the Bankroll Safety Analyzer (units) and Expected Loss (edge × handle) to see whether +15% is a miracle against a 2.7% wheel or a plausible sports sample.

Educational close: 15.00% and $7.50 are (1150−1000)/1000 and (1150−1000)/20. If that is your ledger, you are up $150. If your memory of “sessions” is fuzzy, the $7.50 is fuzzy. Thorp’s quip about measurement before mysticism applies to a bankroll graph as much as to a count.

Return on a pile of capital is a total-return identity, not a trading model. Subtract the starting bankroll from the current bankroll to obtain the dollar delta, divide that delta by the start, and scale to a percent. Average result per session is the same delta divided by the session count. The teaching defaults are a start of 1,000 dollars, a current mark of 1,150 dollars, and twenty sessions. Delta is 150 dollars. Return is 15.00 percent. Average per session is 7.50 dollars. Both outputs share the numerator; only the denominators differ.

Simple return is not an annualised return. Annualisation would need elapsed time. Time-weighted return would chain subperiod returns between cash flows so that a mid-period deposit does not masquerade as skill. Logarithmic return of 1,150 over 1,000 is about 0.1398, or 13.98 log points, versus 15 percent simple; the identity uses simple. Dietz and the fund-accounting literature exist precisely because two wealth points plus a count cannot see a reload.

A deposit of 500 dollars after the start, with a current mark of 1,150, still prints 15.00 percent on 1,000 even if the true pile had become 1,500 and then fallen. The formula cannot see the cash flow. That is the main algebraic caveat. Raising sessions to fifty without changing the delta drops the average to 3.00 dollars while the percent stays 15.00, because the percent never uses the session count. Start 2,000 and current 2,300 over twenty sessions reprint 15.00 percent with a 15.00 dollar average: same trip, different pace.

Negatives and zeros are the same two divisions. Start 1,000, current 1,000, twenty sessions: 0.00 percent and 0.00 dollars. Start 1,000, current 0, ten sessions: minus 100.00 percent and minus 100.00 dollars. Start 1,000, current 850, twenty sessions: minus 15.00 percent and minus 7.50 dollars. One 200 dollar night and nineteen small losers can still average 7.50 dollars if the total is 150; the average is not a robust location statistic. Median, drawdown, and scatter need a series this identity does not have.

Assumptions: start and current live on the same funding basis, sessions are equally weighted, and the only denominator for the percent is the opening pile. Over twenty sessions a sum of uncorrelated session results has variance twenty times the session variance; 150 dollars is one realisation. A test against a zero mean would need that scatter, which is absent. Measurement before mysticism, as Thorp put it, applies to a bankroll graph as much as to a count.