Try the following Strategy: Buy at Market (yep that's it).
Convert to code.
Change BuyAtMarket(bar +1) to BuyAtMarket(bar).
Under Preferences, clear the "Apply Commissions ..." box and clear the "Apply Div ..." box.
In Portfolio mode, click "Percent of Equity" and enter 100%

Now we are buying on the first bar and holding forever with no div and no commissions using all the equity. I think this should be the same thing as buy and hold. Now click "Equity Curve" Tab. The green equity curve should match the blue Buy and Hold Tab. It never does. Why?

I do notice that the BuyAtMarket executes a whole number of shares (not fractional shares) Therefore the green equity curve always shows some unused cash. It looks like the difference between the Blue Buy and Hold and the green 100% Equity Curve is too big to be explained away with the fractional share problem.

How does WL calculate the Blue Buy and Hold line on the Equity Curve?

QUOTE:
The green equity curve should match the blue Buy and Hold Tab. It never does.

I would say "It does" and stay right but will not do it, because to quote Alexandre Dumas, "All generalizations are dangerous, even this one".

For a single symbol backtest using 100% equity sizing, if you started the main (trading) loop from bar 0 (and not on bar #20 as in default Strategy template), unchecked all the trading costs options in Wealth-Lab's Preferences, the result of this test will most likely be a 100% match of the B&H figure (provided that the capital is enough to buy 1 share of the instrument).

However, in a multi-symbol backtest comes to play a very important concept (that explains why it "never does"): dropped trades. One dropped trade and the Strategy equity can no longer match Buy & Hold. Check out the Wealth-Lab User Guide: Strategy Window > Backtesting Strategies > 100% of Equity Sizing > "How can this Cause Dropped Trades?"

"There are two types of programs: mine and the correct ones" Ish Kabibble

Tried it. Works. Problem solved. Thank you