Understanding currency triangulation

I'm trying to learn how 3 currencies that are related between them work together in forex. I made some simple calculations as an example, and although the results seem to be okay on paper, it doesn't reflect on the markets as I thought. This is my example:

I'm working with 3 related pairs:

1. EURUSD with a price of 1.13486
2. EURGBP with a price of 0.71442
3. GBPUSD with a price of 1.58744

Now suppose I have the following trade:

1. Trade 1: BUY 0.07 EURUSD, which means BUY 7000 EUR and SELL 7944.02 USD

I want to decompose that trade in two different trades:

1. Trade 2: BUY 0.07 EURGBP, which means BUY 7000 EUR and SELL 5000.94 GBP
2. Trade 3: BUY 0.05 GBPUSD, which means BUY 5000 GBP and SELL 7937.20 USD

As you see the combined overall outcome of trades 2 and 3 should be almost exactly the same as the outcome of trade 1, because the GBP operations cancel each other (one buys, the other sells).

However, I have tried this live with a demo account, opening at the same time trades 1, 2, and 3, and the combined profit/loss of trades 2 and 3 does NOT equal the profit/loss of trade 1. I have also tested it with some historical values (1 hour candle) and again the results are not even close.

So can anybody guess what is wrong in my analysis?

Your analysis looks correct for this toy example. How different are your results from a live demo test? Is it due to extra trade costs for executing the 2 pairs instead of the 1 pair?

A note of caution regarding applying this analysis using historical values, particularly if you export data from MT4. MT4 doesn't include "blank" candles. So it is very easy for two series to be out of line if you export data and compare just the prices side by side. This makes doing this sort of analysis with the historical data a real pain. You have to create fake bars to fill in the missing data for the different symbols so you can get all the dates/times to line up. If you don't, you can mistakenly assume you have large price discrepancies in the triangular structure when there are no discrepancies of any bankable magnitude.

Actually it seems that the example is in fact correct in practice also. For some reason my previous attempts to verify it failed but I just tried with a new demo test and it's working. As you mention there's some difference due to the extra cost and inexact synchronization, but the difference is less than 2%. So thanks a lot for your confirmation FXEZ, as I was unsure if my analysis was correct.