I think you are right with your calculations. The chance of losing 16 times in a row is 0.21^16.
The biggest issue is not your odds as mentioned before, but the max bet that is into place in any gambling house to protect the house.
This system may have a chance though, as losing 5 times in a row already has tiny odds: 0.0004 or 0.04%
That is not correct in online gambling houses which uses different softwares for monitoring the bets and predicting the outcomes, known as provably fair through MD5 hash function. I have been trying the same bet on crypto-games to check how many times I would lose in a row and surprisingly was 29 times in a row before I won a bet. I kept a 50-50 chance when trying or 2x.
He's only talking about chances of losing 16 times if you think the calculation isn't correct then could you give us the correct answer here? I know you could lose more than that. Last weekend I tried betting with 98% win chance just to increase my stats and after 100 rolls I had 6 losses overall with 2 consecutive losses(chances of this happening is 0.04%).