Statistically thats only true if the players are betting flat bets, whenever you start using a so called ''strategy'' you risk to lose everything easily. You dont need the casino to have infinite funds just put a max bet limit (shouldnt be too big at first) After you make some profit you can start increasing the limit a little bit.
Assuming that you have lots of players that each bet at variable sizes, then with 0% house edge, the house should expect to make nothing.
if you have players betting at max limit, over the long run, you still expect to be even.
If you have players that use martingale, over the long run, you'll expect to have players that win streaks that last until max bet, and you'll have players that lose streaks until max bet.
As the house, you might even get unlucky as some people do reverse martingale on you and win until the max bet.
In the end, as the house, you still expect to make 0 profits at 0% house edge. NO MATTER HOW THE PLAYERS BET.
Thats not how it works, players betting with martingale, say starting with 0.01, the casino having a 1 BTC max bet. You can bet 7 times in a row without reaching the max bet (The chances of loosing 7 times in a row at 50% are 0.78125 % or 1 in 128, meaning that every 128 bets the player expects to lose their max bet and expects to win 64 bets since thats the average martingale sequence. The math is simple, if you win 64 bets, 64 x 0.01 = 0.64, when you bust you are loosing, 0.01 + 0.02 + 0.04 + 0.08 + 0.16 + 0.32 + 0.64 = 1.27 bitcoins meaning a profit of -0.63 each time you are using martingale.