Is it possible to win ALL battles WITHOUT losing any point from ALL of your VIPs and without using the store?

I am beginning to think that this is mathematically not possible.

For example, for Level 11, I counted the number of "turns" it takes for the monsters to amount an attack for Wave 1, Wave 2, and Wave 3. The number of turns needed for the monsters to attack is far less than the number of turns necessary for you to trade up your army to be strong enough to wipe out the entire enemy wave before it attacks. The only way to get around this is if somehow, by chance, you get many (and many) tiles of upgraded units (not the lowest units) so that you can trade up to high powered units quickly. However, if the majority of the units you get is the lowest unit, it is mathematically not possible for you to upgrade fast enough to eliminate ALL of the waves without any monster from any wave firing at least one shot at your VIP.

Can the developer comment on this? Is the battle winnable this way?

I am beginning to think that this is mathematically not possible.

For example, for Level 11, I counted the number of "turns" it takes for the monsters to amount an attack for Wave 1, Wave 2, and Wave 3. The number of turns needed for the monsters to attack is far less than the number of turns necessary for you to trade up your army to be strong enough to wipe out the entire enemy wave before it attacks. The only way to get around this is if somehow, by chance, you get many (and many) tiles of upgraded units (not the lowest units) so that you can trade up to high powered units quickly. However, if the majority of the units you get is the lowest unit, it is mathematically not possible for you to upgrade fast enough to eliminate ALL of the waves without any monster from any wave firing at least one shot at your VIP.

Can the developer comment on this? Is the battle winnable this way?