Gamble or stumble is a state of dilemma. To gamble is to take a decision to take the risk of winning or loosing. It takes a bold step to venture in such act. On the other way round, to stumble could mean to lose balance, to be uncertain and could be risky. It could also mean to get something by chance or to achieve something unexpectedly. Gambling is an adventure into taking a decision to excel or to fail out. Gambling and stumbling are activities of inherent risk which the victim becomes a looser or a winner. The game of football is a venture to gamble or to stumble. Friends, kindly react.
Based on your distinction between gamble and stumble, I will tell you that they mean the same thing. Every gambler is a risk taker because it is known that you may not win, and if you do not win, you will lose your money. This is what you call stumble.
Gambling, as we all know, is not certain. It is not predictable. You never know when you will win, which is why most gamblers are constantly gambling because they believe they may be walking around lucky without knowing it, so they gamble regardless of the uncertainty. This is what you call stumble.
To me, there is no distinction between gamble and stumble. In fact, stumble as you described is simply the nature of gamble.