But on the other hand, I perfectly understand why the gambler possibly took this bet, he probably thought it was a sure game, so making a quick $11k dollars was the goal for him, but unfortunately, seems he forgot that regardless of how small a game odd is, the chances of the gambler winning is still less than 50 percent.
I agree with all you said except the last part. The chances of winning varies depends on the odds. In this case, since the odds are 1.01 then the chance of winning is more than 99% (which is, obviously, higher than 50%).
The 1.01 strategy is very common where gamblers try to make small wins with the lowest risk possible. In order to make a significant profit, you need to place many bets. This case proves that this strategy doesn't work.