Greed or risk, I think that it depends on the mindset and financial strength of the gambler, because what you're worrying about for him might be his adrenaline to keep going in the game. Some people are natural risk takers, they'll want to finish the game no matter the outcome, it doesn't matter to them if they lost, so far they won't lose more than the amount used to place the bet. While others will cash out, out of fear of losing everything, i believe that most reasonable gamblers will fall into this category. Another category are those that very rich, they don't care if they will lose the bet, and cashing out is not an option for them, they're just in it for the thrill.
Personally I'll cash out if given the opportunity to do so, because if i don't and eventually lose the bet, I'd be very heartbroken and blame myself for being greedy. This is probably because I'm not rich, if I'm rich and lose a bet, it'll likely be risk for me.
Greed once enters, a gambler for sure will always put the winnings he gets at risk because greediness pushes him to continue playing gambling in the casino, which is why he always ends up losing.
This happens all the time with gamblers. Now, there are others who may not have this greed in the meantime, but there is a risk that they take when they gamble, and that is that they are willing to beat their partner no matter how much it is, right?
Greed has become the starting point for a more painful end, they, especially gambling addicts, have felt and proven it themselves, it is quite painful but the problem is that their expectations are much higher than the reality that always befalls them (even successive defeats). That is why they are still greedy even though it is clear that the final result is more often a defeat than the results they always expect. Even though they basically got a win at the end of the gambling session, I wouldn't say it was a real win because obviously in that condition they will bring their greed like you said, and instead of getting a much bigger win but the opposite happens.
It's a cycle of addiction that will always be involved with greed at some level, and whether or not a gambler will be greedy depends on the level of involvement of the person in the gambling, usually greed will always play a role in someone who has entered the addiction phase. I don't believe they can control themselves if they are in a state of competing in a bet with anyone including their own partner, because when your adrenaline is pumping then maybe you will not think and consider how much risk you have to take.