Risk in finance and in board games

I find it endlessly fascinating how risk is treated differently in finance, and in board games.

In finance, investments with higher risk usually also have higher average payoffs.  This indicates that risk has negative value which offsets the higher payoffs.  This makes sense, because after all, we like our security.  If you want to mitigate your risk, you can buy insurance, but note that insurance has a negative average payoff; insurance companies still need to make money.

In board games, risk may have positive value.  For the record, I'm thinking of the game I play most often, Dominion, but it works for any board game that has a blend of chance and decision-making, and which has an ongoing score to keep track of who is winning.  That's because in a board game, you don't really care about your average score.  You care about your likelihood of winning.

In a game, if you take a big risk and lose big, then all that happens is you lose until the next game.  If you take a risk and win big, then you beat out your opponent and win the game.  Flipping a coin to determine whether you win or not doesn't seem like a good deal at first, because at most it gives you even chances.  But the key point is that if you are already behind in the game, then you had less than even chances to begin with.

If you're losing, risk has positive value because it evens out your chances.  If you're winning, risk has negative value also because it evens out your chances.

If you're already winning, you want to play conservatively, and you might even sacrifice some of your average score to play safer (just like in finance).  If you're already losing, you want to play riskily, and you might even sacrifice some of your average score to increase your risk.

There is a slight complication that many people often care about their average score rather than their win percentage.  Even if you lost the game, having a higher score indicates that it was a "close game".  And if you have a very low score, that might indicate that you played poorly, not that you took a big risk and happened to lose.  So even in a board game, what counts as "good play" can be subjective, as some people value high scores while other people value winning.

Tying back to finance, for some one-percenters, it's not the money that matters (since they already have enough to live well), but how much status and power they have relative to other elites.  So perhaps there is also a realm in finance where "winning" is what matters the most.