Is there an actual "answer" to this question?
I gave some more thought to this deceptively simple but fascinating question of 100% chance of 25k vs. 50% chance of 100k. Statistics would tell us that, over the course of enough trials, taking the 50% risk for 100k would be twice as rewarding as it would be to play it safe.
For the sake of example, let's say that 4 friends decide to band together, promising that whatever they earn collectively, they would split equally. Now, let's start with the playing it safe strategy. That means they're all going to go home with 25k each.
However, if they all choose to risk for 100k, statistically, 2 out of those 4 friends will win 100k. They then divide the winnings and each would then go home with 50k.
Of course, 4 trials is extremely low so the results can vary drastically. However, the more trials are applied, the more the sampling will even out. When that happens, it definitely pays to risk it all.
Alternatively, smaller groups can "diversify" to compromise between risk and gain. For example, half agree to risk it all while the other half agree to play it safe. In that same example of 4 friends, 2 of them play it safe and bring in 50k, while the other two risk it all. Given the 50% of success, let's say one of them wins and brings an additional 100k, bringing the total to 150k. Divide that by 4, and you have 37.5k of winning each.
Hmm. Actually, if this was a group strategy, I would have everybody risk it all. Diversifying makes sense in many scenarios, but not in this case.
Taking all this in, I'm going to revise my answer and mirror jmjj's response. If it's a scenario on winning, I would risk it, but in the scenario of taking a loss, I would play it safe. But then, we are talking about comparing an all gain, no loss scenario versus an all loss, no gain scenario.
Now, if group strategies were somehow forbidden, then I would say it's up to individual preferences.
Finally, if there is an "answer" to this, or any other insights, please share it already! I must know!
