Written by the TreasureGuide for the exclusive use of the Treasure Beaches Report.
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Game theory is an interdisciplinary approach that draws heavily from psychology and statistics. I'll only introduce a few things about it, and you can follow up on those topics on your own if you want to.
I talked before about the different types of errors you can make when deciding to dig or not dig a target. You might remember me mentioning false positives (thinking a signal is good when it turns out to be trash), and false negatives (a good target that you do not dig). You might also remember how that applies to Covid testing. Again, there are false positives and false negatives. In both cases you could apply decision theory to improve the decision making process.
As detectorists, like with the sciences, we operate with a lot of uncertainty. We can accumulate data, and most of us do that intuitively and informally, but if you apply the science you will become more aware of the errors you might be making and therefore how you might want to adjust your decision making. I've done posts in the past on the math of metal detecting which explores that kind of thing.
Here are some interesting questions that will help you think about your own decision making process.
1. Would you prefer to take 10 cents or a one in ten chance of getting one dollar.
2. Take $1 or a one in ten chance of getting $10.
3. Take $10 or a one in ten chance of getting $100.
4. Take $100 or a one in ten chance of getting $1000.
5. Take $1000 or a one in then chance of getting $10,000.
6. Take one million dollars or a one in ten chance of getting ten million dollars.
Psychologists have learned quite a bit about how people make decisions like this. It is very likely, for example, that you would gamble on a ten percent chance of getting a $100 rather than taking the certain $1, for example. The risk, or cost, of the gamble is so low as to be relatively unimportant, while the possible reward, is significant enough, even though there is only a ten percent chance, to make most people willing to give up the dollar.
Translate that to digging a signal. If you are a dig-everything kind of person, you feel the possible reward could be good enough to be worth digging. You consider things like the time and effort involved in digging, the possible frustration of coming up with another piece of junk and the possibility of getting something good. You place your own value on each of those things. To some people digging a piece of junk is no big deal, while to others it is a pain. As I've explained before, one thing you can gain from digging a piece of junk is information. It can add to your knowledge of what kind of things might be there. That information can change your estimates of the probabilities and change your decision making process. If it is junk, you might be less likely to dig the next borderline signal, but if it is good, you might be more likely to dig the next borderline signal. The information you gather can help you to change your sense of the type of targets that exist in the area, and if you are using that information, that can change your decision making process.
Going back to the questions - people will tend to turn down the certain reward for a chance on a bigger reward, but for most rational people, there is a point at which they will take the certain reward rather than a chance on the bigger reward. Unless you are a real risk taker or are very wealthy, you would probably take a sure million rather than a 10% chance of getting ten million. The richer you are, the more willing you will be to gamble for higher stakes. Your own decision process will depend upon your own situation and view of the world. You will make better decisions when your internal model of the world is more accurate.
Some kinds of targets require a certain type of person. If you don't have much patience or risk-tolerance, that will affect your hunting style.
Some detectorists start out with visions of gold hoards in their head. That is OK, if you can keep at it for what is likely to take a long time to achieve. If you enjoy the process or are able to make other finds that keep you motivated while searching for the big one, that will help you keep going. People who do not simply enjoy the activity of metal detecting will probably give up the hobby before long if they don't have some short term success.
Different people make decisions differently. They have their own operating characteristics. There are people who are adverse to risk, for example, while there are other people will take a lot of risk and go to great lengths to pursue a large payout even if it there is a low probability success.
Metal detecting involves dealing with a lot of uncertainty. You never find out what you missed. You don't have complete information of the situation. That is one reason I often like to check myself. You might think you did well even though you missed the really good treasures by inches or feet.
You are working with a lot of unknowns, but you can model situations and think about different decision strategies and the possible outcomes. People do that informally to some extent, but you can sample areas, quantify things, and construct your own probabilistic models. You probably do that intuitively to some extent, but you can quantify things and gain a better understanding of the likely effect of different decisions.
Are you a person that wants to find something every time you go metal detecting and get very discouraged when you hunt for hours with nothing to show for it? If so, you might not be the type of person to set your sites on a low-probability long-term hunt even if the payout could be big. Not everyone is optimistic enough to hunt for many years for a wreck like the Atocha. They simply do not have the optimism of a Mel Fisher. It didn't hurt, of course, that he found plenty of other treasure before finding the Atocha. You can express that in terms of reinforcement or reward. Some level of success is necessary to keep most people going. Some people need more frequent rewards than others, and some people need larger rewards than others to continue the search. Know yourself and set your goals accordingly.
Here are just a couple of the decision strategies that psychologists have identified. There is the strategy that theorists and academics call the minimax. The minimax strategy is a strategy that minimizes the maximum negative outcome. This strategy would be chosen by people that will not take gambles. They want to minimize the worst possible outcome. If you translate that to the lottery, they rather spend a small amount (little to lose) even if they have a small chance of winning. They want to limit their losses.
Another strategy would be the maximax strategy, which would be used by people who are aggressive and willing to take big risks for big rewards. They are willing to take a long shot if there is a chance of a big reward.
There are a variety additional of different strategies, but I hope you get the idea from those two.
If you want to be more aware of how you make decisions and learn to make decisions more effectively, you might want to study game theory and decision theory. I know I didn't do a great job of presenting this, but I wanted to introduce a few topics to give those of you who want to pursue it, some direction. It is a huge topic and I only had a few minutes to introduce it, even though I have referred to it a little from time to time in the past.
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You know how they say one man's trash is another man's treasure. I think the following is more accurate. One man's treasure is his wife's trash.