Balancing stock market risk and reward

Good work setting up all this testing for your game. I am assuming that these numbers represent the average earnings for each player. If this is true the major concern that I would have is that, a small percentage of high earners are skewing your average of smart concentrated. To put it another way, when it works, it works really well, but most of the time it doesn't work. (As a concrete example 1/5 times this strategy earns 40,000 but the rest of the time it earns close to 0.) This would have two potential ramifications on game play. One is this strategy would have a lower winning percentage. Second if it it is working really well it would maybe unsurmountable by the other players, well before the the game should be over. Can you look at the number of wins for each strategy?

Good luck with your game.

I see you have different Players with different Investment Strategies and then the result of those strategies in comparison with EACH OTHER. But I would propose that "something" is missing...

What I mean is that while the AMOUNTS are reasonable, the PERIOD for these amounts is just as important and missing.

Like Johnny Smart concentrated got the HIGHEST AMOUNT (8434.502). But what concerns me most is the TIME for this amount to be accumulated. See while Johnny Smart diversified got 6877.638 which is lower than the other strategy, what is of more importance is how many TURNS or TIME (Days, Months, Years) was this amount accumulated. If it's 5 Days ... Well then that's maybe a bit worrisome because it doesn't feel NATURAL even for Day Traders who spend all their time buying low and selling high.

But if these amount are like over 2 Months or 60 Days ... Well then those amounts seem more REASONABLE and could work in terms of the game (IMHO).

I know you say this is the average over 10,000 games... So those are END-GAME results averaged out??? It still doesn't tell me what the PERIOD of play is and how further apart the scores will be if there are LONGER or SHORTER games (in some kind of duration/time).

Now my critique in terms of the RESULTS you offer and propose.

Diversified portfolios tend to average out better and over a PERIOD of time (that's what is missing TBH) offer better returns. Concentrated portfolios can win big SOMETIMES and underperform MOST OF THE TIME. It depends on the nature of the investments also. Clearly if this is like Mutual Funds the Energy Funds are more risky but sometimes you can do better (not like I ever made any of my monies doing this...) The idea is that on AVERAGE a fund has diversified shares in various assets performs more AVERAGE too.

So I don't think the game is broken.

I think Concentration usually leads to a higher pay-off, let's say Energy Stocks (for example) which are higher risk tend to pay-off more if there is no recession or some other form of lack luster performance.

BUT... If that were the CASE, everyone would buy into Energy Stocks and that type of investment would become super saturated AND THEN ... The AVERAGE return with regards to profitability would DECREASE...

That's another ASPECT: HOW SATURATED is the market for a type of stock.

The more people buy, the less everyone gets generally speaking. Sure some of the stocks hold some of their value, some may even increase... But I would say that when this happens people with NON-COMMON shares in those companies or stocks would sell some of their PRIVILIEGED shares in order to transform shares into ACTUAL EARNINGS. And at that point in time, the value of the stock will obviously decrease and that's how everyone in the common share pool make LESS monies.

Anyways... I don't get the impression that the game is broken. I think it's spot on. But I would suggest PERIODS/TIME and MARKET SATURATION to further AFFECT the efficiency of trading stocks.

Add those two (2) variables into your game and maybe you can simulate the market a bit more accurately knowing how "reasonable" the earnings are with the overall PERIOD/TIME and figure out SATURATION (could be tougher than TIME) and see how insider trading could influence stocks that INCREASE TOO MUCH... Because then we all know people on the Board of Directors would definitely SELL some of their shares to gain more monies and the overall VALUE of the shares will then on average GO DOWN for most people investing in the stock.

Those are my thoughts. Cheers!

The "Standard Deviation" along with the Average. Why? Because the Average just tells us which AI Player ON AVERAGE does in the Trading of stocks. The "Standard Deviation" tells use the LOWS and HIGHS for each AVERAGE.

So if "Johnny Smart concentrated 8434.502" has a deviation of let's say 1500.00 that means that when you plot the graph "8434.502" is the point and +/- 1500.00 means that the AI Player gets 6934.502 (on the LOW) and 9934.503 (on the HIGH).

Again WHY(?) is this important... You may be wondering. Let me continue with more data and then it will become more apparent to what I am reaching for...

Next if "Johnny Smart diversified 6877.638" has a deviation of 2000.00 that means that his deviation is 4877.638 (on the LOW) and "8877.638" (on the HIGH).

Okay where am I going with all of this...?

Well if concentrated does RELATIVE POOR (7200.00) and diversified does RELATIVELY GOOD (8000.00)... You see that the DIVERSIFIED portfolio does BETTER than the CONCENTRATED one...!

I think this is the INFORMATION you are MISSING to get a better understand on the performance of the various portfolio and investment strategies: their Standard Deviation!

This will reveal how EFFECTIVE the strategies are... PLUS they will show if some of the performances of SOME of the portfolios are more COMPETETIVE that just whatever the AVERAGE is telling you.

Best.

Note #1: Here's what I mean in a RUDIMENTARY way in this sample graph I put together in Paintshop Pro.

And then you can SEE if your game is "broken" or not. What do I mean??? Well if the game doesn't allow the diversified AI players to be within REACH of the the concentrated AI players (in deviation), well then MAYBE(?) you might have an issue. This will be the ultimate "litmus" test to see if the game allows players to encroach and have a good vs. bad game and not always the AVERAGE.

That's something else. How GOOD or how BAD you get as results will also help determine how playable the AI Players are in comparison to each other and also it can help determine how a PLAYER (Human) can possibly stack up to the AI opponents.

Note #2: I know that looks like a primitive graph (and it is) but it conveys one important issue:

Is a BAD concentrated Game within REACH of an AVERAGE diversified Game?

That is the KEY to that graph (the take-away that is important)...

Note #3: Also the other take-away is if the "Low diversified" at 5695.8193 is within reachable range of the Smart Opponents... That also is something to check (again by determining the Standard Deviation).

P.S.: I would really like if you could SHARE with US the results of this exercise (determining the STD DEV) and plotting a graph (similar to my own...) but maybe from Excel or something (screenshot) whatever works. It doesn't need to be FANCY ... Just showing the differences between each AI player.

Note #4: I'm not saying my "sample" graph is realistic or not ... Actually if the results are close to this... Then maybe the game is NOT broken. By my own analysis the Random AI Player scores the lowest but has a higher Standard Deviation. Therefore that AI Player is near the bottom and the Standard Deviation is sufficiently "high" enough to reach the BAD of the "Smart Concentrated" AI Player (lowest or lower range).

So my graph isn't the worst possible outcome and is a sample of a reasonably FAIR game in that the Random player can have a HIGH Standard Deviation (Positive) and be within reach of the lower-end of the Smart Concentrated AI Player. That's MY sample Graph... Still YOURS may look different and may NOT be broken also.

Cheers!

The reason I ask... Because it means that the scores are WILDLY "different". And because of this... I feel like the computation may be incorrect. In mean if the average is 5696.03 and the SD is 3897.52 indicates that the game scores are fluctuating a LOT. Which makes me wonder if the correct MATH was applied to compute the SD.

Here's an example with 5 values:

Mean is 73.0, SD is 26.86

Explanation:

Data set : {82, 44, 67, 52, 120}

Mean is the average of Data set:

M = 82 + 44 + 67 + 52 + 120 = 365 / 5 = 73.0

Standard deviation is square root of variance (σ^2), SD = √(σ^2)

Variance is The average of the squared differences from the Mean.

σ^2 = ((82 − 73)^2 + (44 − 73)^2 + (67 − 73)^2 + 
       (52 − 73)^2 + (120 − 73)^2) / 5

or

σ^2 = (81 + 841 + 36 + 441 + 2209) / 5 = (3608 / 5) = 721.6

SD = √(σ^2) = √721.6 ~= 26.86

Mean is 73.0, standard deviation is 26.86 [Ans]

Please make sure you keep an eye on practical balance.

Thus if the players know that a certain strategy will never result in what they need. Then that strategy is never going to be used.
And thus, a strategy that has 0% chance in succeeding, needs a buff until it does.

Then again, you are only doing this for the ai. Right?

What is your goal?
Do you want each strategy to be roughly giving the same chance to win?
Or do you want each strategy to have at least a, for example, 5% winchance?

In regards to chances to win.
Of course you could try to get close to equal chances. It will be hard. Then again, you always have the same starting conditions, right? But seeing as how you have more than 2 strategies here. I suggest you slowly adjust the lowest victory chance. Eventually, another will be lowest.
Do this until you are switching between 4 out of the 5. Once the 5th is the lowest, ypu can decide to keep that, or make 1 or 2 steps backwards.
I think you can get it between 15 and 25 percent.

Of course, combining strategies will yield better results for the player. But this is something you only look at for fun. And only this really depends on the fortune after a strategy.

High risk high reward is a great start for a low risk strategy afterwards. After all, once you are position 1. You want to keep it and not gamble away.