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So, a couple of unmentioned points, from someone who teaches statistics.

First, the original comment that stripping Marines of their armor save raises the uncertainty of the result is not surprising.

If you fix the number of shots/attacks, the highest variance will occur when the probability of an attack coverting to an unsaved wound is exactly 50%. The further that probability is from 50%, the lower the variance.

Second, while the range of likely values gets larger with more attacks, the probability of being far from the expected value in percentage terms gets smaller. So you are more likely to see double or half the average result with say 5 attacks than with 50, which is probably more pertinent in an actual game.

 Jancoran wrote:


Thats really not the case. Without calculating them you can intuit that they are against you but even failing that, it doesn't ACTUALLY matter whether they favor you or not. The trick is STILL to tilt the odds increasingly in your favor. So perhaps in list building you will need to know what the units do comparatively, But functionality happens on the battlefield and the good Generals are the ones who limit the enemies access to weakness and maximize the enemies vulnerability to strengths.

So knowing the odds doesn't hurt but frankly once the game start there isn't anything you can do about it. At that point, you must do as i suggested: tilt them.

I think knowing each unit's odds of success in the situations and choices that present themselves in-game will still help you make better decisions. It does matter if they favour you if you're trying to decide, for example, if your shots would be wasted or better used elsewhere. You need to know your odds to know which way or how far to tilt.


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 MrEconomics wrote:

Second, while the range of likely values gets larger with more attacks, the probability of being far from the expected value in percentage terms gets smaller. So you are more likely to see double or half the average result with say 5 attacks than with 50, which is probably more pertinent in an actual game.

Agh! Just when I thought I had my head wrapped around it! Would you mind illustrating with an example?

Look up on binomial approximation to the normal curve, the famous bell curve.

The more results you have, the smoother the curve will be., as more results will hit the average.

Basically you have less chance of getting an exact average with more dice, but you have a greater chance of getting 'in the ball park'. Those outlier rolls you get have a much smaller effect overall. When you're rolling 30 dice 2 1's don't matter. When you're chucking 6 they do.

Farseer Anath'lan wrote:
Basically you have less chance of getting an exact average with more dice, but you have a greater chance of getting 'in the ball park'. Those outlier rolls you get have a much smaller effect overall. When you're rolling 30 dice 2 1's don't matter. When you're chucking 6 they do.

Yes, that seems to make sense as with a single dice roll, you can only have one outcome, whereas with a million dice rolls, you would get roughly equal proportions of each of the 6 possible outcomes.

 pocketcanoe wrote:

 Jancoran wrote:


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 MrEconomics wrote:

Second, while the range of likely values gets larger with more attacks, the probability of being far from the expected value in percentage terms gets smaller. So you are more likely to see double or half the average result with say 5 attacks than with 50, which is probably more pertinent in an actual game.

Agh! Just when I thought I had my head wrapped around it! Would you mind illustrating with an example?

Sure.

Suppose you take 4 WS4 S4 Power Sword attacks against Marines. Your probability of getting an unsaved wound from an attack is .25, so you average 1 kill. Using the binomial distribution with n = 4 and p = .25, the probability of getting exactly 2 kills (which is double your average result) is 21.1%.

Now suppose you take 40 WS4 S4 Power Sword attacks against Marines. You now obviously average 10 kills. Using the binomial distribution again but with n = 40 and = .25, the probability of getting 20 kills (again, double the average result) is about 0.04%.

If you're concerned about the fact that all exact numbers are more rare with 40 attacks than 4 (because there are so many possibilities), note that the probability of 2 or more kills with 4 attacks is 26.2%, while the probability of 20 or more kills with 40 attacks is 0.06%.

If you're wondering why this is the case, it's because the average number of kills is proportional to the number of attacks (double attacks, double average kills), while the standard deviation of the number killed is proportional to the square root of the number of attacks (double attacks, increase the standard deviation of number killed by roughly 41.4%).


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nosferatu1001 wrote:
Look up on binomial approximation to the normal curve, the famous bell curve.

The more results you have, the smoother the curve will be., as more results will hit the average.

This isn't why. The approximation works better with a bigger sample size, but the result is also true if you use the actual binomial distribution and don't approximate it.

Sure.

Suppose you take 4 WS4 S4 Power Sword attacks against Marines. Your probability of getting an unsaved wound from an attack is .25, so you average 1 kill. Using the binomial distribution with n = 4 and p = .25, the probability of getting exactly 2 kills (which is double your average result) is 21.1%.

Now suppose you take 40 WS4 S4 Power Sword attacks against Marines. You now obviously average 10 kills. Using the binomial distribution again but with n = 40 and = .25, the probability of getting 20 kills (again, double the average result) is about 0.04%.

If you're concerned about the fact that all exact numbers are more rare with 40 attacks than 4 (because there are so many possibilities), note that the probability of 2 or more kills with 4 attacks is 26.2%, while the probability of 20 or more kills with 40 attacks is 0.06%.

If you're wondering why this is the case, it's because the average number of kills is proportional to the number of attacks (double attacks, double average kills), while the standard deviation of the number killed is proportional to the square root of the number of attacks (double attacks, increase the standard deviation of number killed by roughly 41.4%).

Great, Thanks! That makes it much clearer.

 pocketcanoe wrote:

 Jancoran wrote:


Thats really not the case. Without calculating them you can intuit that they are against you but even failing that, it doesn't ACTUALLY matter whether they favor you or not. The trick is STILL to tilt the odds increasingly in your favor. So perhaps in list building you will need to know what the units do comparatively, But functionality happens on the battlefield and the good Generals are the ones who limit the enemies access to weakness and maximize the enemies vulnerability to strengths.

So knowing the odds doesn't hurt but frankly once the game start there isn't anything you can do about it. At that point, you must do as i suggested: tilt them.

I think knowing each unit's odds of success in the situations and choices that present themselves in-game will still help you make better decisions. It does matter if they favour you if you're trying to decide, for example, if your shots would be wasted or better used elsewhere. You need to know your odds to know which way or how far to tilt.


Automatically Appended Next Post:

 MrEconomics wrote:

Second, while the range of likely values gets larger with more attacks, the probability of being far from the expected value in percentage terms gets smaller. So you are more likely to see double or half the average result with say 5 attacks than with 50, which is probably more pertinent in an actual game.

Agh! Just when I thought I had my head wrapped around it! Would you mind illustrating with an example?

Understand what i am saying. I am not telling you NOT to educate yourself. What Im telling you is that the current situation is what it is. Thats an immutable truth. It IS. so given the situation you are in from round to round, knowing what the odds COULD HAVE BEEN if something is ALLOWED to do its thing is fine, but finer yet is the General who disallows.

 Jancoran wrote:


Understand what i am saying. I am not telling you NOT to educate yourself. What Im telling you is that the current situation is what it is. Thats an immutable truth. It IS. so given the situation you are in from round to round, knowing what the odds COULD HAVE BEEN if something is ALLOWED to do its thing is fine, but finer yet is the General who disallows.

I agree with you that the ability to get their opponent to make mistakes and avoid good moves is critical.

However, many players, even good ones, make mistakes that could be described as "first-order'. That is, they are not mistakes because they failed to anticipate the opponent's reaction, or failed to induce the opponent to do something suboptimal, but because they expend resources (movement, shooting or assaults) in suboptimal ways.

A good lesson from playing poker is that, while you ultimately need to have your opponents make mistakes if you want to be a winner, it is very possible to be good at outplaying your opponents (that is, doing better with the cards you have than you should), and still be a loser. Why? Maybe because some of your opponents play better, but usually it is because you play too many hands. Bad-playing opponents make most hands more profitable, but most hands don't improve by enough to make a positive profit. A quote from a poker book about an anonymous losing player: "The guy plays great, but I don't think he wins. He plays too many hands."

The 40k equivalent of my poker example is shooting at the wrong target. And in at least some cases, intuition may not guide you to what is best. Therefore, a serious player can certainly benefit from doing a little formal statistical analysis.