We can argue about this all we want. Until the rules are changed, you'll be required to deal damage cards properly in any match where there's a TO doing their job.

No question, it's in the rules. While I agree with Zlashie's overall premise, I don't think it's necessary to go back and change the rule. I just think that the rule irrelevant and unobserved.

I hope TOs have better things to do with their time than make sure people are laying down the proper amount of cards. But, you're a TO - do you enforce this? Not to my recollection anyway.

Everyone in our group plays by this rule (dealing All damage cards) even in casual games.

I absolutely enforce it when I am the TO of an event if it comes to my attention that someone is not doing it.

Jim

Dealing facedown damage cards that will never get flipped faceup is equivalent to "burning" cards in Poker.

In Texas hold 'em (as well as in Omaha hold 'em), a card is burned (ie: discarded, dealt facedown) before the flop, before the turn, and before the river.

If you do a Google search to know if this affects the odds at all, the response is overwhelmingly clear. Here's a sampling:

• No. So long as the burn cards are unknown and the shuffle is truly random they have no effect what-so-ever.
• No. The probabilities do not change in any card gave by burning cards.
• No, those cards have no significance to odds calculation.
• No effect whatsoever.
• The number of cards burned and/or dealt have zero affect on your odds.

I invite your to Google it and read through the results until you find an explanation that you find appropriate.

That is a) not entirely true and b) not the same. The arguments most people trot out is that it doesn't matter because the card is somewhere on the table. While it doesn't matter from the gambler's perspective, it changes the cards from which future random events occur (the cards all players are dealt). You are essentially removing one card from the possible cards in which you could be dealt; while you or any other player cannot perceive the distribution, it still changes. So instead of every card being 1/52 chance, it's 1/51 or 0, however you cannot perceive which it is, that's why people make that argument.

However, in X-Wing, if you do not draw the extra damage cards, it is not the same as the burn card because the undrawn damage card is not on the table and can still be drawn.

I don't think this argument is productive anymore. Follow the rules or be called out.

I just tried this in a match and... it's not as cool as I thought it would be. I was very optimistic to begin with but now I think I will just ignore flipping the cards faceup and just get on with it. There's already enough thoughts in my head when playing X-wing

It's in the rules, so if asked by my opponent I would gladly flip 'em faceup. I just don't think I'm going to do it if not asked.

Of course, if any of the cards are revealed, it gives you more information and therefore changes the probabilities.

Technically speaking, your awareness doesn't change the probability at all.

That is a) not entirely true and b) not the same. The arguments most people trot out is that it doesn't matter because the card is somewhere on the table. While it doesn't matter from the gambler's perspective, it changes the cards from which future random events occur (the cards all players are dealt). You are essentially removing one card from the possible cards in which you could be dealt; while you or any other player cannot perceive the distribution, it still changes. So instead of every card being 1/52 chance, it's 1/51 or 0, however you cannot perceive which it is, that's why people make that argument.

However, in X-Wing, if you do not draw the extra damage cards, it is not the same as the burn card because the undrawn damage card is not on the table and can still be drawn.

I don't think this argument is productive anymore. Follow the rules or be called out.

This is plain wrong.

No matter how many cards I discard off the top of a standard, complete, shuffled deck of cards, the probability that the next card I draw is the Ace of Spades is 1/52.

Probabilities depend on available information. If you don't have any new information, the odds, from you point of view, do not change.

"So instead of every card being 1/52 chance, it's 1/51 or 0"

Each card's probability has a 1/52 chance of falling to 0, and 51/52 chance of rising to 1/51.

And, miraculously: 1/52 * 0 + 51/52 * 1/51 = 1/52

"You are essentially removing one card from the possible cards in which you could be dealt; while you or any other player cannot perceive the distribution, it still changes."

No, the distribution does not change. It only changes if you know what has been discarded.

There's a whole concept in probability theory that deals with probabilities of an event occurring, given that another even has occured.

It's called conditional probability.

I dare you to try it. Write a program that does the following, run it a few thousand times, and look at the distribution:

• Shuffle a standard deck of cards
• Discard 10 cards
• Draw the next card

The distribution is flat. Each and every card has the same probability of turning up.

So, if I were to do the following:

Instead of drawing the top card off a full damage deck, discard all cards except one. Then, draw that card.

You would argue that:

Even though you don't know what cards were just discarded, the distribution just changed.

The probabilities of what your top card is is no longer 7/33 for a Direct Hit, it's actually now either has a probability of 0 or 1 of being a Direct Hit.

Would you also argue that, if I buy a scratch off lottery ticket, my chance of wining are not 1 / X thousand, but they are either 1 or 0?

I mean whether I know or not what's under the scratch-off-coating doesn't change the fact that I'm either going to win or lose, right?

Of course, if any of the cards are revealed, it gives you more information and therefore changes the probabilities.

Technically speaking, your awareness doesn't change the probability at all.

Would you also argue that, if you buy a scratch off lottery ticket, your chance of wining is not 1 / X thousand, but they are either 1 or 0?

I mean "technically speaking, your awareness doesn't change the probability at all", right?

Seriously, what difference is there between the "discarded facedown damage cards" problem, and the "scratch off lottery ticket" problem?

If anyone wants to have some fun with weird probabilities, try on the Monty Hall Problem for size:

"Seriously, what difference is there between the "discarded facedown damage cards" problem, and the "scratch off lottery ticket" problem?"

Of course, if any of the cards are revealed, it gives you more information and therefore changes the probabilities.

Technically speaking, your awareness doesn't change the probability at all.

Would you also argue that, if you buy a scratch off lottery ticket, your chance of wining is not 1 / X thousand, but they are either 1 or 0?

I mean "technically speaking, your awareness doesn't change the probability at all", right?

Seriously, what difference is there between the "discarded facedown damage cards" problem, and the "scratch off lottery ticket" problem?

But the really new thing here (the rule that almost nobody uses) is that we are not talking about facedown damage cards. The rules state that we flip all damage cards faceup when a ship dies - so that by end-game we have a lot of knowledge about what could possibly be left in the damage deck. If we know that 6 out of 7 Direct Hit cards are out of the damage deck (lying in a faceup discard pile) and there are 14 cards left in the damage deck we have a much lower probability of drawing that last Direct Hit -> 1/14 chance/risk of a Direct Hit.

edit: clarity

But the really new thing here (the rule that almost nobody uses) is that we are not talking about facedown damage cards. The rules state that we flip all damage cards faceup when a ship dies - so that by end-game we have a lot of knowledge about what could possibly be left in the damage deck. If we know that 6 out of 7 Direct Hit cards are out of the damage deck (lying in a faceup discard pile) and there are 14 cards left in the damage deck we have a much lower probability of drawing that last Direct Hit -> 1/14 chance/risk of a Direct Hit.

When we flip them over, do we flip them one at a time (thus being able to see and count them all, if we have that presence of mind, or are they flipped over in a pack and thus we only get to see one of the damage cards?

And then, even if we do get to see all the cards, and even if we do have a Rain Man level of awareness of those cards, how much advantage does it really give us?

But the really new thing here (the rule that almost nobody uses) is that we are not talking about facedown damage cards. The rules state that we flip all damage cards faceup when a ship dies - so that by end-game we have a lot of knowledge about what could possibly be left in the damage deck. If we know that 6 out of 7 Direct Hit cards are out of the damage deck (lying in a faceup discard pile) and there are 14 cards left in the damage deck we have a much lower probability of drawing that last Direct Hit -> 1/14 chance/risk of a Direct Hit.

And then, even if we do get to see all the cards, and even if we do have a Rain Man level of awareness of those cards, how much advantage does it really give us?

While I'm not going to argue it's a big deal, but do really think you need to be "Rain Man" to figure out at least probabilities in a deck of 33 cards? There's 2 of each card except for direct hit (7), and there are 8 pilot and 25 ship cards. It's not that tough if your wondering the chances of a direct hit, a particular card, or a type of card.

First. I'm going to ignore the strawman arguments. Next, I'm not sure if you're implying this is a Monty Hall problem, but I don't believe it is. I think it's a form of a hypergeometric distribution. It lacks most of the properties of a Monty Hall problem, such as a priori of any kind (especially if they are not dealt face up), choice, and Monty. I've even opened up a StackExchange question to see what other mathematicians think:

http://math.stackexchange.com/questions/1193086/unknown-card-monty-hall

Second, whether you see the cards or not has no bearing on what the card is or it's distribution.

Third, it doesn't really matter if you lack the capacity or interest to track the information. It's in the rules and I expect myself and my opponents to follow them.

That's the last I will say on this.

Of course, if any of the cards are revealed, it gives you more information and therefore changes the probabilities.

Technically speaking, your awareness doesn't change the probability at all.

Would you also argue that, if you buy a scratch off lottery ticket, your chance of wining is not 1 / X thousand, but they are either 1 or 0?

I mean "technically speaking, your awareness doesn't change the probability at all", right?

Seriously, what difference is there between the "discarded facedown damage cards" problem, and the "scratch off lottery ticket" problem?

But the really new thing here (the rule that almost nobody uses) is that we are not talking about facedown damage cards. The rules state that we flip all damage cards faceup when a ship dies - so that by end-game we have a lot of knowledge about what could possibly be left in the damage deck. If we know that 6 out of 7 Direct Hit cards are out of the damage deck (lying in a faceup discard pile) and there are 14 cards left in the damage deck we have a much lower probability of drawing that last Direct Hit -> 1/14 chance/risk of a Direct Hit.

edit: clarity

The discussion you're quoting is referring to cases where the cards are not flipped face up. It was mentioned in multiple previous comments which you apparently did not read: "As long as none of the cards are revealed", "Dealing facedown damage cards that will never get flipped faceup".

As long as the cards remain facedown, they have no impact on the probabilities of what the next card will be.

As soon as you flip them faceup, they affect the probabilities.

If this seems unintuitive to you, see it like this:

• You're about to flip 10 coins.
• What are the odds you'll get 10 heads? Answer: 1 / 2^10
• Now, you've flipped the 10 coins but I'm hiding the results from you.
• What are the odds you'll got 10 heads? Answer: 1 / 2^10
• Ok, now I show you 5 of the coins. They're 5 heads.
• What are the odds you got 10 heads? Answer: 1 / 2^5

I get that unflipped cards don't affect probability. The discussion here is how flipping dealt cards of dead ships affect gameplay. Or more specifically, how high level players can use this information to better judge the probability of getting a certain crit card.

This will have no effect in the early game when no cards (or very few) cards have been flipped but for late game (when loads of cards have been flipped) you should be able to count Direct Hits and now your risk/chances better.

First. I'm going to ignore the strawman arguments. Next, I'm not sure if you're implying this is a Monty Hall problem, but I don't believe it is. I think it's a form of a hypergeometric distribution. It lacks most of the properties of a Monty Hall problem, such as a priori of any kind (especially if they are not dealt face up), choice, and Monty. I've even opened up a StackExchange question to see what other mathematicians think:

http://math.stackexchange.com/questions/1193086/unknown-card-monty-hall

Second, whether you see the cards or not has no bearing on what the card is or it's distribution.

Third, it doesn't really matter if you lack the capacity or interest to track the information. It's in the rules and I expect myself and my opponents to follow them.

That's the last I will say on this.

No, I did not mean to compare this to the Monty Hall problem. It isn't a Monty Hall problem.

The answer on StackExchange that references Hypergeometric Distributions was under the assumption that the distribution of cards in the deck is unknown.

How would you respond to this series of questions?

I somehow doubt that this'll be enough to convince you, but oh well, at least I've tried.

I get that unflipped cards don't affect probability. The discussion here is how flipping dealt cards of dead ships affect gameplay.

I 100% agree that, if the cards are going to be flipped face up they need to be dealt out since it will give information to the players and could, if only situationaly, have an impact on gameplay.

That said, you should read some of s1n's posts... He's been arguing for a few posts now that cards that have been discarded face down somehow affect the probability of what the next card you draw will be.

Here are some quotes from s1n's posts so you don't have to go back and read them... (emphasis mine)

"If you choose not to draw those cards, whether you see them or not, you have altered the stocastic distribution. The chance of any one card is altered, whether you perceive that distribution or only part of it."

"You are essentially removing one card from the possible cards in which you could be dealt; while you or any other player cannot perceive the distribution, it still changes. So instead of every card being 1/52 chance, it's 1/51 or 0, however you cannot perceive which it is, that's why people make that argument."

"whether you see the cards or not has no bearing on what the card is or it's distribution."

Because it's in the rules:

From page 10 of Core Rule book: 7. Deal Damage: If the defender was hit, it loses shield tokens or receives Damage cards based on the damage it suffers.

I get that unflipped cards don't affect probability. The discussion here is how flipping dealt cards of dead ships affect gameplay.

I 100% agree that, if the cards are going to be flipped face up they need to be dealt out since it will give information to the players and could, if only situationaly, have an impact on gameplay.

That said, you should read some of s1n's posts... He's been arguing for a few posts now that cards that have been discarded face down somehow affect the probability of what the next card you draw will be.

Here are some quotes from s1n's posts so you don't have to go back and read them... (emphasis mine)

"If you choose not to draw those cards, whether you see them or not, you have altered the stocastic distribution. The chance of any one card is altered, whether you perceive that distribution or only part of it."

"You are essentially removing one card from the possible cards in which you could be dealt; while you or any other player cannot perceive the distribution, it still changes. So instead of every card being 1/52 chance, it's 1/51 or 0, however you cannot perceive which it is, that's why people make that argument."

"whether you see the cards or not has no bearing on what the card is or it's distribution."

This is why I hate the fact that people use statistics as an argument.

Statistical analysis is only right when you do one thing: Measure many outcomes.

let me draw an example: Have you ever played Settlers of Catan? A Maxwellian distribution of two dice says that 7 has the highest probability.

What the analysis of maxwellian distribution does not take into account is few rolls. When you are doing 2 or 3 rolls, yes you are more likely to get a total of 7 but this is only information you know once you have done enough rolls to see the outcome.

If you are doing only one roll with two dice, you are equally likely to get any number. This may strike you odd, especially since the statistics tell you that this is bulls**t. But dice have physical properties. When you roll them, they will bounce according to Newtons Laws, and they will eventually come to rest. Neither does the dice nor the laws of physics know about Maxwellian distributions, so any outcome is likely.

This is exactly what you see when you play Settlers of Catan. If you collect information on a 1000 games of Catan, yes you will get a maxwellian distribution for your dice, but if you only collect data from 1 game of Settlers of catan, it will most likely not be maxwellian in form.

Infact it is possible to play Settlers of Catan a thousand times and not having a single game with a smooth maxwellian distribution, whilst the total is still a smooth maxwellian distribution!

This is the same case with a stacked set of cards in a specific distribution. They are physically stacked. Yes, probabilities do change (as S1n mentions, and it even does so when removing face down cards, the difference is that you do not know the probability changes, but it does occur.), but this is only something you can know when you have done the deed many times. For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you.

I am not arguing against you, just giving my opinion. Statistics is a worthy tool, but many forget that statistics are strong with large amounts of data and very VERY misleading with only a few pieces of information (such as saying any function is a straight line only by drawing two coordinates on your graph.)

This is why I hate the fact that people use statistics as an argument.

Statistical analysis is only right when you do one thing: Measure many outcomes.

let me draw an example: Have you ever played Settlers of Catan? A Maxwellian distribution of two dice says that 7 has the highest probability.

What the analysis of maxwellian distribution does not take into account is few rolls. When you are doing 2 or 3 rolls, yes you are more likely to get a total of 7 but this is only information you know once you have done enough rolls to see the outcome.

If you are doing only one roll with two dice, you are equally likely to get any number. This may strike you odd, especially since the statistics tell you that this is bulls**t. But dice have physical properties. When you roll them, they will bounce according to Newtons Laws, and they will eventually come to rest. Neither does the dice nor the laws of physics know about Maxwellian distributions, so any outcome is likely.

This is exactly what you see when you play Settlers of Catan. If you collect information on a 1000 games of Catan, yes you will get a maxwellian distribution for your dice, but if you only collect data from 1 game of Settlers of catan, it will most likely not be maxwellian in form.

This is the same case with a stacked set of cards in a specific distribution. They are physically stacked. Yes, probabilities do change (as S1n mentions, and it even does so when removing face down cards, the difference is that you do not know the probability changes, but it does occur.), but this is only something you can know when you have done the deed many times. For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you.

I am not arguing against you, just giving my opinion. Statistics is a worthy tool, but many forget that statistics are strong with large amounts of data and very VERY misleading with only a few pieces of information (such as saying any function is a straight line only by drawing two coordinates on your graph.)

Statistics and Probabilities are 2 different things. A nice way to put it...

If you have a jar of red and green jelly beans:

• A probabilist starts by knowing the proportion of each and asks the probability of drawing a red jelly bean.
• A statistician infers the proportion of red jelly beans by sampling from the jar.

When you are rolling dice and drawing cards, probabilities are what's important since you know the distribution of cards in the deck and the faces on the dice.

"If you are doing only one roll with two dice, you are equally likely to get any number."

Not really. If you consider the sum of both dice, there is a ~16.6% chance you'll get a sum of 7 and only a ~2.7% chance you'll get a sum of 2.

If you consider each die individually, you are equally likely to get 6 on die A and 6 on die B as you are likely to get 2 on die A and 5 on die B.

"For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you."

Yes, of course the deck is shuffled at the beginning and not the order of the cards is fixed.

This doesn't mean that discarding cards face down somehow affects the probability that the next card you draw is card X.

If I shuffle a standard deck of cards, am I more likely to draw the 7 of Hearts if I take the card on top of the deck, or if I discard 6 cards first?

This is why I hate the fact that people use statistics as an argument.

Statistical analysis is only right when you do one thing: Measure many outcomes.

let me draw an example: Have you ever played Settlers of Catan? A Maxwellian distribution of two dice says that 7 has the highest probability.

What the analysis of maxwellian distribution does not take into account is few rolls. When you are doing 2 or 3 rolls, yes you are more likely to get a total of 7 but this is only information you know once you have done enough rolls to see the outcome.

If you are doing only one roll with two dice, you are equally likely to get any number. This may strike you odd, especially since the statistics tell you that this is bulls**t. But dice have physical properties. When you roll them, they will bounce according to Newtons Laws, and they will eventually come to rest. Neither does the dice nor the laws of physics know about Maxwellian distributions, so any outcome is likely.

This is exactly what you see when you play Settlers of Catan. If you collect information on a 1000 games of Catan, yes you will get a maxwellian distribution for your dice, but if you only collect data from 1 game of Settlers of catan, it will most likely not be maxwellian in form.

This is the same case with a stacked set of cards in a specific distribution. They are physically stacked. Yes, probabilities do change (as S1n mentions, and it even does so when removing face down cards, the difference is that you do not know the probability changes, but it does occur.), but this is only something you can know when you have done the deed many times. For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you.

I am not arguing against you, just giving my opinion. Statistics is a worthy tool, but many forget that statistics are strong with large amounts of data and very VERY misleading with only a few pieces of information (such as saying any function is a straight line only by drawing two coordinates on your graph.)

Statistics and Probabilities are 2 different things. A nice way to put it...

If you have a jar of red and green jelly beans:

• A probabilist starts by knowing the proportion of each and asks the probability of drawing a red jelly bean.
• A statistician infers the proportion of red jelly beans by sampling from the jar.

When you are rolling dice and drawing cards, probabilities are what's important since you know the distribution of cards in the deck and the faces on the dice.

"If you are doing only one roll with two dice, you are equally likely to get any number."

Not really. If you consider the sum of both dice, there is a ~16.6% chance you'll get a sum of 7 and only a ~2.7% chance you'll get a sum of 2.

If you consider each die individually, you are equally likely to get 6 on die A and 6 on die B as you are likely to get 2 on die A and 5 on die B.

"For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you."

Yes, of course the deck is shuffled at the beginning and not the order of the cards is fixed.

This doesn't mean that discarding cards face down somehow affects the probability that the next card you draw is card X.

If I shuffle a standard deck of cards, am I more likely to draw the 7 of Hearts if I take the card on top of the deck, or if I discard 6 cards first?

Not really. If you consider the sum of both dice, there is a ~16.6% chance you'll get a sum of 7 and only a ~2.7% chance you'll get a sum of 2.

If you consider each die individually, you are equally likely to get 6 on die A and 6 on die B as you are likely to get 2 on die A and 5 on die B.

You have to think outside of probabilities. That is why Settlers of Catan is such a great example. Yes, you are more likely to have a specific outcome, but this outcome is completely irrelevant until you have done enough experiments to settle it.

The best example is for you to take two dice and roll em three times right now. Statistics tell you that you will most likely roll a 6, 7 or 8. In fact, if the probabilities somehow were information gathered in your dice, the best outcome to secure the theory is for you to roll exactly 7 then 6 and/or 8. However, this is not what we see in the world.

Let me explain. When you put water on a heater, you expect it to raise in temperature and eventually boil, right? The reason for this is the same thing. Particles of higher energy (READ higher temperature) are more likely to give energy to particles with lower energy than they are of receiving. The effect this has is that the cold water on the hot stove exchange energy until the water has reached enough energy to boil. The distribution in which this happens is a Maxwellian distribution too. What is remarkable for particles is that, if there werent trillions of particles in about any macroscopic object you can hold in your hand, you could have scenarios were a stove could freeze water or a refrigerator will burn your food.

This is the same thing, and it is why probability is so very devious. Yes, I agree that the sum of the dice will yield probabilities as you mentioned, but as I told you, the dice does not know of probabilities. Everything it knows is that when you roll your dice, any number may appear, and it is only when you have done enough rolls that it becomes apparent.

It is the exact same strategy poker players use to have consistent income in the game. Instead of going for high stakes that have high probabilities of them winning, they play many smaller games were the loss and wins arent as devastating. In a million dollar game, even with 60% chance of success, there is still a 40% chance of failing and all it takes is one wrong turn. But, when you play a thousand games, you WILL have an even distribution and thus 60% chance of success reads 100% chance of success over time compared to what you started with.

If I shuffle a standard deck of cards, am I more likely to draw the 7 of Hearts if I take the card on top of the deck, or if I discard 6 cards first?

Two scenarios exist. Either you are more likely to draw 7 of hearts, or your chances are zero. Even if you did not look on the top 6 cards.

This is because probabilities change regardless of whether or not you know it does. When removing 6 cards from the pool, you are left with a smaller total and thus the probabilities increase except for the case where you drew the card you want in the first 6 top cards. Again, poker!

But remember that these probabilities are irrelevant if you only try it once.

Totally shocked that this thread is still going on and it hasn't devolved into pilot gender wars or a Lancer wish list.

The original poster hasn't even replied in over 69 posts.

The answer is simple:

• If it's casual play, it doesn't matter.
• If it's tournament play, it is required.

This is why I hate the fact that people use statistics as an argument.

Statistical analysis is only right when you do one thing: Measure many outcomes.

let me draw an example: Have you ever played Settlers of Catan? A Maxwellian distribution of two dice says that 7 has the highest probability.

What the analysis of maxwellian distribution does not take into account is few rolls. When you are doing 2 or 3 rolls, yes you are more likely to get a total of 7 but this is only information you know once you have done enough rolls to see the outcome.If you are doing only one roll with two dice, you are equally likely to get any number. This may strike you odd, especially since the statistics tell you that this is bulls**t. But dice have physical properties. When you roll them, they will bounce according to Newtons Laws, and they will eventually come to rest. Neither does the dice nor the laws of physics know about Maxwellian distributions, so any outcome is likely.

This is exactly what you see when you play Settlers of Catan. If you collect information on a 1000 games of Catan, yes you will get a maxwellian distribution for your dice, but if you only collect data from 1 game of Settlers of catan, it will most likely not be maxwellian in form.

This is the same case with a stacked set of cards in a specific distribution. They are physically stacked. Yes, probabilities do change (as S1n mentions, and it even does so when removing face down cards, the difference is that you do not know the probability changes, but it does occur.), but this is only something you can know when you have done the deed many times. For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you.

I am not arguing against you, just giving my opinion. Statistics is a worthy tool, but many forget that statistics are strong with large amounts of data and very VERY misleading with only a few pieces of information (such as saying any function is a straight line only by drawing two coordinates on your graph.)

Statistics and Probabilities are 2 different things. A nice way to put it...

If you have a jar of red and green jelly beans:

• A probabilist starts by knowing the proportion of each and asks the probability of drawing a red jelly bean.
• A statistician infers the proportion of red jelly beans by sampling from the jar.

When you are rolling dice and drawing cards, probabilities are what's important since you know the distribution of cards in the deck and the faces on the dice.

"If you are doing only one roll with two dice, you are equally likely to get any number."

Not really. If you consider the sum of both dice, there is a ~16.6% chance you'll get a sum of 7 and only a ~2.7% chance you'll get a sum of 2.

If you consider each die individually, you are equally likely to get 6 on die A and 6 on die B as you are likely to get 2 on die A and 5 on die B.

"For the individual game itself, the distribution is locked and nothing changes and you cannot know how the probabilities affect you."

Yes, of course the deck is shuffled at the beginning and not the order of the cards is fixed.

This doesn't mean that discarding cards face down somehow affects the probability that the next card you draw is card X.

If I shuffle a standard deck of cards, am I more likely to draw the 7 of Hearts if I take the card on top of the deck, or if I discard 6 cards first?

[...]

Your whole argument that "probabilities are irrelevant if you only try it once" is wrong. Statistics are irrelevant if you only try an experiment once.

But we KNOW the distribution that results from rolling a pair of dice. We HAVE done enough experiments to "settle it".

Similarly, we KNOW the distribution of a damage deck. We don't need to shuffle the deck, draw the top card and repeat the experiment thousands of times to figure out that, by golly, there's a 7/33 chance that I'll draw a Direct Hit!

I agree that you cannot draw statistically significant conclusions based on a small sample size. But that is totally besides the point here - we aren't doing statistics to try and figure out the distribution, we KNOW the distribution and we are looking at the probabilities that come with that distribution.

I have 33 damage cards at the start of play. My TIE gets obliterated by a Range 1 Yahtzee shot from a Phantom as I roll no evades. I deal out 5 damage cards and place them faceup in the discard pile.

I'm no mathematician, but even without seeing which cards are now out of play, I understand that the remaining 28 cards is a different pool of possibilities than the 33 I started off with, when it comes to which critical hit effects my ships might suffer later in the game. It doesn't matter if I know what the odds are or if I can make use of that information. The game state has changed somewhat. Convince me that it hasn't.

In poker, the essence of the game is to judge probability and act upon it. Is my hand strong enough to warrant a 32% chance of getting the straight on the fifth card?

"It gives high-level player better information": Except for lists containing Rexlar Brath, it does not grant any "better information", because you cannot use that information in any way. Rexlar Brath is one out of many pilots and I would argue that the rule is more of a annoyance than it is for making Rexlar Brath stronger (and stronger I mean slightly better when you count the probability in your head and spend 4min pondering whether or not it is a good idea to spend your focus token when there is x% chance of drawing a [insert Damage Card you are looking for here]). Is the Rexlar Brath combo with this irrelevant rule necessary for the flow of the game? No it is not, and I would argue that a 0point Defender title could be added which says "Action: You may look at the top 5 cards of the damage deck", which would grant a much better flow of the game than having to draw and discard a whole lot of cards for no particular reason other than "it says so in the rules".

Sorry, but I am still not convinced that this rule should be a rule.

Calculation is an EPT that allows anyone to spend a focus to change a single eyeball to a crit. IG88 can equip both a Heavy Laser cannon, which can't crit, and a Mangler cannon which will always crit if it hits, simultaneously.

You may not be able to keep track of what every single damage card flipped face up was, but there are people who can. Just like there are people who can look at a ship on the table, and predict every single possible ending location for it because they know its dial, its actions, and the results of all of those combinations even with Advanced Sensors. The people who can do both of these things are the people who blow up 100 points of ships while only fielding 86*, 5 times in a row, and walk out of the store with the champion plaque.

Edit: Typo

In a similar vein, the rules tell us to deal facedown damage cards before dealing faceup damage cards. If you do this out of order, you're arbitrarily tampering with the way the game is supposed to be played. Your opponent has every right to make you flip them back over in the proper sequence -- and should.

I think it's sheer laziness to ignore the rules here.

There is a common house rule that you can use a placeholder (1 straight or 2 straight template) in order to measure or move through ships. Strictly speaking, that's against the rules. You're supposed to hold your template above the ships and eyeball the final position. But in this case, the house rule is usually better than the rules as written. But it isn't lazy.