"Three bad kinds of randomness, and one good one"

#2
I prefer "near and far" randomness over "input and output" randomness because the terms more closely approximate the meaning and also suggest a continuum. Input and output are typically conceived as discrete things without grey between. Regardless of term selection quibbles, It's really good to examine when information relevant to the player's decision becomes visible to them, so I'm very much a fan of the general idea behind the terms. Very important and useful game design concept. It's good to have more written about that.

On discord we discussed how "uniform" is confusing as it is presented in this article because it also means something in statistics that contradicts its usage in this article. (Thanks to @Kdansky and @tribound for good discussion on that topic.) A bunch of suggestions for replacement terms were made, including @Hopenager 's curated vs. raw randomness and my bag vs. dice randomness.

Some results (memorable to me, at least) of the discussion we had are:
* Basic mechanical distinction can be drawn between random selection with replacement vs. without replacement.
* Randomness can be "past-dependent" in various ways, though the most common way is to pull from a bag without replacement until the bag is empty, then refill it. Hopenager mentioned in his game, BBB, he biases chances towards seeds the player doesn't have in stock at the moment. That's another way of doing past-dependent randomness.
* When you've got a lot of items in the bag, you end up approximating dice randomness pretty closely, and when with dice randomness you have a lot of trials, you end up approximating bag randomness.

@vivafringe suggested a different dimensional analysis of randomness, which is near-far on one axis and impact on the other. Impact is how many or how strongly randomness can erase player decisions.
 

Zera

New member
#3
@evizaer Your third * is especially interesting. But if you took it to the extreme - a bag with 1 item or a dice rolled ∞ times - you'd essentially have determinism. So where is the perfect balance, I wonder?
 
#4
Most of the essay is very similar to what you’ve said before on randomness and I broadly agree. However, I do have minor disagreement.

I haven’t got on the discord, but I have to agree with the sentiment that your terminology is not ideal, I’m afraid. “Input” and “output” just aren’t related words, at least not closely, to your definitions of “input randomness” and “output randomness”, and the linguistic binary distinction is in tension with the fact that - as you know - the two exist on a spectrum. I thought about this long and hard and came up with “propistemic” and “epipistemic”, from the Greek epi, pro, and epistemos. Yes I am a big nerd. My second favourite choice would be “pre-/postinformative”, which is just a Latin equivalent of the former. The concept is really about the time difference between the player being informed about the result of the randomness and the event. The more time before, the more propistemic/preinformative, or in your vocabulary, the more input-y it is. The more time after the event, the more epipistemic/postinformative. “Uniform/Variable” are serviceable, although I personally would opt for “fair/unfair” instead.

I also am very unconvinced by your concept of meaning. Firstly, it is ambiguously defined:
“Keith Burgun” said:
Information in games gets its meaning from its relationship to other aspects of the game state, including the history of game states; but most of all, it gets its meaning from your input.
So is information‘s meaning derived from its significance relating to the unfolding of the game-state? Or is it derived from how closely determined it is by player input? Or what?

But, whatever this concept of meaning is, you also fail to justify why it is desirable.

I agree with your subsequent conclusion, that output/epipistemic randomness is undesirable in strategy games. But I don’t think this concept of “meaning” is necessary. Here is an alternative proof, with which I’m sure you are familiar, since you probably authored it yourself at one time:

Assume that strategy games should tend to involve maximal feedback on player decisions. Feedback is constituted of the facts of the game-state. Epipistemic randomness affects the game-state after the decision and before feedback, while propistemic affects the game-state before the decision. Therefore epipistemic can corrupt feedback, whereas propistemic does not have this flaw.

Similar proof can show that randomness should be as propistemic as possible, not just propistemic to any degree.
 

keithburgun

Administrator
Staff member
#5
Yeah I agree input/output aren't ideal. I originally took them from the Ludology podcast which coined them and I've been working with them for so long at this point I feel like it's less ideal to change it at this point. People are just starting to kinda catch on - Riot did a video a year ago about the difference between input and output randomness - they used those terms! - and I'm quite confident it's because they follow my work, as an example. Ultimately labels for stuff don't matter that much to me.

So is information‘s meaning derived from its significance relating to the unfolding of the game-state? Or is it derived from how closely determined it is by player input? Or what?
I'd kinda say "both" is my answer here. It's the unfolding gamestates as manipulated by the player. Think of it like turn 50 in Go, where you placed each stone yourself. You have a kind of "ownership" over this weird set of shapes you've made. Or building a little town in Sim City, or making a garden. Maybe it's even related to Marx's (and I guess Locke's?) ideas that you own something when you work on it, the products of your labor, you feel like they are "yours". Whereas things you didn't work on and manipulate, are just "some stuff". Does that make sense? Sorry if I didn't do a better job of explaining it in the article.
 
#6
I think the right way to think about feedback is from the player's perspective. The purpose of feedback, from the player's perspective, is to inform them about what they can change to do better. Perfect feedback is the game telling them to do X when Y happens to have a higher chance of winning, or to give them a winning list of moves, or something else that is totally degenerate from a design perspective. As a designer, you want the feedback to be some combination of strong and weak hints at what could be done better. So the quality of the feedback has to be carefully maintained at a player-tantalizingly moderate and suggestive level.

A common flaw in discussions about feedback is that all feedback is treated as if it were occurring on the same level of analysis. "Win" or "loss" is "clear feedback" in the sense that the game is telling you something in no uncertain terms, but the process of disentangling the various factors that led to a win or loss is also aided by feedback on smaller scales. For instance, losing a piece in chess is systemic feedback that you probably failed locally. Double pawns and pieces hanging with no protection in vulnerable areas suggests more medium-term failures of strategic thinking.

Obvious bad things happening is typically feedback that what you did recently was wrong. Randomness instead makes it so sometimes when bad things happen it's a lot harder to tell what decision(s) you made was wrong. Sometimes randomness' influence punishes you when you may have done nothing wrong. The player has to exercise more skill to interpret this feedback. To some extent, this is good. Understanding what went wrong is an important part of growing as a player, and being able to tease apart subtly distinguished threads of causality is something that players should be rewarded for, and well-designed games should give the player an environment where such a display of intellect and systems knowledge is valuable. *BUT* the best way to achieve this is through complex emergent deterministic interactions, not near randomness. Designing complex emergent deterministic interactions is way harder than peppering a game with output randomness, though!

It's critical to remember that players can aggregate feedback. The player can compartmentalize randomness that occurs at a low level (say, rolling dice to hit or for damage numbers). The player can account for other actions *around* the randomness that created a false-positive punishment. Did they move their guy into harm's way when they could've skirted the edge of the enemy's range? Did they leave their guy out of cover to get to the objective one turn earlier? Did they take pot shots at this dangerous enemy last turn instead of grenading them for a certain kill?

This suggests that deterministic (or less-random) actions can act as ballast against the typically noisy feedback provided by a near randomness event like rolling to hit. And that applies all the way up the layers of analysis, from the lowest to highest level of feedback, since they aggregate. A very noisy game like Slay the Spire can have significant skill involved because there is enough deterministic ballast for good players to differentiate themselves from bad players.

The ballast analogy is a little off-putting because it suggests that determinism is discardable. It is not. deterministic actions are the core of the game--the very backbone. You can think of the near randomness as a kind of variation ballast. Too much of it and a game sinks under the weight of all the variation--the player can't keep their head above water through their actions alone and needs a lot of luck. Too little of it and your game floats up to the heavens where all is determined by the creator.
 

keithburgun

Administrator
Staff member
#7
For instance, losing a piece in chess is systemic feedback that you probably failed locally.
Is this actually true / a good way of putting this? Often, losing a chess piece is not a failure of any kind, but a smart spending of a resource. I'm not being pedantic here, my point is that losing a piece is not an "obvious bad thing", and I would go further to say that there probably shouldn't really ever be obvious "locally bad things" in games. Things are only bad when you put them into the larger frame and see how the tradeoffs ultimately (and I do mean ultimately!) worked out.

Anyway I think I agree with what you're saying, but I would strongly reject this idea that the player is looking at the win loss *and then also separately* looking at a bunch of "purely positive/negative things that happened" during the match. The quality of things that happened during the match are informed by that final win/loss state, is my big point. But I might be talking past your point.
 
#8
You're taking what I said more literally than as it was intended. Of course the quality of the player's decisions is on a spectrum. I was using good/bad as a shorthand for like "some amount of positive/negative feedback."

Aggregation doesn't mean "and separately win/loss." The player figures out how to do better by aggregating a bunch of decisions and their results that the player assesses were, to varying degrees, positive or negative at multiple levels of analysis, including (but not limited to) at the trivial low level of "losing a piece", at the mid level of "nice pawn structure", and at the ultimate and highest level of win/loss.

Losing a piece is definitely negative feedback, but a player can of course balance it out by having that be a part of the trade. You can then compare the quality of the pieces involved in the trade and see a differential as a punishment/reward. These are small-scale ways the system indicates to the player how well they're doing--the player most definitely will know better than this simple signposts, they're just the smallest level of feedback, and I was trying to illustrate that feedback comes in at least two layers. I brought up the "you lost a piece! BOO!" level of feedback because it's the same level as hit-chance output randomness.
 
#9
Just to say, in case I have anything to say on this dilemma - I think Keith’s problem with calling losing a pawn negative feedback is because a given move involving losing a pawn isn’t necessarily a bad move in relation to the goal, checkmate the king, which is of course the only inherent systemic “good”. However, although sacrificing a pawn could be beneficial to the goal, this is not because getting rid of a pawn is beneficial. A priori we still know that losing a pawn is bad, because you have fewer tools available as a result with which to checkmate the king. It’s just that in some cases, the beneficial side-effects of the sacrifice can outweigh the loss. E.g. “I may have lost my pawn, but as a result I could move my knight into play!”

So evizaer’s (“incidental”?) feedback is valid, although he may have wrongly implied that it exists independently of the goal (this is why Keith is disagreeing).

Certain non-game-ending changes to the game-state (losing a pawn) are, when regarded a priori, detrimental to the goal, and therefore provide negative feedback; although in particular instances can be beneficial when considered in the context of its wider consequences. I think this should satisfy both Keith and evizaer...
 
#11
Here's some more direct criticism of the article. (Adapted from a discord discussion with Tribound.)

When my guy misses in X-Com, that fact—that he missed instead of hit, or vice versa—has very low systemic meaning. The odds, like the fact that you have an 81% chance to hit, has a bit more systemic meaning in that it is connected to how you trained your guy, where you positioned your guy, what weapon you gave him, and so on. But the fact that he misses or hits itself – that 0 or 1 boolean flag – has no systemic meaning; no relationship to the player at all yet. It just came into existence, and at that same moment, it is affecting the game state permanently.
Here, Keith gives a bunch of ways that the output randomness in XCOM has meaning, then says it doesn't have meaning. At the very least, I think this points to some nuances that I didn't get out of the original statement of the model.

I'm deriving the (perhaps partial) contradiction from this particular expression of "meaning":

These abstract data-bits start to matter to us, and start meaning something, once we’ve had a relationship with them. In interactive entertainment, this means, “once we’ve been able to make a few decisions with this simple abstract data-bit in mind”.
This seems consistent with the fact that the odds above vary based on a bunch of player-controlled factors. As far as I can tell, this is a substantial relationship between player input and numbers sufficient to establish meaning for the result of the output randomness if the game isn't straight up lying to you about the odds. The 0 or 1 does seem to me to have meaning in the context of all those player-controlled factors Keith lists. It lets the player write off their 0 as "damn, bad luck, so I may have done the right thing."

As stated in the article, this doesn't seem to cohere.

Maybe Keith is making the argument that this compression down to a non-deterministic 0 or 1 result is bad, because it effectively erases some input from the player. Not only does the 0 or 1 not capture the nuances of what went into calculating the odds, it additionally has randomness involved which also erases all the work the player did to manipulate the odds. A 0 from a 20% chance is the same as 0 from a 90% chance.

But I don't buy this argument. Players do not evaluate random events in isolation like this. There is certainly some fuzzing of feedback involved, but it seems to me still plenty of meaning if you consider the player is going to roll the dice a bunch of times and each time their odds manipulations will sway things based on their skill. The random variation of output randomness can be largely widdled down by deterministic mechanisms in this way.

Besides, Keith is fine with erasing all the details of what the player did during a match and handing them a 1 or 0 win/loss result instead of a score which may reflect in more detail the effectiveness of their play. So I don't think the "erasing the past" argument is necessarily a strong one alone within his framework.
 
#12
1.

The thing about the input / output randomness distinction is that as a distinction it is agential (based on player psychology) rather than systemic (an actual objective mathematical property of the game system).

In other words, I agree that it "feels" like there is a distinction between input/output randomness, the same way that it feels different to gain 5 points versus take 5 points from your opponent. But mathematically there is no clear distinction.

I will grant that the concept has been helpful to a lot of us as designers, because (a) player psychology does matter and (b) input/output randomness at least gestures in the direction of many systemic properties.

My goal is not to undo the progress earned by applying the terms input/output randomness, but rather to do even better. We can and should be more precise. I think many here would agree that mathematically clear descriptions of systems can be super helpful in the design process. I do not think input/output randomness is mathematically clear, even when viewed as a spectrum. What variable is the spectrum even measuring? What does it even mean for some kind of randomness to be more "input-y" or more "output-y" than another?

This is where I say yet again that "output randomness is just input randomness for the next turn." Keith, I know you have heard this critique a thousand times before and that you do try to address this critique in your article. But I do not find your addressing of the critique satisfactory. I am not failing to see the match as a structure. In fact, it is precisely because I am thinking about the match as a whole that I hold the perspective that I do.

I know you have prescriptive goals here. But speaking purely descriptively for a moment, would you actually deny that each player decision in a random game is necessarily both preceded and followed by randomness?

2.

If we view the match as a whole, then we can see that one useful systemic distinction might be between "early" and "late" randomness. I have used this distinction in my own design and analysis and found it useful.

Early Randomness -- Occurs in the first half of the game, before the majority of player decisions.​
Late Randomness -- Occurs in the second half of the game, after the majority of player decisions.​

And this is just one of many more precise distinctions that input/output randomness only gestures toward. As I said, I don't think input/output randomness is totally unhelpful, and part of the reason it has been a powerful and sticky concept is that it does imply a whole bunch of useful ideas in a general sort of way.

For example another systemic distinction implied by input/output randomness might be the "utility range" of randomness. Utility here is defined as the degree to which something increases the percentage chance of the player winning the match.

Utility Range -- The disparity between the utility of the best random outcome and the worst random outcome.​

In a traditional roll-to-hit situation the disparity of outcomes is big and stark. Hitting is clearly good, missing is clearly bad. In contrast, in a dice placement euro game, the disparity is less stark. A 1 and a 6 are both pretty good. They both can be placed on the board and used to acquire resources. Maybe some resources are better than others, but the difference in utility is not as large.

I think a smaller utility range is another piece of the puzzle that unpacks more precisely what people are complaining about when they say they don't like "output randomness."

Anyway, I could go on proposing distinctions, but I'll stop there.

3.

My main point is that precise systemic descriptions are useful to game designers and we should push to be more rigorous with these things. Input/output randomness does not have a rigorous definition, one that actually means something on the systemic level. As a sort of vague idea cluster, input/output randomness may serve a purpose in pointing us in a fruitful design direction. And as an agential description of the kind of randomness that turns players off it may help us to design better for player experience. But I worry it can potentially be limiting if people treat it as being more precise than it actually is.
 
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#13
I don't find your formalisms to be significantly more precise, while also being less useful, than the input and output distinction.

The midpoint of a game is indeterminate abstractly, and indeterminate at most points in a game. The utility range is *also* indeterminate abstractly in many games. For example, in a dice allocation game, it may not be better abstractly to roll a 1 or a 6, but it may be significantly better for a player situationally, i.e. in a specific match, because they've built their board to gain more utility for 6s than 1s or vice versa. (There is more to explore here, and I think the utility range idea is legitimate. It merits further discussion.)

I think you're missing the point and formal substance of the input/output distinction. There are describable systemic differences between more-input and more-output randomness. You can measure the (usually metaphorical but sometimes literal) distance between what state player actions can effect and what state the randomness effects. Output randomness is very close. For instance, in some vaguely D&Dish game, a hit chance on an attack, or revealing something that might be able to attack you the turn (or next turn after) it appears out of fog of war. Input randomness is further, e.g. an enemy appears at the edge of the map and it's four turns until he can attack you; a randomized symmetric map layout stays constant throughout a match and feeds into decisions throughout, but doesn't favor you or your opponent abstractly while being available for players to review potentially before the match even starts. I can provide more examples and more detailed analyses if desired.

This nature of this substantive and measurable systemic difference is why I chose the terms "near" and "far" over input and output.
 
#14
After Jon Perry put me on a train of thought, I’ve concluded that input/output randomness, or near/far (though I would argue those terms aren’t descriptive, if life wasn’t so short) is not a very useful concept. Really we are concerned about the impact of randomness on win-chance, and Keith has suddenly invented this very shaky concept of “meaning” to justify a belief we don’t really need justified.

For example, Keith, in the article, cites random map generation in Roguelikes or 4X games as a good example of input randomness. But to take the example of Civ, where there is FoW all around, you can send your scout out in any direction to explore any obscured part of the map. Where you explore first is likely to inform your future decisions, for example, about where to settle your next city. But ideally, the map gen distributes resources evenly enough that where you send your scout first doesn’t in itself have a significant impact on overall win-chance.

The FoW somewhere is lifted after you decide to move the scout to that position, so it is “output” randomness. Yet could you have an issue with it? Maybe, if you clearly defined “meaning” and showed how it was ideal. I for one am not convinced! So long as it is meticulously balanced, output randomness can be fair.
 
#15
I'm not convinced about the "meaning" thing at all. I think we can skip it and talk about the validity and usefulness of categories of randomness.

I'm just interested in the near/far randomness thing. Why is it not descriptive? Seems at least solid enough a concept that I can work with it and tell you if one instance of randomness is nearer or further than another.

Win chance is not enough to describe the role of randomness in game design. Randomness when executed well adds variety to gameplay at the cost of diminished player agency. Randomness forces variation from fixed routes the player could predict. This causes each play to be different regardless of player input. Games where important events happen irrespective of player input (or only vaguely involving player input) tend to give the player less of a feeling that they're meaningfully participating--they don't feel like they have much agency in their results in these games.

You can design all kinds of win-chance preserving randomness that make for terrible games. You could, for instance, just roll a d100 and assign win or loss based on if the result is above or below the percentage win chance you desire. It's important that strategy games preserve player agency, thus we care about when information is available to the player and when, with respect to decision points, randomized information is revealed.
 
#16
I'm just interested in the near/far randomness thing. Why is it not descriptive? Seems at least solid enough a concept that I can work with it and tell you if one instance of randomness is nearer or further than another.
I believe input randomness, as Keith describes it, introduces concrete information (that is, factual, and not just odds) to the player before the player uses that information in making a decision that affects the game-state meaningfully in relation to win-chance. Output randomness, however, introduces concrete information to the player after the player has made the decision that will use that information to impact win-chance.

When the player decides to settle their city on a certain tile in Civ, they have made that decision after being introduced to the random tile layout. But when the player decides to order a given unit to shoot in X-Com, they have decided before the information impactful upon win-chance - the hit or the miss - has been introduced to the player.

So input and output randomness can be as near or as far as each other, but they sit on opposite sides of the player decision. 7B85F378-ABD9-4D27-91E4-D91873150D2C.jpeg
This is why I advocate for using preinformative/propistemic vs. postinformative/epipistemic.

Win chance is not enough to describe the role of randomness in game design. Randomness when executed well adds variety to gameplay at the cost of diminished player agency. Randomness forces variation from fixed routes the player could predict. This causes each play to be different regardless of player input. Games where important events happen irrespective of player input (or only vaguely involving player input) tend to give the player less of a feeling that they're meaningfully participating--they don't feel like they have much agency in their results in these games.
I think your starting point, the ultimate reason you value randomness, is that it “forces variation from fixed routes the player could predict” at the cost of “player agency”. But I believe agency, properly defined, is actually tied up with win-chance in such a way to make your argument much the same as mine. Clearly, if there’s an 80% chance to hit, but you still might miss, there is a loss of player agency. The real problem with this kind of randomness is that it impacts win-chance, ie. is unfair. If you got to roll the dice before making a decision, it would still be unfair, and thus there would still be a shortfall of player agency, since the hit or the miss still impacts win-chance independently of player actions.

But where randomness is fair - such as well-balanced map gen - it still takes away player choice - since the player doesn’t get to decide how the map is laid out - but is perfectly acceptable, and does not take away player agency, since it does not impact win-chance independently of player decisions. This is so for input and output randomness.
 
#17
You don't need to have a win condition for people to feel agency (or not feel agency) in a game. Look at Minecraft pre-Ender Dragon, or any number of survival/endless games that are currently trending. For this reason I don't think win chances are a necessary component of this discussion. Some part of win chance is an aggregation of the divergences that randomness causes over the course of a game. These divergences are at least in part echoes of damaged agency, but the substantial part of the actual damage is in the nearer term than win chance captures. Win chance is too far away and nebulous most of the time to be a reasonable alternative to looking at what information is available to the player and what the rules suggest that information means.

An analogy: I'm trying to talk about the physical mechanism of a disease, you're insisting that we spend our time talking about mortality rates.

But where randomness is fair - such as well-balanced map gen - it still takes away player choice - since the player doesn’t get to decide how the map is laid out - but is perfectly acceptable, and does not take away player agency, since it does not impact win-chance independently of player decisions.
Random map generation takes away player choice by determining the subset of viable strategies the player can feasibly pursue in this match. If it does not have this property, the player won't care about it because it doesn't make a practical difference in how the system operates.

Any specific dice roll in an XCOM mission has no impact on win-chance independently of player decisions, since the player gets to deterministically decide much of the context of each dice roll which we'd call output randomness. Dice rolls can often be avoided all together.
 
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keithburgun

Administrator
Staff member
#18
would you actually deny that each player decision in a random game is necessarily both preceded and followed by randomness?
No, of course not. That's impossible to deny. But what's crucial is that with input randomness, in all cases, the random information has had time to be processed by the player before it changes the game state in a permanent sort of way (this is probably something I should talk about more). I don't think of my way of thinking about it as being very "psychological". It's just what I've said before - you want the final outcome to be as accurate a description as possible of the player's understanding of the system. Output randomness, and variable randomness, both sever that. It feels like a very mechanical statement that I'm making, not a psychological one.

Any specific dice roll in an XCOM mission has no impact on win-chance independently of player decisions, since the player gets to deterministically decide much of the context of each dice roll which we'd call output randomness.
I think this is the wrong way to think about it and massively under-estimates the amount of damage that even one dice roll does in an otherwise coherent system.

For example, on turn 10, the player takes a shot with 87% chance to hit, and now misses, which means that next turn the alien can kill him. From that point on, now, the entire match is now tainted by this random information that the player had nothing to do with and could do nothing about. Sure, next turn they could do some entirely non-random stuff like run around or just take point blank shots at 100% accuracy or something, but already the entire state is noise-mangled to the extent that this match is not necessarily a good reflection anymore of the player's understanding of the system.
 
#19
You stated that in a way where you focused entirely on results and not at all on player actions leading up the randomness. Yeah, there's nothing the player can do about the specific one-off event if the dice fall against them, but the game is a whole bunch of such events. Uniform randomness wouldn't protect you against that kind of thing in a one-off situation, either. Good game design, I think, leads to many random trials over which better planning and play around the randomness clearly pays off over the medium-term. This is the case for both output and input randomness. I think fair output randomness takes the form of many trials that each have relatively small effects which are far outweighed by the player's influence in setting up situations using deterministic actions. XCOM is definitely not good at this.
 

keithburgun

Administrator
Staff member
#20
Yeah, there's nothing the player can do about the specific one-off event if the dice fall against them, but the game is a whole bunch of such events.
Yeah but it's not like another random severing of the chain of game-states un-does the initial severing. It just means the final outcome is now even more and more noise-influenced, with each one of these.

Good game design, I think, leads to many random trials over which better planning and play around the randomness clearly pays off over the medium-term.
I think if you believe that uniform (or even more uniform) randomness isn't possible, then yeah it at least feels better for players to have the non-uniform randomness be adding noise to the outcome consistently as you're saying. But this is more of a "psychological comfort" measure than anything that repairs the damage.

I think fair output randomness takes the form of many trials that each have relatively small effects which are far outweighed by the player's influence
Hmm, if you're saying this I feel like I haven't communicated what I want to say. Because I am certainly NOT saying that, you know, better players won't still win more even in a chaotic, variable/output random game. All I'm really saying is that the more output randomness / variable randomness you have in a game, the more matches it takes to get reliable feedback. It's basically just what people already know about Poker, that you can't judge how good I am at poker from watching me play one match of it.