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Game Theory and Starcraft 2

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00Visor
Profile Blog Joined February 2011
4337 Posts
July 08 2011 15:30 GMT
#1
I feel that a lot of viewers/fans and quite some pro gamers and casters have a wrong understanding of Game Theory and how it applies to Starcraft 2.
I am a math student and poker player so this aspect of the game catches my interest a lot.

Not being predictable
This is one of most obvious topics. And most players and viewers understand this to some extent.
If you are predictable, your opponent doesn't need to scout a lot and can prepare and counter you early and easy. One good example is Idra who always went for the long macro game and was beaten by cheese or players who macroed very hard as well because they didn't have to fear big attacks. Now Idra mixes in a lot of timing attacks (some call them all-in) and that proves to be quite successful.
A good pro gamer should be able to play every style: cheese, gimmicky things, timing attacks, allins as well as macro games. Then your opponent has to prepare and fear everything. If you never cheese, your opponent can just play very greedy and will get an economic lead. Many pros don't do cheese (maybe pride?) at all and many fans really "hate" cheese. Some say it`s to risky and good players shouldn't play risky. I will cover in another topic why this is wrong.
Most koreans understand this and mix in cheese, as well as players like especially Naniwa. (who has one of the best game theory understandings imo)

Cheese needs to be there
From a game theory standpoint, cheese needs to be there. If there was no danger of early attacks, there would be no need to build units and every player would just expo first. We could then skip the first 5 minutes of the game. In my oponion it also makes the game more interesting and challeging because it adds this mind game aspect, makes scouting important and provides different types of games. I even enjoy most cheeses (esp. from good players) because they show some action in the first minutes of the game and still often transition into a standard game.

Playing safe/risky 1
Does risky/safe play exist in Starcraft 2? And if yes, is it bad?
The first question is debatable, because there are 2 interpretations:
- risky/safe in respect to preparing for gimmicky/cheesy stuff or executing these
- risky/safe in respect to the result of the game
These interpretations are entirely different, but often seen as the same.
You can't play Starcraft risky/safe regarding the outcome of a game. Simply because there is only "win" or "loose".
You can't compare it to games like Soccer/Basketball/Hockey or Poker. In most sports there is a time limit. So if you are in the lead, you can play defensive/safe. In Poker you can play risky and risk a lot of chips or play smaller pots.
If the possible outcomes are only win and loose, there is no possible risky strategy (e.g. Tennis). If you know you win 60% by playing standard and 70% by playing some cheesy/gimmicky strategy, than this is all which defines your expectation and variance. How can the latter one be more risky?
That especially applies to BoX matches, where there is the question if a player should play safe or risky if he is in the lead or behind. Well he just has to look at the actual game and you should play that style which will most likely win it for him. He can't play defensive like in Soccer.

Playing safe/risky 2
Now I talk about the first interpretation. "Risky play" like cheese, all-ins, (and also fast expos) and "safe play". Many pros and viewers think that optimal play should be safe, for example Tyler critized MC for not playing very safe and risk too much.
It may be true when you are facing far worse players. Then you win the game propably 90-95% by playing safe and be more risky wouldn't be beneficial.
But when facing other pros - and the level at the top is very close - it is not true.
First of all (and worst) you are predictable if you never play risky AND always play safe. Your opponent doesn't need to do some risky play then, he can play greedier and unsafe and outmacro you.
Playing safe will slow down your macro and cost a lot. Even against worse players this will get you behind quite often. So you have to "cut some corners".
The critique of risky play is often that you rely on a build order win rather than micro/macro. This may be true but if you are confident that is improves your winning%, why not?
I don't like the term "allin" used in this context, because it means (like in poker) that you either win or loose. But often the game still continues and even if the allin didn't end the game, it did do enough economic damage. (in fact many intelligent pros don't expect to end the game with an "allin" but do enough damage).
Battles are often decided by a few additional units. That`s the reason it is important to cut some corners to get more units or pull workers to win a battle which would leave you behind if you don't do economic damage. (and the reason why so called "all-ins" are so strong)
Even against worse players some pros choose to not play very "safe" and end the game rather quickly. They are so confident with their micro and that the early attack will almost never leave them behind. A good example is Naniwa`s run at MLG Dallas. He proxy gated and 4gated almost every game. And went 24-0. So was this risky play?
zul
Profile Blog Joined February 2010
Germany5427 Posts
July 08 2011 15:39 GMT
#2
I agree with everything you wrote and would like to add something. Risky play isn`t just an Allin Attack, but also a very greedy playstyle. Every good player trys to cut edges to get a strong economy, but some overdo it and get killed by such small amount of units, that should only be able to do some harras.
keep it deep! @zulison
tyCe
Profile Joined March 2010
Australia2542 Posts
Last Edited: 2011-07-08 15:52:58
July 08 2011 15:50 GMT
#3
I enjoyed your game theory viewpoint of SC2. Something that I think you missed is the importance of scouting and how it affects your expectations and therefore your optimal response.

However your critique of "risky play" and "safe play" is a little lacking because the whole idea behind Tyler or IdrA's safe play is their firm belief that their mechanics are superior and that as long as they can survive the early game, they will win against the perceived lesser player. While playing so passively does make them predictable, my point is that Tyler and IdrA actually have adopted game theory in their thinking and their calculations rule that they should play safely. We have seen IdrA cheese players who he perceive to be his equal or better like Jinro and MC, but Idra definitely needs to work on his execution.

Edit: I suppose that the lofty views of some players of their mechanics may be harming their application of game theory. Build orders in SC2 are sometimes so hard countering that long game macro mechanics simply cannot salvage the situation.
Betrayed by EG.BuK
00Visor
Profile Blog Joined February 2011
4337 Posts
July 08 2011 15:56 GMT
#4
On July 09 2011 00:50 tyCe wrote:
I enjoyed your game theory viewpoint of SC2. Something that I think you missed is the importance of scouting and how it affects your expectations and therefore your optimal response.


Of course scouting and reacting is very important. But I think this is understood by most so I didn't cover it especially.

On July 09 2011 00:50 tyCe wrote:
However your critique of "risky play" and "safe play" is a little lacking because the whole idea behind Tyler or IdrA's safe play is their firm belief that their mechanics are superior and that as long as they can survive the early game, they will win against the perceived lesser player.


I wrote that it may be good vs far lesser players.
In Broodwar it was easier to outperform with mechanics. This is not possible like Tyler and Idra want in SC2. And the problem is that the "perceived lesser player" often is not.
Cuiu
Profile Joined March 2011
Germany410 Posts
July 08 2011 16:15 GMT
#5
i hate the word cheese in association with sc2
and i dont get it wtf has cheese with a game to do
cheese cheeser cheesy wtf
yeah its a slang
but who was that stupid person to call something like that cheese
and than evolve to a insult "nerf you stupid cheeser"
should i be offended or something
omg he called me a cheeser i hope he will die slowly


im not with the community who complains about every early aggressive build
aaa what a lame game he is such a cheeser

wtf thats so stupid
when i see a zerg is going hatch first i trow all i have to break him
i get all my scvs i get all my units
i would take my supply depots when i could
he takes the risk to die to early aggression
so i just attack
when i fail then he is probably the overall better player and i will lose anyway
Mordoc
Profile Joined April 2011
United States162 Posts
July 08 2011 16:18 GMT
#6
Good post, I don't think it'll be some revelation for most posters, but it was a good read.


Safe>Cheesy>Greedy>Cheesy
Randomaccount#77123
Profile Blog Joined May 2010
United States5003 Posts
July 08 2011 16:38 GMT
#7
--- Nuked ---
Thereisnosaurus
Profile Blog Joined February 2010
Australia1822 Posts
Last Edited: 2011-07-08 16:43:45
July 08 2011 16:43 GMT
#8
You can't play Starcraft risky/safe regarding the outcome of a game. Simply because there is only "win" or "loose".
You can't compare it to games like Soccer/Basketball/Hockey or Poker. In most sports there is a time limit. So if you are in the lead, you can play defensive/safe. In Poker you can play risky and risk a lot of chips or play smaller pots.
If the possible outcomes are only win and loose, there is no possible risky strategy (e.g. Tennis). If you know you win 60% by playing standard and 70% by playing some cheesy/gimmicky strategy, than this is all which defines your expectation and variance. How can the latter one be more risky?
That especially applies to BoX matches, where there is the question if a player should play safe or risky if he is in the lead or behind. Well he just has to look at the actual game and you should play that style which will most likely win it for him. He can't play defensive like in Soccer.


While this shows a decent understanding of game theory it doesn't show a decent understanding of the realities of professional starcraft. For one, suggesting that a game of professional starcraft is single iteration zero sum is a wee bit foolish. A starcraft 2 game is more like a single game (within a set, match, tournament and season) of tennis than anything else. The player must take into account, for example

> optimum revealing of information such as build orders, micro ability, tricks and tactics in order to gain maximum advantage over the game, match, tournament or series of tournaments.

> optimum expending of energy reserves to gain the optimum win chance in a certain scenario where energy is not infinite over the course of a match, a tournament or series of tournaments.

>Score as a resource expendable to gain advantages in future series. playing a super risky cheese even knowing you will lose guaranteed if it gives you a percieved advantage in future games and doesn't eliminate you may be a worthwhile trade if it can be made

> metagame/career winnings. If say player X plays standard and wins 90% of tournaments gaining Y money and player A plays flashy, crazy tactic based games and wins 10% of tournaments gaining B money, but also C from endorsements, sponsorships, streaming and canned fan drool, if B+C > Y then player A can be said to 'win' at SC2 over player X if money is the only score system. This states that playing risky/cheese strategies that have a lower percentage chance of winning a single non iterated game may actually be more valuable to a player in an iterated scenario, so the highest %win chance strategy within a game is not always the best strategy.


Your arguments are solid, but you're looking at a very narrow aspect of SC2's metagame of progaming. If those were the only variables around you'd be right, unfortunately, they're not so things are a wee bit more complex than basic game theory can deal with.
Poisonous Sheep counter Hydras
Milkis
Profile Blog Joined January 2010
5003 Posts
July 08 2011 16:44 GMT
#9
On July 09 2011 00:30 00Visor wrote:
I feel that a lot of viewers/fans and quite some pro gamers and casters have a wrong understanding of Game Theory and how it applies to Starcraft 2.
I am a math student and poker player so this aspect of the game catches my interest a lot.

Not being predictable
This is one of most obvious topics. And most players and viewers understand this to some extent.
If you are predictable, your opponent doesn't need to scout a lot and can prepare and counter you early and easy. One good example is Idra who always went for the long macro game and was beaten by cheese or players who macroed very hard as well because they didn't have to fear big attacks. Now Idra mixes in a lot of timing attacks (some call them all-in) and that proves to be quite successful.
A good pro gamer should be able to play every style: cheese, gimmicky things, timing attacks, allins as well as macro games. Then your opponent has to prepare and fear everything. If you never cheese, your opponent can just play very greedy and will get an economic lead. Many pros don't do cheese (maybe pride?) at all and many fans really "hate" cheese. Some say it`s to risky and good players shouldn't play risky. I will cover in another topic why this is wrong.
Most koreans understand this and mix in cheese, as well as players like especially Naniwa. (who has one of the best game theory understandings imo)

Cheese needs to be there
From a game theory standpoint, cheese needs to be there. If there was no danger of early attacks, there would be no need to build units and every player would just expo first. We could then skip the first 5 minutes of the game. In my oponion it also makes the game more interesting and challeging because it adds this mind game aspect, makes scouting important and provides different types of games. I even enjoy most cheeses (esp. from good players) because they show some action in the first minutes of the game and still often transition into a standard game.

Playing safe/risky 1
Does risky/safe play exist in Starcraft 2? And if yes, is it bad?
The first question is debatable, because there are 2 interpretations:
- risky/safe in respect to preparing for gimmicky/cheesy stuff or executing these
- risky/safe in respect to the result of the game
These interpretations are entirely different, but often seen as the same.
You can't play Starcraft risky/safe regarding the outcome of a game. Simply because there is only "win" or "loose".
You can't compare it to games like Soccer/Basketball/Hockey or Poker. In most sports there is a time limit. So if you are in the lead, you can play defensive/safe. In Poker you can play risky and risk a lot of chips or play smaller pots.
If the possible outcomes are only win and loose, there is no possible risky strategy (e.g. Tennis). If you know you win 60% by playing standard and 70% by playing some cheesy/gimmicky strategy, than this is all which defines your expectation and variance. How can the latter one be more risky?
That especially applies to BoX matches, where there is the question if a player should play safe or risky if he is in the lead or behind. Well he just has to look at the actual game and you should play that style which will most likely win it for him. He can't play defensive like in Soccer.

Playing safe/risky 2
Now I talk about the first interpretation. "Risky play" like cheese, all-ins, (and also fast expos) and "safe play". Many pros and viewers think that optimal play should be safe, for example Tyler critized MC for not playing very safe and risk too much.
It may be true when you are facing far worse players. Then you win the game propably 90-95% by playing safe and be more risky wouldn't be beneficial.
But when facing other pros - and the level at the top is very close - it is not true.
First of all (and worst) you are predictable if you never play risky AND always play safe. Your opponent doesn't need to do some risky play then, he can play greedier and unsafe and outmacro you.
Playing safe will slow down your macro and cost a lot. Even against worse players this will get you behind quite often. So you have to "cut some corners".
The critique of risky play is often that you rely on a build order win rather than micro/macro. This may be true but if you are confident that is improves your winning%, why not?
I don't like the term "allin" used in this context, because it means (like in poker) that you either win or loose. But often the game still continues and even if the allin didn't end the game, it did do enough economic damage. (in fact many intelligent pros don't expect to end the game with an "allin" but do enough damage).
Battles are often decided by a few additional units. That`s the reason it is important to cut some corners to get more units or pull workers to win a battle which would leave you behind if you don't do economic damage. (and the reason why so called "all-ins" are so strong)
Even against worse players some pros choose to not play very "safe" and end the game rather quickly. They are so confident with their micro and that the early attack will almost never leave them behind. A good example is Naniwa`s run at MLG Dallas. He proxy gated and 4gated almost every game. And went 24-0. So was this risky play?


http://www.teamliquid.net/blogs/viewblog.php?id=204175

You might be interested in this
Yoshi Kirishima
Profile Blog Joined July 2009
United States10364 Posts
July 08 2011 16:49 GMT
#10
Wow, nice Milkis :D

Also, totally agree OP. It's really frustrating how people cannot understand the importance of the existence of cheese (and generally any early aggression) or that cheese is something you don't or want to do as a pro.

I think you could explain more what game theory is though, I think most people will have misconceptions of it. Maybe you could even talk about a Nash equilibrium xD
Mid-master streaming MECH ONLY + commentary www.twitch.tv/yoshikirishima +++ "If all-in fails, all-in again."
kNightLite
Profile Blog Joined December 2010
United States408 Posts
July 08 2011 17:05 GMT
#11
Although this is an interesting opinion piece there isn't any actual game theory in it. Which is too bad, as I was hoping for some applications.

For example, choosing your opening BO could benefit from a Nash equilubrium analysis. Prisoner's dillema could be applied to expansion timing. Evolutionary theoretics could explain standard unit mixes, and predict where the metagame (most people on the web use that term wrongly) will shift.
Clog
Profile Joined January 2011
United States950 Posts
July 08 2011 17:16 GMT
#12
Knowing that cheese is necessary doesn't make it that much more fun to watch
NesTea | LosirA | MVP | CoCa | Nada | Ryung | DRG | YongHwa
djengizz
Profile Joined August 2010
Netherlands42 Posts
July 08 2011 17:35 GMT
#13
Let me start of with saying i'm no expert in game theory. All the game theory i picked up comes from my poker career and i might be wrong in some of the things i'm going to say.
However i got the feeling that you are really misapplying some of the GT concepts when it comes to Starcraft.

Some things i don't think you take into account:
-Game theory assumes equal skill
-Game theory doesn't consider metagame
-To apply game theory to a game of incomplete information we need to fill in the blanks (we're making assumptions and guestimates to formulate a game theory optimal strategy)


From a game theory standpoint, cheese needs to be there.

I don't think so. Cheese needs to be there to deny some information making your opponents optimal strategy vs you harder to determine (in other words: making guestimates becomes harder).

If the possible outcomes are only win and loose, there is no possible risky strategy (e.g. Tennis). If you know you win 60% by playing standard and 70% by playing some cheesy/gimmicky strategy, than this is all which defines your expectation and variance. How can the latter one be more risky?

How about two games with the exact same expected value but one of them has higher variance. Game theory wise, since they have the same EV they are equally valid. Still i might want to take a lower variance ('safer') style because of metagame aspects like playing above your bankroll in poker or the finals of a large tournament in starcraft.
Another aspect in playstyles is the way you fill in the blanks and the fact that your opponent reacts to your actions. Both are style dependent. Compare this to a LAG or a TAG in poker (notice that TAG is often considered 'solid play' ) which might have the exact same winrate and expected value but don't have the same variance.
Also as already mentioned it's sometimes perfectly acceptable to play in a way that doesn't yield you the highest EV because of metagame aspects. Consider examples like setting up a maniac image at a pokertable to yield higher results later on or a big fish at the table who is going to leave once he looses his stack. These concepts are not covered by GT.


Many pros don't do cheese (maybe pride?) at all and many fans really "hate" cheese. Some say it`s to risky and good players shouldn't play risky. I will cover in another topic why this is wrong.

It feels to me that you only look at win % when considering cheese and it's viability but i think you should also consider skill. To make the analogy to the poker world again i think it's more similar to shortstacking in poker (which is generally frowned upon as well). If i have to play superior opponents i should resort to a short stack strategy because i want to limit my decision making (in which my opponent is superior) and play a high variance style. The same can be said of cheesing. I don't want to play a long game against a better opponent (in poker i usually only play a flop and either push or fold) because his superior skill is more likely to come out on top when more decision making is involved. It also makes no sense when you are practicing (some people consider ladder as practice) to pick a strategy that limits this decision making. This is why it's frowned upon and called cheap by some people, the high variance part of those strategies (and the fact you will never reach an infinite sample to even out the variance) make them risky.

I do agree however that in a BOx it might be completely viable to 'mix things up' and 'balance your ranges' by throwing in a cheese. But again this is a metagame concept which is not covered by game theory.
SoKHo
Profile Joined April 2011
Korea (South)1081 Posts
July 08 2011 17:41 GMT
#14
On July 09 2011 01:15 Cuiu wrote:
i hate the word cheese in association with sc2
and i dont get it wtf has cheese with a game to do
cheese cheeser cheesy wtf
yeah its a slang
but who was that stupid person to call something like that cheese
and than evolve to a insult "nerf you stupid cheeser"
should i be offended or something
omg he called me a cheeser i hope he will die slowly


im not with the community who complains about every early aggressive build
aaa what a lame game he is such a cheeser

wtf thats so stupid
when i see a zerg is going hatch first i trow all i have to break him
i get all my scvs i get all my units
i would take my supply depots when i could
he takes the risk to die to early aggression
so i just attack
when i fail then he is probably the overall better player and i will lose anyway


I think it came from the Korean BW commentators. At least that is where I first heard it. Why do you feel so insulted and hate the word cheese so much? When you all-in a hatch first (which is standard zerg play), every game, you probably won't improve at all. To become a better player, you need to play standard. I like to incorporate cheese in a tournament game.
"If you don't understand my silence, you won't understand my words"|| Big Nal_rA fan boy!! Nal_rA, Bisu, Huk, MC, Hero fighting! SKT1---->
chaopow
Profile Joined March 2011
United States556 Posts
July 08 2011 17:51 GMT
#15
This is true. You absolutely can't play the same style in every game if you are a pro gamer. BUT, if you are an average joe on the ladder, I would probably recommend playing straight up and standard. I went from bronze to masters based on playing standard builds, but now I am having to mix up my bag of tricks if I want to win sometimes. Against players better than me, I will cheese, all in, or take large macro risks. Although pro players usually don't cheese because of this, sometimes they do.

Pure cheese, risky play, or macro play is all not that good. Idra was a great example of pure macro play, but people figured him out and started to cheese him or play risky. Not many pure cheesers/ riskers win tournaments, but I believe there are some in the GSL A/S.

Mixing up your builds is absolutely right, but I think casters and streamers are just trying to teach most players to play standard, as that is truly the best way to play. In the top tier, where it actually matters, they understand the game and mix their builds very well. An example I kind of like is Huk. Hes gotten insanely good, and can 4gate all in you, canon rush, or play an incredible macro game. He can be very aggressive or play defensively if hes getting attacked.
Soowoo AD.
Zocat
Profile Joined April 2010
Germany2229 Posts
July 08 2011 17:53 GMT
#16
On July 09 2011 00:30 00Visor wrote:
You can't play Starcraft risky/safe regarding the outcome of a game. Simply because there is only "win" or "loose".
You can't compare it to games like Soccer/Basketball/Hockey or Poker. In most sports there is a time limit. So if you are in the lead, you can play defensive/safe. In Poker you can play risky and risk a lot of chips or play smaller pots.


Imagine the following SC2 situation:
TvP. Your army values are about equal.
You, the T, drop the P's mainbase and start attacking buildings. Do you retreat after killing a pylon / a warpgate or do you push into the probeline and try to kill all the probes?
You can risk your whole drop (a lot of chips) or retreat and take away your small advantage (small pot).

Now imagine you did kill all his probes and got away with your drop. Obviously you have a big economic lead.
You now dont need to proceed with your planned timing attack (against an opponent with equal army value), possibly engaging in a bad position, since over time your advantage will increase. You can now play defensive, setting up good positions when a fight is about to happen.
Since your opponent is behind he has to take risks to make a comeback. And you can exploit those risks. Similiar how in football the team behind has to open up the defense and try to score a goal. And the leading team can exploit the open/free space by utilizing fast counter play.
L3gendary
Profile Joined October 2010
Canada1470 Posts
July 08 2011 18:01 GMT
#17
Your whole 2 paragraphs about risky/safe are utterly wrong because you assume that starcraft is a game of pure luck and one only needs to choose the strategy that would give the greatest chance of winning based on past results (treating all games equal apparently without respect to who you're playing), instead of a game where your strategy depends on scouting.
Watching Jaedong play purifies my eyes. -Coach Ju Hoon
makmeatt
Profile Blog Joined June 2011
2024 Posts
Last Edited: 2011-07-08 19:15:45
July 08 2011 19:15 GMT
#18
Cheese annoys lower leaguers because there are players that perform them almost all the time to grind the ladder position.
Cheese annoys higher leaguers because some of cheeses are incredibly powerful and easy, to the point where some strategies should be ruled out because of the danger (the infamous hatch first on Tal'Darim).
Also, when discussing game theory in relation to Starcraft 2, people tend to underestimate the aspect of time, which I personally see as the fifth resource.
"Silver Edge can't break my hope" - Kryptt 2016 || "Chrono is not a debuff, you just get rekt" - Guru 2016
Yoshi Kirishima
Profile Blog Joined July 2009
United States10364 Posts
July 08 2011 19:20 GMT
#19
On July 09 2011 02:41 SoKHo wrote:
Show nested quote +
On July 09 2011 01:15 Cuiu wrote:
i hate the word cheese in association with sc2
and i dont get it wtf has cheese with a game to do
cheese cheeser cheesy wtf
yeah its a slang
but who was that stupid person to call something like that cheese
and than evolve to a insult "nerf you stupid cheeser"
should i be offended or something
omg he called me a cheeser i hope he will die slowly


im not with the community who complains about every early aggressive build
aaa what a lame game he is such a cheeser

wtf thats so stupid
when i see a zerg is going hatch first i trow all i have to break him
i get all my scvs i get all my units
i would take my supply depots when i could
he takes the risk to die to early aggression
so i just attack
when i fail then he is probably the overall better player and i will lose anyway


I think it came from the Korean BW commentators. At least that is where I first heard it. Why do you feel so insulted and hate the word cheese so much? When you all-in a hatch first (which is standard zerg play), every game, you probably won't improve at all. To become a better player, you need to play standard. I like to incorporate cheese in a tournament game.


This is such a twisted view. What is "better"? The only way you can concretely determine performance is by how much you win, which is what performance is. If you can cheese your opponents every game and win the GSL, is that not worth it? Don't consider that maybe you won't be able to play long macro games like the rest, because again, only the results matter. If you cheese every game and win every tournament, are you a good player?

Of course that example is to the extreme, but I hope you get the point. (Look at thebest though, he was quite successful in the super tourny and made much more money than players playing "standard" like idra).
Mid-master streaming MECH ONLY + commentary www.twitch.tv/yoshikirishima +++ "If all-in fails, all-in again."
R0YAL
Profile Blog Joined September 2009
United States1768 Posts
July 08 2011 19:26 GMT
#20
Cutting corners is risky because you are sacrificing stability in favor of an advantage later in the game. You are more vulnerable in the now, but if the game goes on to the later stages you will have the advantage.

Allins are risky because if you fail you just lose.
Absence of evidence is not evidence of absence.
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