When reaching top ranks , I would often employ the worst case, best case, probable case analysis. It’s pretty useful in life, but goes something like,
Given the current position and for each play I want to make, what are
The best case outcomes
The worst case outcomes
The likely case, based on my gut feel and heuristics
Then act accordingly. Sometimes I play to the best case, worst case, likely case.
I can give examples for each,
Best case, if I have potential lethal from hand if I high roll and I’m confident my opponent likely has lethal I play to the best case. The usual pattern here is I’m trying to come back or equalize or just win.
Worst case. If I’m confident my threat can be answered, I won’t over commit to the board and try to bait out removal.
If I’m sure card drawn on t4 that was held all game must be a combo piece I’ll wait until hand is low to drop dirty rat.
What I noticed is that in modern Hearthstone, worst case analysis is almost pointless, you always try to go for the highroll or play against the most likely response. I can’t think of a single time worst case analysis was useful in like the last few years.
I really think this game would be better if it was relevant again. But with power creep and massive power spikes no one plays with measure, just abandon.
For proper piloting purposes, you are not even offering the correct answer in your multiple choice. The closest to the correct concept is “likely case,” but there are two important concepts that you are missing.
Not singular, but plural. You don’t play towards one outcome, you play towards multiple outcomes simultaneously. If A is 40% likely, B is 30% likely and C is 20% likely, then a play that wins under both B and C is better than a play that only wins under A. It’s always wrong to focus on particular cases, and correct to look at the cases as a collective that add up to 100% probability.
Not cases, but wins. A great way to lose games is to play around your opponent having answers too much. The reason is that these cases are rarely convertible into wins in the first place. If you hold back minions against board clear, sure, you might have some moment where you smugly pat yourself on the back before a predicted removal. But if that holding back doesn’t translate into a win at the end of the game, then it was NOT a better play — and the sad truth is, the vast majority of these “clever” plays only feel clever, they don’t win games. If it’s a situation where if they have it then you just lose, there is no playing around that; your only good play is to hope that they don’t have it.
That’s because it’s always been bad, as I explained above. It was bad in Magic the Gathering before Hearthstone even existed. The game didn’t get worse, you got smarter; that’s why it seems bad to you now.
If you’re an aggro deck you’re not going to play around marin into zilliax/reno/whatever for 0 mana as you’re just going to lose on that anyway.
If you’re removal warrior vs another slow deck then mabye you keep the brawl in hand and take that extra 6 chip damage to face
But to give a straight answer for the most part no… with all the nonsense in hearthstone today the game is slowly devolving into the first few cards winning/losing the game for you so holding an ok play for a potentially better play on later turns might cost the game as you dont end up making it to the later turns
Example would be that duplicating shaman 4/5 taunt… dump it on turn 4 if thats the most sensible play rather than holding for a turn 5 or 6 play as it might become suboptimal at that point and you waste the chance to just get it down and potentially alter your opponents play.
No, not really. “Playing for the worst case” pretty much always means playing to lose slower over playing to lose hard. They’re both still losses. There is no performance gain to be bad in playing for the worst case.
I play to the worst case scenario whenever I can, but if I feel like I’m losing if it happens anyway, then I play pretending like that play is impossible to happen - I literally go all in
But the truth is, it’s become way too hard to play around worst case scenarios, because there’s so many surprises possible nowadays with class identities ceasing to exist. I’ve had impossible things happen, such as Warriors casting Tsunami, so I don’t think that the future of HS will rely on worst case scenario analysis for a long time.
I do this as well, but lately I’ve been using less probability math when I play because I kinda just forgot how to do it after not using it for a few months-- since I took a break from May - August.
It’ll take some time for me to get used to my old thinking patterns again while I’m playing HS. So far though it has made almost no difference.
Why would you not always pick the most likely case? Coupled with fact you had implied in another thread you fall into the gambler’s fallacy, you have a few improvements to do in your understanding of probability if you want to improve your game.
This is the key insight. I just don’t know if we’re wording it correctly.
The point is that it’s a waste of effort to try to play around something that you can’t play around. If you’re going to lose anyway, then you just have to assume it won’t happen.
Part of skill is knowing the limitations of skill. Being realistic about what skill can and cannot do
Because, you can hedge your bets. You can take into account a few most likely scenarios and see if there is a play that is good for the most outcomes that are probable.
The phrase of the OP “most likely OUTCOME” implies to me the most likely RESULT of the game. If it meant “most likely SCENARIO [as in most likely situation]” it’s another discussion entirely and you could say “it might be very likely for that to happen but I don’t play based on that because I may lose anyway”.
If you want to talk about likely and unlikely scenarios the mathematics of that analysis are well known; you first derive percentages of likelihood and percentages of how successful a scenario is; then you just compare the products of “likehood X success” (basically the Expected Value of Economics).
If you’re behind you should be playing towards what can win you the game (if it’s only one or a few things), aka playing to your outs. There is no point in trying to lose slower - you have to go for the dramatic unlikely things that might turn the game around. In which case you’ll either lose faster OR you might win an otherwise impossible game.
if you’re ahead (depending on how far), it’s a good idea to play around the one thing that might cost you game. Examples are letting your health get low when that can be avoided, playing a minion for zilliax to rush into if you have lethal from hand) or overextending on the board when that’s not necessary (playing a 4th minion - I’ve been seeing more mind control tech lately) and getting wiped with aoe etc.
if it’s a more or less even position then that’s a wash and a judgement call depending on circumstances. All of the above is highly contextual based on what happened in the game and the better you get the better decisions you’ll be able to make on what is the best thing to do at any given time.
Not necessarily. If what can cost your game is very unlikely then you might be making the total effort for that match clearly worse; e.g. it might be 10% likely for an opponent to drop a board clear that will cost your game 90% of the time; but at the same time it might be 20% likely to make your game position stronger by 50%.
In the first case the expected outcome is a negative 9% but in the second the expected outcome is a positive 10% so even if the 1st case is more “brutal” to imagine it’s still not clever to avoid because it’s very unlikely while the second is more common to happen (more “expected”) even if it’s also unlikely to occur.
It seems you’ve missed an important point: all of us, including you and me, are notoriously bad at accurately estimating probabilities. There’s a very good reason I avoided mentioning probabilities in my initial explanation. If you’re interested in delving into why this is such a common blind spot for humans, feel free to start with these:
Barnsley, L., Lyon, P. M., Ralston, S. J., Hibbert, E. J., Cunningham, I., Gordon, F. C., & Field, M. J. (2004). Clinical skills in junior medical officers: A comparison of self-reported confidence and observed competence. Medical Education, 38(4), 358–367. https://doi.org/10.1046/j.1365-2923.2004.01773.x
Berner, E. S., & Graber, M. L. (2008). Overconfidence as a Cause of Diagnostic Error in Medicine. American Journal of Medicine, 121(5 SUPPL.), S2–S23. https://doi.org/10.1016/j.amjmed.2008.01.001
Callender, A. A., Franco-Watkins, A. M., & Roberts, A. S. (2016). Improving metacognition in the classroom through instruction, training, and feedback. Metacognition and Learning, 11(2), 215–235. https://doi.org/10.1007/s11409-015-9142-6
Carnap, R. (1951). Logical Foundations of Probability (T. S. Gendler & J. Hawthorne (eds.); Vol. 3). Routledge and K. Paul.
Ehrlinger, J., Johnson, K., Banner, M., Dunning, D., & Kruger, J. (2008). Why the unskilled are unaware: Further explorations of (absent) self-insight among the incompetent. Organizational Behavior and Human Decision Processes, 105(1), 98–121. https://doi.org/10.1016/j.obhdp.2007.05.002
Gilovich, T., Griffin, D. W., & Kahneman, D. (2002). Heuristics and biases : the psychology of intuitive judgment. Cambridge University Press. https://searchworks.stanford.edu/view/4815978
Kruger, J., & Dunning, D. (1999). Unskilled and unaware of it: How difficulties in recognizing one’s own incompetence lead to inflated self-assessments. Journal of Personality and Social Psychology, 77(6), 1121–1134. https://doi.org/10.1037/0022-3514.77.6.1121
Kyburg, H., & Teng, C. M. (2001). Uncertain inference. Cambridge University Press.
Lam, J., & Feller, E. (2020). Are We Right When We’re Certain? Overconfidence in Medicine. Rhode Island Medical Journal, 103(2), 11–12.
Lechuga, J., & Wiebe, J. S. (2011). Culture and Probability Judgment Accuracy: The Influence of Holistic Reasoning. Journal of Cross-Cultural Psychology, 42(6), 1054–1065. https://doi.org/10.1177/0022022111407914
Lichtenstein, S., Slovic, P., Fischhoff, B., Layman, M., & Combs, B. (1978). Judged frequency of lethal events. Journal of Experimental Psychology: Human Learning and Memory, 4(6), 551–578. https://doi.org/10.1037/0278-7393.4.6.551
Miller, T. M., & Geraci, L. (2011). Unskilled but aware: Reinterpreting overconfidence in low-performing students. Journal of Experimental Psychology: Learning Memory and Cognition, 37(2), 502–506. https://doi.org/10.1037/a0021802
...and that's just the tip of the iceberg.
The consensus is clear: humans are terrible at probability. All of us. And if you think you’re the exception, well, there’s a mountain of research to suggest otherwise.
So, how do we handle probabilities accurately? The short answer: we don’t— at least not in our heads. Instead, we use tools like calculators, computers, or even a simple sheet of paper. Without these, we’re adrift.
You’re telling me you can mentally calculate the probabilities of every possible outcome? Psssh. There’s extensive scientific evidence to the contrary, and ironically, that same research can explain your overconfidence.
Rather than attempting mental calculations, we should lean on the concept of a “roll-out.” A roll-out (RO) is a series of plays, simulating a sequence that may or may not include your opponent’s responses. Think of it as running a simulation.
With enough roll-outs, you asymptotically approach optimal play. There’s a proof that roll-outs converge to the minimax algorithm (if a UCT bound is used): Kocsis, Levente; Szepesvári, Csaba (2006). "Bandit based Monte-Carlo Planning". In Fürnkranz, Johannes; Scheffer, Tobias; Spiliopoulou, Myra (eds.). Machine Learning: ECML 2006, 17th European Conference on Machine Learning, Berlin, Germany, September 18–22, 2006, Proceedings. Lecture Notes in Computer Science. Vol. 4212. Springer. pp. 282–293.
Minimax is provably optimal, but that’s not the end of the story. The real challenge is balancing “Exploitation vs. Exploration.” How much time do you spend exploring new options versus refining your understanding of the ones you’ve already examined? If you’ve played strategic games well, like chess or Hearthstone, this dilemma should feel familiar. If it doesn’t, it suggests you’re probably not very strong at any of them.
But go ahead—keep mentally calculating the probability your opponent has an answer. Fantastic use of your time.
The “3-case rule” I mentioned (worst case, best case, likely case) offers three roll-outs you should always consider if you’re serious about playing any strategic game. It’s not exhaustive, but once you get good at a game (chess, for example), you’ll develop an intuition for when to explore vs. exploit—when to search for new lines or evaluate tactics more precisely. A strong intuition can guide your roll-outs, improving their accuracy.
Ah, so you’ve never learned how to bait removal? Fascinating. While the game may have evolved past that, baiting removal was once critical—just not in today’s Hearthstone, where it’s mostly irrelevant. But in more measured games (like earlier versions of Hearthstone), it absolutely mattered.
If your philosophy is sound, then why does checking in poker exist? Why not go all-in every time? The answer should be obvious. Good players know when to check. You sound like an average club-level chess player who knows how to attack but hasn’t yet grasped that a solid defense is often far more vital.
I’m no MTG expert, but I’ve seen enough top-tier games to know that’s completely false. Your point is only half-true in modern Hearthstone because the game has lost the concept of limited resources—opponents now effectively have infinite value, discover options, etc.
But in sane games like (perhaps older?) MTG, chess, and poker, worst-case analysis remains very relevant to accurate play.
Yup, exactly.
I recently lost to a Death Knight who somehow had the Druid dragon legendary that spawns a nest. It must have been some kind of Highlander DK for the nest to even trigger. And not only did it trigger, but he hit top-tier high rolls off the nest every single turn. He got the dragon that makes no card cost less than 2 (which saved him from lethal) three times, then got Alexstrasza to drop me from 30 health to 15, swinging the game entirely.
Another example: I had lethal lined up against a Reno Hunter for the next turn. All my opponent played was the beast that copies their last turn’s play. He had drawn and played two Marin treasures the turn before (Wand + Crown). Then he gets insane value from the Wand, and follows up with 3 Leeroys from the Crown, hitting me for over 30 damage in a single turn.
If you try to play around things like that, you might as well never play at all—you’ll just end up paralyzed by indecision because literally anything could happen.
See above. The short answer: what you think is the likely case almost certainly isn’t and if you think it is you likely suffer from overconfidence.
However, I think there is an important distinction between being incompetent, and being completely incapable. Some humans are very bad with probability and other humans are merely kinda bad with probability. That’s what makes the game fun. If we were all good at it, it’d be automatic, and the fact that it’s actually quite difficult is a good thing from a game design perspective.
I’m not trying to say that the sum of multiple probabilities approach is easy. I agree that it’s essentially impossible to execute perfectly. I am saying that the sum of multiple probabilities approach is correct, and if you replace that with an oversimplified “rollout” you might make the calculations less intimidating, but you’re not actually solving the problem anymore, but a strawman of the problem.
“Rollouts” are nevertheless a somewhat necessary simplification technique, as I’ll example later in this post, but it should be recognized as simplification and used at the appropriate times.
Of course I have silly. But those plays feel better than they actually are. Trying too hard to bait is really just baiting yourself.
And I’ll say that the average midwit poker player check-raises too much, too. It’s the same in this analogy: you delay aggression to try to get the opponent to overcommit. Can you understand how someone could check-raise too often?
I’m not saying that any case that has a probability is irrelevant. What I’m saying is that play that assumes the worst case is always wrong.
Since you apparently also enjoy poker, let’s consider this somewhat famous hand:
Very clearly, here Ms Selbst, who is a far better player than I am, considers the worst case relevant. But at the same time, she doesn’t play into it exclusively. She moves forward with the second nuts because it’s more likely that her opponent has the third nuts or a bluff, than she has the first nuts. Selbst is clearly embracing my philosophy of calculating the sum of all probabilities, which as betting progresses eventually simplifies into what is essentially one of your rollouts — there are a LOT of technically different hands pretty much getting thrown into the “bluff” bucket here.
I think Hearthstone has an equivalent to the “bluff bucket” — a lot of cards your opponent could have in hand simply aren’t going to be relevant to the situation, and can be lumped together in their irrelevance. This can make calculations significantly easier, which is good considering that they’re already inhumanly difficult.
This hand is famous because it was indeed a worst case scenario. Again I say, the worst case was relevant. However, I will die on the hill that Selbst folding would have been the wrong play here, given the information available to her. Tunnel visioning on the worst case is an error.
Btw, I dabbled in Big Spell Druid, as well, but before this patch xD It was fun, but definitely nowhere close to Mage’s strength
P.S. I’m deeply offended by your not accepting me for a friend (I think for the 2nd time). I really am. I’m hurt.
Imagine the scenario - you got sick of grinding Mage on EU in dumpster ranks and decided to go check on your NA account to try some of the risky new decks, such as XL InsanityLock or XL Painlock (for the love of God, why would anyone choose to start with MORE hp in a deck which thrives around 8-15 hp??), and the first game I play is immediately against a fellow forumer!!
I thought it was destiny. So I sent you a friend request, but to no avail
What I like to do is imagine myself in the sacred timeline, MCU style. If I play A instead of B, that means Alternate-Me played B instead of A, and since I’m here and he’s not, that means I made the right choice to further my universe’s existence.
Basically, if nobody comes back from the future to stop me, or ports me into the TVA, then my decision couldn’t have been THAT bad. This makes me feel better about myself since the alternative is a sharp slide into existential dread; in a reality we cannot conclusively prove even IS real, how can I possibly make a “good decision” in hearthstone unless I convince myself that I’m already making the best one?
