Hearthpwn

Hello, I noticed looking at streams and playing vs friends and ladder - that not everybody thinks about likelyhood of outcomes in RNG situations so much. Sure they remove minions if they want their Ragnaros to hit right target, but not everybody is giving thought to juggles and bombing from Doctor Boom Boom Bots.
I hope this thread can bring discussion about statistics about what approach is correct for those who are interested and maybe some puzzling situations and what is the correct play. Best play is not obvious every time.
I will start with example situation, what is the correct play and some math behind it. Try to go with your guts what would be your play and than click on spoiler to find out if your play is correct.

Situation:
If you think right play is obvious, find out if you are right and how much better that play is than others in spoiler below.

IT IS YOUR TURN, you used your heropower to heal yourself already - Raptor is just your useless topdeck obviously.
Your goal is to choose which one of 3 obvious lines of play is best (that means have lowest possible % of losing on board next turn, and win is obviously better than just surviving)
(Yes, my MSPaint skill are 10/10 Kappa)

Every possible play and proof which play is best in this situation (it will maybe suprise you):

If you have no trouble to make correct RNG play every time even if there is Nozdormu somehow - I am sorry for wasting your time if you have read that far, maybe share your take on interesting situations. If i made mistake anywhere, please let me know and if you have some interesting hearthstone-math situation you want to share or want me or others to analyze please contribute :)

Thanks to player Bieftaki (EU) for helping me setup some screenshots.

Cheers, Beesman

Nice little challenge. Well done.  I went through the first 2 scenarios in my head. The third was never really a viable option.  I went back and forth and decided that the best chance to win was option one, due to the fact that you have 2 ways to win by attacking slime with boombot.  If you attack slime, then the bot has a chance to hit slime or face for a chance to win. I understand the percentages are different, but not many people will calculate exact percentages at that moment. Option 2 was also an option in that you have cleared off 2 of their characters, so you have a better chance of clearing the last minion or the bot hitting face for the win.  I guess I kind of look at how many different possibilities are there to win / survive based on my bad luck of bots hitting for 1-2 a lot.

id consider two options:

1) "yolo rag style": attack slime with boombot > either it will hit face for 4 and u win, or it will hit slime and u win

2) "probably safest way": attack slime with dr.boom, clear recruit with boombot and then there is good chance u can clear last minion or win game by hitting face for 4

im not feeling like doing the math, but if i were to go with my gut, i think i would take the option 2, even tho it would be much closer call then id like :)

i might also take into consideration, if he already played 2x Truesilver Champion, if he could have one in his hand, id probably go with option 1.

And that is the reason of this post, i also thought 2nd way would look for a lot of people "safer" just cause it kinda is in board control situation somewhere in mid game, and thats why people do these kinds of play without thinking about it for few seconds (or untill rope Lifecoach style). But in this case "yolo rag style" is not yolo at all and is in fact straight up better. And people roping that get this throuh their head would win in this situation twice as often as those who wouldn't think about that turn and thinks safe play is the second one.

My point is not that everybody should be roping always, my point is lots of people play fast "safe learned" plays without noticing they are making litterally bad play - and than they complain about rng so much.

Quote from Mister_Smith »

You've obviously put a lot of work into this and while i immediately thought of the first possibilty being the correct one you made me question wether the intuitive choice is the correct one or not.

You should make more of these :)

Thank you :)
Ofcourse It's more interesting if you look at the situation in comparison with very similar situations - just easy example: Paladin having only 2 hp or Paladin having one more dude in play shake the probabilities.
And you don't have to calculate every outcome to exact fractions, it's just good to stop for a second before making play that looks safer but looses twice as often :)

Just; People should not complain about RNG untill they make best probability for their RNG :D

Very very great post and I thank the OP for posting this. I would go by the first option by gut instinct, but once I have done the math I calculated the same. I was surprised actually (3rd option just felt unnecessary by the way)

One small, very minor thing we don't calculate is the possibility of a consecration or quartermaster topdeck. In that case, a 1-1 dude will push for the lethal so it shakes the possibilities of survival. Whereas if at least the paladin's board is clear, only a truesilver will kill you in that turn (and-or tirion maybe, also depends on your remaining cards).

By the way, what is the correct play if you are not in possible lethal range and you are not pushing for lethal?

Quote from ambershee »

Well, you have to hit the slime with the boom bot - if you don't, you've almost certainly lost. You need the bot to either hit the opponent for 4, the farseer for 3 or the slime for 1 (in which case you win).

The stats are irrelevant, really - the situation is kind of obvious. Victory will be entirely determined by RNG ;)

IRRELEVANT? This type of analysis will provide you the best decision to make. You are correct that all decisions still rely on chance, and you can win or lose with any of the three proposed attack orders. But if you go to Vegas to gamble, and I tell you one table plays 50% odds (2:1 payout on a coinflip), and another plays 10% odds (2:1 payout on calling a 10 sided die) .... your opinion on "irrelevant" statistics will change. You could win or lose a dollar at either  table, but there is definitely a better decision.

Quote from Primalsplit »

Very very great post and I thank the OP for posting this. I would go by the first option by gut instinct, but once I have done the math I calculated the same. I was surprised actually (3rd option just felt unnecessary by the way)

One small, very minor thing we don't calculate is the possibility of a consecration or quartermaster topdeck. In that case, a 1-1 dude will push for the lethal so it shakes the possibilities of survival. Whereas if at least the paladin's board is clear, only a truesilver will kill you in that turn (and-or tirion maybe, also depends on your remaining cards).

By the way, what is the correct play if you are not in possible lethal range and you are not pushing for lethal?

Thank you,
You are absolutelly right - my "survive%" should be splitted to state of the board where surviving 1/1 is way more threatining than cleared board thanks to consecration and quartermaster as you pointed out. But the "correct" play is superior in this exact scenario either way.
If you are not pushing for lethal the "looking safer" play is more apealing imho because clearing palladins dudes is relevant and you have your useless raptor threatining the 3/3. That all would obviously depend on you remembering what cards have been played so far, how many more hp palladin has etc.
Cheers

Quote from PunisherUSA »

Quote from ambershee »

Well, you have to hit the slime with the boom bot - if you don't, you've almost certainly lost. You need the bot to either hit the opponent for 4, the farseer for 3 or the slime for 1 (in which case you win).

The stats are irrelevant, really - the situation is kind of obvious. Victory will be entirely determined by RNG ;)

IRRELEVANT? This type of analysis will provide you the best decision to make. You are correct that all decisions still rely on chance, and you can win or lose with any of the three proposed attack orders. But if you go to Vegas to gamble, and I tell you one table plays 50% odds (2:1 payout on a coinflip), and another plays 10% odds (2:1 payout on calling a 10 sided die) .... your opinion on "irrelevant" statistics will change. You could win or lose a dollar at either  table, but there is definitely a better decision.

Thanks, Exactly.

I would improve the original quote of ambershee: "Victory will be entirely determined by RNG ;)"
To:"Victory will be entirely determined by RNG, And RNG will be entirely determined by probability, so prepare it correctly."

I always like these kinds of brain teasers, good stuff. I actually run a Nozdormu every now and then just because people don't do well under pressure more for fun than wins although it was better when miracle and slower decks were en vogue. With only 3 life and an assured loss next turn, you have to go boom bot into slime and hope for the best. The "safer" play would be my pick if I had 4 or 5 health rather than the yolo. I frequently mention it but RNG is something that a skilled player can minimize pretty effectively in HS and most of the complaints are unfounded. A good player will almost always bring RNG down to a 50-50 situation and at worst a 33.3% chance, if you aren't shaping the outcomes to that point then the fault is more yours than RNG's. Something like a boom bot is a double whammy of RNG because you have the RNG of what the bomb hits and then the RNG of the amount of damage, people that complain about Dr. Boom miss that fact a lot. Yes, it is a lot of potential value, but not guaranteed in the least. 

I got it right.  I mean, if you take a little bit to think about it you can come up with fractions pretty quickly.

Attack BoomBot into Slime, 4 Targets x 4 Outcomes each = 16 total outcomes.  7 of them are favorable to you (Slime 1,2,3,4; Hero 4, Earthen 3,4).  So we have 7/16 chance of Living/Winning.

Attack 1/1 with Boombot, and we have 2 targets x 4 outcomes = 8 total outcomes.  3 are favorable (Hero 4, Earthen 3,4).  So we have 3/8 chance of Living/Winning.

Attack 3/3 with Boombot, and we have 3 targets x 4 outcomes = 12 total outcomes.  3 are favorable (Hero 4, Earthen 3,4).  So we have a 3/12 chance of winning.

Obviously the 3/3 is the wrong play.  So just quickly calculate 7/16 (43%) vs 3/8 (37%) and you'll see that the "Yolo play" is actually the correct one.  [Or, simply reduce the other one to get 3.5/8.  Which will easily tell you that it's better]

Your way works just as well, but I can do my way much faster in my head.

Nice thread :)

Situations like these also often arise for me with Mad Bomber Madder Bomber and other cards where you don't know how much dmg you will do to the minion you actually want to kill. I tried to think of a good case, but couldn't come up with one. Mostly it's about whetever you hit with your minion first to weaken the guy and assuring the kill or if you wanna try your luck and see if your minion can survive while his die giving you a hit to your opponents face and one extra minion still on board.

Quote from Ururt »

Nice thread :)

Situations like these also often arise for me with Mad Bomber Madder Bomber and other cards where you don't know how much dmg you will do to the minion you actually want to kill. I tried to think of a good case, but couldn't come up with one. Mostly it's about whetever you hit with your minion first to weaken the guy and assuring the kill or if you wanna try your luck and see if your minion can survive while his die giving you a hit to your opponents face and one extra minion still on board.

Yes, Bombers are great point as well. Easy situation i can imagine you ment is for example - you need to survive next turn and your hp is low - so bombing your face would be horrible, you also need to kill yetti on your opponents side and you got your 2/2 on board and Madder Bomber in hand.
Attack yetti with 2/2 and risk more % of your own face dmg take?
Don't attack and risk more % to not be able to kill the yetti?
That depends on your hp, his hp, your board, his board etc.
The "more correct" aproach is always calculable but people tends to have some "safer play order" in their heads and they will stand by it no metter you disprove it is safer in that situation.
I believe players that don't get themselves in this confort zone of "safer plays that surelly works better every time beacause i saw arena player on stream do it" improve their game results AND expirience greatly.

good job on the thread.

Really cool concept, thanks for putting numbers behind this scenario.  Would love if you had more :D, great thread!

Quote from HS_TheKiD »

Really cool concept, thanks for putting numbers behind this scenario.  Would love if you had more :D, great thread!

Thanks, I am just finishing my examination period, so i don't have much time to make more atm. but i might do magathread with multiple analysis right after. I was thinking about finding missplays in tournaments situation and analyze them since commentators these days are so dull they just say "they both played perfectly" even if it's easy to spot one player made mistakes and the other one didn't.