Bad luck or bad strategy?
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forceOfHabit
- Posts: 8
- Joined: May 5th, 2014, 7:16 pm
Bad luck or bad strategy?
"I challenge you to a duel!"
Alice and Bob are each down to their last soldier in a Battle for Wesnoth. Alice is down to a fully healed Dwarvish Thunderer (1st level 34 hp). Bob has a slightly wounded Dwarvish Dragonguard (3rd level 36 out of 59 hp).
"I challenge you to single combat, using only our thunder sticks. We stand and fight until one of us dies," says Alice.
"Sure!", answers Bob. "I have more hp, and I do more than twice as much damge (40-1 vs 18-1). I only have to hit you once to win and you have to hit me twice."
"We fight on neutral ground, say in a cave, so we both have a 50% chance to hit," says Alice.
"Why should I agree to this?" asks Bob. "I could win more easily fighting with my dagger."
"What's the fun in that? " asks Alice, "I'll even let you go first."
"OK!," says Bob and starts the combat. When the dust settles Alice has won!
"Oh that's ridiculous, " grouses Bob, "You were just lucky."
"So I was, " says Alice, "But your strategy was still bad. Better strategy would have decreased your chance of losing by over 20%."
"What?", says Bob, "That's ridiculous. There was no strategy involved."
"Sure there was. By attacking first you actually *increased* your chance of dying from 11/75 to 14/75! In fact, you even *doubled* your chance of losing in the first two rounds alone. Unlucky? Sure, but foolish too!"
Alice and Bob are each down to their last soldier in a Battle for Wesnoth. Alice is down to a fully healed Dwarvish Thunderer (1st level 34 hp). Bob has a slightly wounded Dwarvish Dragonguard (3rd level 36 out of 59 hp).
"I challenge you to single combat, using only our thunder sticks. We stand and fight until one of us dies," says Alice.
"Sure!", answers Bob. "I have more hp, and I do more than twice as much damge (40-1 vs 18-1). I only have to hit you once to win and you have to hit me twice."
"We fight on neutral ground, say in a cave, so we both have a 50% chance to hit," says Alice.
"Why should I agree to this?" asks Bob. "I could win more easily fighting with my dagger."
"What's the fun in that? " asks Alice, "I'll even let you go first."
"OK!," says Bob and starts the combat. When the dust settles Alice has won!
"Oh that's ridiculous, " grouses Bob, "You were just lucky."
"So I was, " says Alice, "But your strategy was still bad. Better strategy would have decreased your chance of losing by over 20%."
"What?", says Bob, "That's ridiculous. There was no strategy involved."
"Sure there was. By attacking first you actually *increased* your chance of dying from 11/75 to 14/75! In fact, you even *doubled* your chance of losing in the first two rounds alone. Unlucky? Sure, but foolish too!"
Re: Bad luck or bad strategy?
Well, that's certainly... a bit unintuitive. 
Re: Bad luck or bad strategy?
Agreed, took almost a minute to play it out in my head.
Re: Bad luck or bad strategy?
I actually had this happen one game except they were both thunderers. My opponent thought it was weird that I moved my thunderer to stand next to his but didn't attack it.
"There are two kinds of old men in the world. The kind who didn't go to war and who say that they should have lived fast died young and left a handsome corpse and the old men who did go to war and who say that there is no such thing as a handsome corpse."
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forceOfHabit
- Posts: 8
- Joined: May 5th, 2014, 7:16 pm
Re: Bad luck or bad strategy?
Velensk, that's awesome. I was pretty surprised when I noticed this so I'm impressed you actually got to use it in a game. I really posted this for people who complain about how important luck is in the game just to illustrate that correct strategy is trickier (and more important) than you might think.
Re: Bad luck or bad strategy?
forceOfHabit wrote: "Sure there was. By attacking first you actually *increased* your chance of dying from 11/75 to 14/75! In fact, you even *doubled* your chance of losing in the first two rounds alone. Unlucky? Sure, but foolish too!"
Why? I am confused here.
Re: Bad luck or bad strategy?
I reread it. In my case, both thunderers needed two hits so not quite as incredible. EDIT: In my defense here, if you remembered to apply resistances the thunderer would take two hits (but then the dragon guard would take 3)
It's because it's not who gets the first hit that counts but who gets the finishing hit.
In the given scenario If the dragonguard fires first he's got a 50% chance to win right away and a 25% chance to take a hit (25% both miss). However, if he fires first that means that the thunderer gets to fire first the next round giving that thunderer a 50% chance to kill him if he got a hit the first turn (so 50% of 25%) and the dragonguard never gets a second shot. Now, if the thunderer fires first, there's still a 50% chance he dies on in the first round (50% chance of getting the first hit is somewhat better) however the dragon guard gets off his second shot befoer the thunderer gets his second (which he needs to kill, the first hit is irrelevant if he doesn't get the second shot off). So altogether fireing second the first round gives the thunderer the best odds of even having a chance to kill (which are still slim mind you).
It's because it's not who gets the first hit that counts but who gets the finishing hit.
In the given scenario If the dragonguard fires first he's got a 50% chance to win right away and a 25% chance to take a hit (25% both miss). However, if he fires first that means that the thunderer gets to fire first the next round giving that thunderer a 50% chance to kill him if he got a hit the first turn (so 50% of 25%) and the dragonguard never gets a second shot. Now, if the thunderer fires first, there's still a 50% chance he dies on in the first round (50% chance of getting the first hit is somewhat better) however the dragon guard gets off his second shot befoer the thunderer gets his second (which he needs to kill, the first hit is irrelevant if he doesn't get the second shot off). So altogether fireing second the first round gives the thunderer the best odds of even having a chance to kill (which are still slim mind you).
"There are two kinds of old men in the world. The kind who didn't go to war and who say that they should have lived fast died young and left a handsome corpse and the old men who did go to war and who say that there is no such thing as a handsome corpse."