# Video game math problem

#### Johny17

##### New Member
OK so in a certain video game you battle against monsters. When you're getting attacked, you have a 33% chance of blocking the attack with a shield. If you fail to block the attack, you then have a 44% chance to dodge the attack instead. (Blocking and dodging both do the same thing: they allow you to avoid damage completely). My question is, what is the probability of avoiding damage? In other words, what is the chance that'll I'll be able to either block or dodge an incoming attack? I tried on my own but I just can't wrap my head around this.
I tried to create some kind of formula for this but I ended up more confused. Take this in its simplest form: the chance of flipping a heads either on the first try or on the second try. you would do successes/total outcomes = 2/3 = 66.66% chance. But if you do the same math with a dice and rolling evens or odds you get about 57% even though the odds are the same 50/50 for each try as the coin flip.

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#### fed2

##### Active Member
When you're getting attacked, you have a 33% chance of blocking the attack with a shield. If you fail to block the attack, you then have a 44% chance to dodge the attack instead. (Blocking and dodging both do the same thing: they allow you to avoid damage completely). My question is, what is the probability of avoiding damage?
you are damaged if you fail to block the attack, and given that you fail to block, you fail to dodge. so damaged = (1 - .33) * (1 - .44). not damaged is 1 - damaged.

#### Johny17

##### New Member
you are damaged if you fail to block the attack, and given that you fail to block, you fail to dodge. so damaged = (1 - .33) * (1 - .44). not damaged is 1 - damaged.
Thank you fed2 for your fast reply I appreciate this greatly . I've gotta say though I don't believe this is the answer I'm looking for unfortunately. It doesn't fit correctly.
First off, "given that you fail to block, you fail to dodge." I know in the real world this is true but not in the video game haha. If you fail to block, the game then gives a second chance to avoid damage by attempting to dodge. You get an attempt to block first(33%) then upon failure an attempt to dodge(44%). If you succeed right away in blocking, the dodge attempt does not happen. Thats conditional upon failing to block.

Here's how I know the (1-.33)•(1-.44) formula isn't correct:
Let's say my block chance was 50% and my dodge was also 50%. If you plug that in you would get (1-.5)*(1-.5)=.25
I don't know what the probability of avoiding damage would be if both values were 50, but im 100% certain that it would be higher than 50%. It couldnt possibly be .25. For a scenario as simple as both values being 50, you could maybe compare this to trying to flip a heads on the first try but if you fail you're allowed a do-over.