Watch practically any Hearthstone constructed streamer for very long and you're apt to hear them complain about their warrior opponent playing the 2 casting cost card Fiery War Axe on turn 2. It lets the warrior attack for 3 damage twice, which is a huge setback for most aggressive decks. It makes it tricky to decide what creatures to play early when I have a choice in the matter. Heck, if I knew for sure that they had a fiery war axe then I might even decline to play a creature right away. Especially if I had an unstable portal in my hand. But if they don't have one then leading with a mechwarper is way better...
So I've been wondering... What are the actual odds that they have a fiery war axe in hand to kill my 2 drop? To give them the best chance at having one you'd assume they mulligan away every single card that isn't a fiery war axe. I'm not even sure that's an unreasonable assumption to be honest. It's so much better than any other card they could have early and pretty much ensures they'll get to the mid/late game in order to use their other more powerful cards. Maybe they'd also keep something like armorsmith against a known aggressive deck? This is one of those places where I wish I had the cards to play around with more decks so I could get a feel for what their decisions would actually be like.
If you're going second then you start with the coin and can play your 2 drop on turn 1. This means the warrior gets to look at 3 cards in their initial opening hand, and then 3 cards after they mulligan them all away and 2 draw steps. So they need to whiff on a 3 card hand and then whiff on a 5 card hand. This nets out to them having a 44.4% chance of having a fiery way axe on their turn 2 to use against my mechwarper.
If you're going first then you no longer have the coin and can only play your 2 drop on turn 2. This means they get to look at 4 cards in their opening hand, then 4 more cards and 2 draw steps. So they'd need to whiff on a 4 cards hand and then whiff on a 6 card hand. This nets out to them having a 52.6% chance of having fiery war axe on their turn 2 to use against my mechwarper.
So, does a warrior ALWAYS have fiery win axe? No. No, they really don't. If they have the coin then they're a little bit of a favourite to have one, and if they don't have the coin they're a little bit of a favourite to not have one. Overall they'll only have one a little under half the time.
I can see why it's frustrating though. Personally I've won 58.5% of the time against control warrior with my mech mage deck and my feeling for how that match goes is I win if I get an early rush in, or if I get a stealthed archmage antonidas. And I lose if the game goes long and I don't get infinite fireballs. Them having the war axe means my early rush is almost certainly destined to fail, but when they don't have one, and they don't rate to have one, I get my rush on and get a strong edge. They can stunt me with an armorsmith into a coined death's bite too, so it's not the only determining factor, but I suspect if I'd actually been tracking turn 2 FWAs it would be positively correlated with their chance to win.