Did Black King actually have an advantage? We find out.

Despite the demands for Karazhan's chess encounter to be ported over as a Tavern Brawl, A Game of Friendly Chess was not popular, roughly 10 times less so than Top 3. A day or so after release, the community started theorizing that Black's win-rate had to be astronomically higher than White's simply due to having The Coin and an extra card, we've analyzed a sample of over 100k games of the brawl to find out exactly what's going on.

The logic behind Black having an advantage isn't far fetched, after all, this isn't your traditional brawl where you may be running a more powerful minion than your opponent. Here both players have the same deck, but one goes first and the other gets two moves as a response. That's a huge difference. And the result of that? White's win rate across all games was 44%.

Because of this you certainly have your work cut out for you as the White King, so let's take a look at specific methods that increase your chance at claiming victory.

Just like when you were facing down the Black King, one of the biggest indicators of whether you'll win or not is determined by your minions double-hitting the opponent's. For example, in a board state where White has two Pawns, Black has just one and coins out a Black Rook which will only hit one of those the odds of White winning skyrocket to 61% from that alone. Compare that to a more standard opening of White Pawn, Black Pawn, White Pawn + White Pawn, Black Rook + Coin and White's chances drop down to only 29% simply because the Rook gets a double hit.

It's interesting to note that according to our statistics, White actually has a slightly higher win rate - 45% vs 44% - when passing on Turn 1. In any situation, Black has the highest win rate when using The Coin on Turn 2 which slowly trends downwards until Turn 5 when it's possible to have an even larger swing.

Best Time To Use Coin

Turn Win Rate
2 61%
3 55%
4 54%
5 55%

 

Some of the folks at Hearthsim analyzed the tree in a minimax way to find out how White can best turn the tides of the brawl into its favor. They found that if White passes, Black responds with Black Pawn on Turn 2, White plays two White Pawns for Turn 3 and Black plays a few Black Pawns in response, this leaves White with a 40% chance of winning. But if White opens with a pawn - assuming optimal play - and Black reacts with a single Black Pawn, White has a huge choice to make. It can either play White Pawn  (which is responded to by a single Black Pawn for a 32% win rate), which Patashu says is "not a great idea!" Or White can play two White Pawns, which is responded to by coining out a Black Rook for a 29% win rate or The Coin and three Black Pawns for a 31% win rate. But if Black can't do either of those plays, White has a 54% chance of winning, which much, much better than the 44% overall baseline.

Here are the two recommendations that one of our analysts had (again, assuming you're playing against an optimal opponent):

  • If you want to gamble on your opponent NOT having a rook or 4 black pawns in hand, open with a white pawn - 54% chance of winning if right, ~30% chance of winning if wrong. 
  • If you want to play it safe, open by passing - 40% chance of winning without much opener variance.

 

Hopefully you enjoyed this look into the actual statistics behind A Game of Friendly Chess. Special thanks to HSReplay.net for providing us access to the stats and to Jimbo and Patashu of Hearthstone Science for helping us translate all the information.

Want to take a look at the stats for yourself? This brawl, in particular, is interesting because so much of it is about understanding the chances that both you and your opponent have to make the ideal play so win rate statistics like this can prove invaluable!

  • WW = Win rate for White
  • G - Percentage of games that reached this point.