Shuffle iT Forum

Dominion => General Discussion => Topic started by: EntropySpark on 03 January 2020, 08:25:10 AM

Title: Mitigating First Turn Advantage
Post by: EntropySpark on 03 January 2020, 08:25:10 AM
In multiple games today, I've gone second, then lost due to my opponent getting an extra turn. In one game, I lost by three points, and would have been able to buy a Duchy on my turn to tie, and in another game, I lost by one point, and would have been able to buy a Province to win.

Both of these would have been mitigated if Dominion had a rule similar to Splendor and Istanbul in which every player is guaranteed to have the same number of turns. However, this would also mean that only the last player can get a win by finding a way to clear a third pile, often at great expense, plus a few victory points to win the game. If the first player did the same thing, it would give subsequent players one turn in which they know to buy victory points, rendering the smite moot.

I realize that this is balanced in part by the first player being determined randomly, but it still feels bad to invest twenty minutes into a game only for it to have been determined by the initial coin flip, whether I win or lose. Is there a way to improve on this?
Title: Re: Mitigating First Turn Advantage
Post by: bchia on 07 January 2020, 06:52:45 AM
Don't get into a buying war with a player that went first.

Don't buy the second to last province if you cannot pull ahead by more than 6 (or more in games with many +buy or trashing power to gain provinces).
Title: Re: Mitigating First Turn Advantage
Post by: EntropySpark on 07 January 2020, 08:58:32 AM
I'm not looking for specific advice for how to play as Player 2, but those are further examples of how the first player has an advantage.

Suppose there are two Provinces left (each player has three), and both players are on what is likely their final shuffle, without any +Buys. (The same principles generally hold with them, but let's simplify this example.) If Player 1's next turn reaches 8, he can buy the Province, so that Player 2 is racing to buy the final Province before Player 1 does, and they'll each buy Duchies and Estates in the meantime. As long as Player 2's deck is roughly as good as Player 1's, they have a very good chance of tying, but are much more likely to lose than win.

However, suppose that Player 1's next turn reaches 5, and they buy a Duchy. If Player 2's next turn also reaches 5, that's fine, they match Duchy for Duchy. However, if their next turn reaches 8, they have a terrible dilemma. If they buy the Province, then Player 1 just has to buy the next Province before Player 2 does, otherwise trading Duchy for Duchy, or even falling behind to one Estate, for a victory. Not guaranteed, but also rather likely if their decks are similar, as Player 2 just drew a very good hand, and is unlikely to get that same buy power until the next shuffle. If Player 2 instead buys a Duchy specifically because of this dilemma, then they had to underplay their hand. If Player 1's next draw reaches 8, they can buy the next Province, and Player 2 still needs to catch up as in the previous scenario, but they already drew a hand that reached 8, and are less likely to be able to replicate it in a future hand.

Granted, this is a slight simplification, as players can also get unlucky with falling just short with 7 or over-extending to 10 and beyond, which will also make future attempts at 8 less likely, but the general principle holds that when the game comes down to the Provinces, Player 1 has a clear advantage and the tie-breaker, which is effectively half a point for Player 2 if there's a turn imbalance, is not sufficient.

I'm curious to know what the stats are from online 2-Player games for how often Player 1 wins, particularly if you only look at games that ended with cleared piles instead of an early resignation.
Title: Re: Mitigating First Turn Advantage
Post by: xtruffles on 30 January 2020, 05:33:55 AM
First player has a 57% chance of winning