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Flip Vs Shuffle -- Limiting randomness in a way that benifts players

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Joined: 05/25/2010

Hey, first post here but I've lurked for a little while. Currently working hard on my own game (who here isn't) and I thought I would post some things I wrote a while back about my game. The discussion was between me and a collaborator when he questioned the games choice of using simultaneous turns. I implemented simultaneous turns to speed up gameplay as well as decrease the rules in the game that force an imbalance onto games.

In traditional games where turns alternate one player is given a clear advantage by going first. Different games have ways to compensate for this (extra cards is the most common), however this isn't perfect. There is no accurate conversion of value for going first in terms of cards. Especially since in games that use it the value of each card is determined by your deck and your opponents deck so greatly.

What also bothered my about alternate turns is that in a 3 game match like most tournaments use for card games there is a distinct 2 to 1 advantage for one player going first. This bothered me since it's all determined by the first coin flip. It felt unfair to me as a player to have something so important as turn order for three games decided by a coin flip. Rules like "loser picks' help but you still have that imbalance.

Simultaneous turns prevented this in my eyes by giving each player exactly equal footing at the start of the game. No advantage is given to either play by the rules. I hated the idea of making a system that dictated one player be given advantage over the other, perceived or real. Alternate turns did this in my eyes so we avoided it.

Now my collaborator disagreed saying that the very nature of card games is that one player has an advantage from the shuffling of the decks. And that the "deck screw" in any form is just as likely to limit a players chance to win a tournament as any coin flip. I disagreed and that led to this mathematical break down I thought I'd share (apologies in advance,t he tables don't translate well):

In each 3 game match, if we look exclusively at these three games, a coin flip will introduce imbalance by providing one player 2 game starts to 1.

For these three games, player A (who we will assume wins the flip) has an advantage 66% of the time (2 of 3 games).

This ratio shifts slightly as we increase the number of games per match.

# of Games in Match ||| # of Games in favor of A ||| % of games in favor of A

As you can see the more games we play per match the percentage of games that favor one player over the other decreases as it approaches perfectly fair at infinity. But at a low number of games per match we see a large split at 66% in favor of player A. As you increase the number of matches played, obviously this goes away as Player A and Player B share the same chance of having this advantage, thus minimizing the effect. However, in the scope of one match, we can clearly see an advantage being given to one player. And since in most tournament settings, one match is all it takes to be eliminated from consideration of 1st place, this raises concern.


Now for deck shuffling, let us assume a shuffle is equally as likely to produce a bad hand as it is a good hand. This is of course false since a good player will design decks to be more consistent, but let us assume a 50% success rate in obtaining a favorable shuffle for this example.

This means in the scope of one game each player has the following likelyhoods:

A. Both Players have a good hand: 25%
B. Both Players have a band hand: 25%
C. One player has a good hand, the other a bad hand: 50%


One Player has an advantage (C): 50%
Neither Player has an advantage (A+B): 50%

That is one game. Expanded to three games and focusing on one player:

# of Bad hands player A sees ||| % Chance of occurring

So the chances over three games for player A to have less bad hands than the other is as follows:

Player A Bad hands ||| Player B has less than more than N Bad Hands ||| % Chance of occurring
0 (12.5%) ----1+ (87.5%)----10.93%
1 (37.5%) ----2+ (50%)----18.75%
2 (37.5%)----3 (12.5%)----4.69%
3 (12.5%) ----null----0%

Sum total of Chances = 34.37% Chance Player A is going to be advantaged over player B in the scope of 3 games.

As we can see, this is a much smaller number than the 50% seen above for the coin flip. Further, on a game by game basis, player A and player B both share no advantage over one another in terms of shuffle (50% at game level). Where as the flip will be giving player A an advantage 66% of the time!

The randomness of shuffle does not inflict any game imbalance at the scope of one game. When each player sits down their shuffle is equal likely to harm and help them (this is still assuming 50% failure of their deck, which is high). When they sit down the flip is going to give them an advantage 66% of the time. This is an issue that simultaneous turns resolves. And even if you don't agree with that logic, even with decks that fail at horrendous rates, we can see the shuffle is much less likely to benefit one player over the other over a course of a game (34.37% opposed to 50%).

So with that all said, how do you guys try to limit rules that give one player an advantage over the other?

Pastor_Mora's picture
Joined: 01/05/2010
First things first

My answer to your question is: SURE I make rules to limit unbalances between players. I think this applies to any game. Balance is a necessity unless you specifically design a game with unbalanced characters/factions (many wargames do).

But, first of all, I think if you get a lousy starting hand 50% of the time, well, something smells for me. I'd say you can make the starting hand larger so the chances shrink.

Second, instead of cutting off advantages for a player, why don't you add advantages for the others to balance them out? I prefer a game with particular advantages for everyone than a game with no advantages for anyone.

Keep thinking!

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