This is a question for any RPG fans.

There are two players with the following statistics:

Player1:
Strength - 15
Defence - 0
Agility - 5
Health - 75
Speed - 5

Player2:
Strength - 5
Defence - 5
Agility - 15
Health - 50
Speed - 10

They're in a turn based battle and it's your job to figure out who's most likely to win (because you'll get lots of gold if you bet on the right person or something). Here's how the stats affect a battle:

• Health * 5 = Hit Points
• Player's Agility / (Player's Agility + Opponent's Agility) = Player's chance to successfully attack the Opponent
• Player's Strength - Opponent's Defence = Damage dealt (amount reduced) to Opponent's Hit Points in successful attack of the Opponent
• Player's Speed / (Player's Speed + Opponent's Speed) = Player's chance to go first at the start of a battle

I hope this makes sense and I wonder if anybody will actually want to do it.

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An additional note for clarity:
The battle is turn based to the effect that once one player has attempted to attack their opponent (successfully or not), it will then be the opponents turn and vice versa (the player to attack first, at the start of the battle, is decided at random according to the rule above involving the Speed attribute). Also, whether a player hits successfully on their turn or not (see the effect of the Agility stat above) is randomly generated for each turn and not the same result for all of their attacks throughout the battle (although, I'm not sure this makes a difference to the answer, but I believe it will simplify things).

Qualitatively the second player always strikes first and has a much greater chance of inflicting damage. They both hit with the same amount of damage, so I'd bet heavily on the second one.

-Dan

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Thank you for your interest.
I'm pretty sure it's possible to go beyond estimation and prove which player has a greater chance of winning. They don't both hit the same amount of damage but I agree with you in that Player2 is more likely to win.

Initiative:
The first player has 33% chance to go first, the second 67%.

Chance to hit:
The first player hit 25% of the time, the second player 75%.

Damage:
The first player do 10 the second player 5 HP damage.

Hit Points (HP):
First player has 375 HP and second player 250 HP.

The first player does on average 2.5 HP / round of combat. Thus it will take him 100 rounds to kill the second player.

The second player does on average 3.75 HP / round of combat. Thus it takes him 100 rounds to kill the first player.

So on average it takes them the same time to kill each other. The one thing that will make a difference is the initiative. As player two wins the initiative 67% of the times, he will win 67% of the times as well on average.

Correct! You win lots of gold for betting on the winner.