If / Else / Switch returning the wrong results

I'm making a Rock-Paper-Scissors-Lizard-Spock (Big Bang Theory, the tv show) using ReactJS and i'm facing some kind of abstract issue.

switch (this.state.playerOnePick === 'Rock') {
    case((this.state.playerTwoPick === 'Scissors') || (this.state.playerTwoPick === 'Lizard')):
    return (
        <div>
            <h1>Player One wins !</h1>
            <h2>P1: {this.state.playerOnePick} P2: {this.state.playerTwoPick}</h2>
        </div>
    );
        break;
    case((this.state.playerTwoPick === 'Paper') || (this.state.playerTwoPick === 'Spock')):
        return (
            <div>
                <h1>Player Two wins !</h1>
                <h2>P1: {this.state.playerOnePick}
                    P2: {this.state.playerTwoPick}</h2>
            </div>
        );
        break;

}

switch (this.state.playerOnePick === 'Lizard') {
    case((this.state.playerTwoPick === 'Spock') || (this.state.playerTwoPick === 'Paper')):
        return (
            <div>
                <h1>Player One wins !</h1>
                <h2>P1: {this.state.playerOnePick} P2: {this.state.playerTwoPick}</h2>
            </div>

        );
        break;
    case((this.state.playerTwoPick === 'Scissors') || (this.state.playerTwoPick === 'Rock')):
        return (
            <div>
                <h1>Player Two wins !</h1>
                <h2>P1: {this.state.playerOnePick} P2: {this.state.playerTwoPick}</h2>
            </div>
        );
        break;

}

Rock vs Paper is returning the right results, no matter who's picking it, when P1: Rock, P2: Lizard, P1 wins as expected, but when P1: Lizard P2: Rock, it is returning that P1 wins..

What it returns me when P1:Lizard P2:Rock

There is nowhere where Lizard is supposed to win vs Rock...

(playerOnePick and playerTwoPick are correctly updated as the player pick a weapon)