Well, the naive approach is to always tell the truth. But there’s an interesting asymmetry there: from your friend’s perspective, if they guess the same suit that you find, their best move is to double down on their initial guess (knowing themselves to have a positive EV within that suit).
From yours, it doesn’t look like that: if they guess the correct suit but the wrong value, you know their best move is to double down, but you also know whether or not that doubling will succeed. Failing a double-down loses them twice as much as failing on an ordinary bet, so from the perspective of minimizing their losses, you’re given an incentive to lie about the suit (which would lead them to guess something you know to be wrong) if their initial guess had the suit but not the value right. You should still tell the truth if they got both right.
Of course, this only works if you don’t reveal the cards to your friend (the win rates shouldn’t reveal that you’re ever lying) or if your friend is bright enough to follow the reasoning. If you do and they’re not, revealing your choices might screw up your coordination enough to wreck the strategy, meaning that your best move goes back to the naive version.
And all bets are off if you have deontological reasons not to lie, even in a case like this.
Well, the naive approach is to always tell the truth. But there’s an interesting asymmetry there: from your friend’s perspective, if they guess the same suit that you find, their best move is to double down on their initial guess (knowing themselves to have a positive EV within that suit).
From yours, it doesn’t look like that: if they guess the correct suit but the wrong value, you know their best move is to double down, but you also know whether or not that doubling will succeed. Failing a double-down loses them twice as much as failing on an ordinary bet, so from the perspective of minimizing their losses, you’re given an incentive to lie about the suit (which would lead them to guess something you know to be wrong) if their initial guess had the suit but not the value right. You should still tell the truth if they got both right.
Of course, this only works if you don’t reveal the cards to your friend (the win rates shouldn’t reveal that you’re ever lying) or if your friend is bright enough to follow the reasoning. If you do and they’re not, revealing your choices might screw up your coordination enough to wreck the strategy, meaning that your best move goes back to the naive version.
And all bets are off if you have deontological reasons not to lie, even in a case like this.