Say....On Redcloak's turn, draw a card. If it's a number card (not A/J/Q/K, as in not a strong dungeon), draw a second card. If
that's not a number card either, draw a third card. If any of the drawn cards (no matter how many are drawn) is the Gate, the round ends. Otherwise, discard the drawn cards and add one to number of turns Redcloak's taken.
On MitD's turn...choose one to five cards, without revealing them until they've all been chosen. Once revealed, if the number on the lowest
non-Gate number card (Aces are considered 1 here) is less than the number of cards drawn, MitD has been caught and the round is about to end.
- If the MitD reveals the Gate and is not caught, congratulations! Add half the count of remaining cards in the deck as a penalty to Redcloak's turns taken, add another 10 as a penalty while Redcloak scouts around elsewhere after the search is finished, reshuffle the deck and go back to Redcloak's turn with the new deck.
- If the MitD reveals the Gate and is caught, the round ends (Redcloak's going to check the ones he saw MitD messing with first).
- If the MitD is caught without revealing the Gate, add one half the count of remaining cards in the deck as a penalty to Redcloak's turns taken (he still has to find the Gate), and the round ends.
- Otherwise (not caught, no Gate), go back to Redcloak's turn.
And of course, as MitD is the player the goal is to maximize how many turns it's taken Redcloak to find the Gate during a round. It might be a good idea to set an upper limit along the lines of "MitD wins if the deck has to be reshuffled when Redcloak has over two hundred turns", if only for the psychological benefit of there definitely being an end in sight.
Intentional design points:
- There's no dead play: All cards are revealed before they're discarded, and the deck is reshuffled if the hand lasts past the Gate being revealed, so the unplayed deck will contain the Gate at all times it's being drawn from.
- With all cards revealed before being discarded, keeping track of which cards have been discarded can inform discard decisions.
- MitD discarding one card is always safe, so the player has a not-directly-losing option available at all times.
- Redcloak draws multiple cards more often than one, so MitD constantly playing safe isn't viable long-term.
If I were doing this
seriously, I'd want to do more number crunching and trials on it*, but I think this is sufficient for mediocre expectations.
*
Spoiler: But the Monte Carlo Method is FUN
Show
So I ran ten million trials on a shuffled deck (with one of the 3s replaced with an arbitrarily high number since the Gate card doesn't count here), to see what the maximum safe number of discards off a fresh deck would be.
Discard Chain Length |
Max Safe Chains |
Safe Chains |
Approx. Safe Chance |
1 |
1494410 |
10000000 |
100.00% |
2 |
2513349 |
8505590 |
85.06% |
3 |
2252006 |
5992241 |
59.92% |
4 |
2062564 |
3740235 |
37.40% |
5 |
1134391 |
1677671 |
16.78% |
6 |
426931 |
543280 |
5.43% |
7 |
102068 |
116349 |
1.16% |
8 |
13460 |
14281 |
0.14% |
9 |
804 |
821 |
0.01% |
10 |
17 |
17 |
0.00% |
So discarding 3 is safe more often then not, and drawing above 5 would be quite risky (hence the limit of 5 cards in the rules). This, of course, is assuming a fresh deck so it doesn't account for the odds of Redcloak having discarded multiple cards at the beginning, nor how the odds of drawing a particular card increase as other cards are discarded.