Best strategy

[Pickomino]

Anyone care to discuss their heuristic for playing to optimize their chance of winning?

[Dicetails]

Wait for 3+ 5s or paws before locking thouse numbers , only lock in a 1s of 1,2,3 if possible is about it

[ILetYouWin]

Pickomino Basic Strategy

I usually think about it in this general framework to keep it the game moving. After a while, you do the math without thinking. But for the first couple of time you might need some paper.

Faces:
F = {1,2,3,4,5,W}Value function:
v(W) = 5v(i) = i

Tiles:
T = {21,...,36}

Worm value function:
w(t) =

1 for t in [21–24]

2 for t in [25–28]

3 for t in [29–32]

4 for t in [33–36]

State variables

Define a turn-state:

s = (n, A, sigma, hasWorm, tau)

Where:

n = dice remaining

A = set of face types already taken

sigma = current sum

hasWorm = 0/1

tau = your exposed top tile (or null)

Bust probability (this one is clean and important)

Let:

b = |A| = number of distinct faces already used

Then:

p_bust(n, b) = (b / 6)^np_survive(n, b) = 1 − (b / 6)^n

Basic stats

Interpretation: Duh, you bust if all dice show faces you’ve already used.

Expected value of continuing

Define:

EV_roll ≈p_survive * E[future worm gain]− p_bust * Loss

Where:

Loss ≈w(tau) + lambda

w(tau) = worms you lose if you return your top tile

lambda = future value loss from removing the highest grill tile

You can sort of intuitively know this part. 

Stopping value

EV_stop = worms from best achievable tile given sigma

This includes:

exact match (including steals)

fallback to highest tile below sigma

Constraint:
must have hasWorm = 1 or EV_stop = −Loss

Decision rule (core result)

Roll again if:

p_survive(n, b) * E[delta_worm_gain]

p_bust(n, b) * Loss

Otherwise stop.

Worm threshold structure (the hidden math)

The reward function is discontinuous:

Threshold jumps at:

25

29

33

Equivalent statement:

delta_worm = 0 almost everywheredelta_worm = +1 at {24→25, 28→29, 32→33}

Implication:

Going 26 → 28 = zero value increase

Going 28 → 29 = real gain

Therefore expected value is dominated by threshold crossing probability, not raw score

Optional “steal term” (for extra pretension)

If sigma matches opponent tile u:

EV_stop = w(u) + opponent_loss_weight * w(u)

You can set opponent_loss_weight = 1 or 2 depending on whether you want to model swing value.  How much money did you bet would factor in I suppose if you had the balls to use this part. 

Final “theorem” version

Optimal Pickomino play reduces to:

Roll again iff

(1 − (b/6)^n) * E[worm gain from threshold crossing or stealing]

(b/6)^n * (worms lost + future grill value loss)

Corollary:

Pickomino is not a push-your-luck game.It is a finite-horizon stochastic control problem with discontinuous rewards and nonlocal failure penalties which is why some people say it is harder to win then Scythe with all expansions. 

Short punchline version

Bust probability = (b/6)^n

Only thresholds matter: 25, 29, 33

Value = worm gain − catastrophe risk

You don’t roll for points. You roll for phase transitions in a piecewise constant reward function. And if you get a bad roll, none of this matters since the game is 56.9448% out of your control.

[Finalg]

Actually it's 56.9451%

[SonataKnight]

I posted a guide in the Strategy Tips section of the game.

Remember: the numbers don't matter; it's the number of insects you collect. Always have your opponent's and your own insect counts in mind to determine how risky you should play. In a close match where your points differ by only one or two insects, you should generally play it safer.

When you start the game, you are at no risk of losing tiles, so it's always better to risk going for larger-valued tiles with three or four insects rather than just collect a tile with one or two insects. This is also true whenever you have no tiles. One larger-valued tile with four insects is going to be better than two or three tiles with only one or two insects, so you can afford to fail one turn if the opponent is only managing to pick up lower-valued tiles.

When starting your roll, keep in mind, you have to have at least one claw in order for your final roll to be valid. However, you typically need at least two or three each of claws, 5s, and 4s in order to be able to collect the higher-valued tiles. If you don't see multiples of the higher numbers, collect a single 1, 2, or 3.

Also keep in mind your opponent's last collected tile is always available to steal. You should target your rolls to steal their tile whenever possible, even if it means taking their lesser-valued tile over the chance for a higher-valued tile, especially if you're behind in the number of insects, though it may situationally depend on what the other available tiles are.

On subsequent rolls, you'll need to balance the number of remaining dice you have with the numbers you have available to roll for and the tiles you have available to collect, as well as ensure you have a claw to ensure your roll is valid, but the same general rule applies: take multiples of claws, 5s, and 4s. You do not want to be left with less than four dice without a claw, however, so prioritize getting a claw if a better-valued selection would leave you with less than four dice remaining to roll a claw.

I also posted examples of how to play certain rolls in certain scenarios.

[Fonky family]

Pas de stratégie a ce. Jeux car vous jouer avec des tirages de dé préfigurer au moment de la conception du jeu. Vous n'avez pas a jouer mieux ou moin bien.
C'est la même chose avec tous. Les jeux de dé et même de cartes.