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1) Do a full circle before throwing the dice.
2) If that doesn't work, slingshot the dice (Pull them backwards and hurl them)
3) If you are re-rolling, try and ricochet them with each other: Dice will touch whatever is on the table. I abused this mechanic so much to reroll a 6 by seeing how the die is facing then pummeling the die into an already existing die.
4) Get the Dice Blessings: They're OP! I reached like 24 once with the Add+1 to each die Blessing and Gambling Jewel!
Other than that, it's just pure RNG!
Presumably that is why there are so many passive buffs to aid the player with them. Off the top of my head you've got the Gamblers Ring (+2 to total roll), Protector's Armor (1 extra reroll), Colbjorn's extra dice, Divine Intervention (blessing, reroll lowest dice) and another blessing that adds +1 to every dice. There are probably more I'm forgotting.
But yeah, all RNG.
Also @Greig91 that makes a lot of sense to me. There are definitely quite a few equips and blessings that help specifically with dice rolls.
Therefore you reroll anything less than 3 -- and reroll the 3 too if you're feeling lucky.
That is all.
A lot of the time you should reroll 4s and 5s too. It depends what the target score is.
It depends what the target is. You aren't trying to score "as high as possible", you're trying to score "more than this specific number".
Easy example: Plenty of gambits want you to roll a 15. Your first roll is 4-4-2. Are you going to keep those 4s?
The best decision also depends on how many rerolls you have remaining.
Very few gambits want you to roll a 15 out of 18, those that do expect you to have a blessing/ring to mitigate the numbers.
If you are seriously in a situation where you must roll 15s with no buffs, then yeah, reroll your 4s or 5s and go for broke. Otherwise, never ever reroll them because you'll be stacking the odds against you.
I won't comment on the exact frequency, but 14+ targets occur often enough to be relevant.
All the other equipment* grants additional free rerolls (2s and 5s after the first throw from the helmet and 1 extra reroll from the armor), the extra reroll shifts the calculus towards being better odds for rerolling 4s in more situations, for the first reroll.
Incidentally, you shouldn't be rerolling 5s to go for broke against a 15, just 4s and lower. Rerolling 5s is only relevant on even higher targets.
*There is one blessing that works the other way, if you're fortunate enough to get it.
If I needed a 9, I would roll a 12 or higher on the first roll every time, but if I needed a 11 or more (I don't recall ever seeing a 10), I would always fail. Wouldn't matter how I would reroll. Tried tossing the dice, flipping them as described above, waiting for particular faces to show, nothing had any particular effect.
Before I start, I'll move the stick to get the throw prompt to appear. Then, when one or more dice has this corner facing upwards, I'll make sure I'm not moving the stick AT ALL and tap the throw. The dice should be dropped straight onto the table on the opposite corners and then fall onto one of the three sides next to those corners. With some luck, the dice won't roll any further or knock into each other, and the unfavourable numbers of 1, 2 and 4 will end up facing the table.
Otherwise, I try to roll without moving when a die has a 6 facing upward.
I don't think it's 100% RNG.