The reasoning behind option 2 is completely ignoring the concept of dependent outcomes. In this example, four foci have already been rolled. This does not magically impact the results of the next four dice.

I think you need to look at how dice probabilities work a little more closely, Mynock has hit the nail on the head.

To put it another way: If I flip a coin 50 times and get heads every time; what are the odds the next flip will be heads? 50/50.

Ignore probabilities. Dice are sentient and like to screw you over (except mine, so please be kind to me at the tournament tomorrow please dice?), so if you re-roll all four you won't get an eyeball

I think it totally depends on the situation more than it depends on the dice.

If I need 4 hits, then I probably go greedy and reroll all 4.

If I just need 1-2 hits then I probably go conservative and reroll 3.

Probability being the driving force behind both, but also what my target number is heavily influences how I approach it.

These topics make my head hurt.

Ignore probabilities. Dice are sentient and like to screw you over (except mine, so please be kind to me at the tournament tomorrow please dice?), so if you re-roll all four you won't get an eyeball

This man understands dice.

Green Dice are an illusion. I disbelieve!

option 1, To be more precise, the chance of getting at least one focus when rolling 4 red dice is about 70%*.

option 2, rolling 8 dice all together is the same as rolling 8 dice one at a time, or 4 dice twice. the probability of getting 5 or more focuses when rolling 8 red dice is about 3%.

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Youre contradicting yourself. In deciding between rerolling 3 or 4 dice, you state the odds of rolling a focus with 4 dice at 70% in option 1, then reword it in option 2 saying rerolling a focus is at 3%. It cannot be both.

I normally don't really focus on probabilities too much as it takes away my pleasure and reasoning of playing this game. (this is just my opinion). But OP's reasoning seems to make no sense to me... It reminds me of people who go to casinos to play roulette and bet on certain numbers or colours dependent on what colour or number came before. It makes no difference, the odds are always the exact same and the casino always wins in the end

option 2, reroll 3 dice: dice rolls are independent from one another, rolling 8 dice all together is the same as rolling 8 dice one at a time, or 4 dice twice. the probability of getting 5 or more focuses when rolling 8 red dice is about 3%. Since we already know that 4 results are all focuses, the probability of having at least another focus in the next 4 results is about 3%.

That is not how this works. You're looking at two different events:

1. Getting 5+ focus results when rolling 8 dice

2. Getting 5+ focus results when rolling 8 dice, given I have already rolled 4 dice and gotten 4 focus results.

If you have already rolled 4 focus results, and you are wondering whether rolling another 4 dice will get you at least 1 focus, you're basically looking at the event "Getting at least 1 Focus on 4 dice", which is a pretty good chance.

Roulette, on a proper wheel, is about as random as can be. Perhap a supercomputer could measure inputs fast enough to make the call but otherwise...

Proper randomness doesn't care what came before it. You may see a brief pattern emerge but sometimes the planets align and strange things can happen. If you roll 4 attack dice you should expect something close to [hit/crit] [hit] [eye] [blank] but what you actually get can vary.

option 1, To be more precise, the chance of getting at least one focus when rolling 4 red dice is about 70%*.

option 2, rolling 8 dice all together is the same as rolling 8 dice one at a time, or 4 dice twice. the probability of getting 5 or more focuses when rolling 8 red dice is about 3%.

You need to re-read option #2. It's 5 or more focuses not one.

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Youre contradicting yourself. In deciding between rerolling 3 or 4 dice, you state the odds of rolling a focus with 4 dice at 70% in option 1, then reword it in option 2 saying rerolling a focus is at 3%. It cannot be both.

If you have a focus result and Ezra, I'm having a hard time seeing why I'd ever voluntarily reroll that. It's as good as rolling a crit.

If you have a focus result and Ezra, I'm having a hard time seeing why I'd ever voluntarily reroll that. It's as good as rolling a crit.

I think the idea is that of the dice you reroll, you are likely to end up with another eyeball anyway. Having two eyeballs does no good in the situation presented by the OP. (TL, no focus). So there's no reason NOT to reroll all 4 dice in the hopes of ending up with exactly 1 eyeball.

option 1, To be more precise, the chance of getting at least one focus when rolling 4 red dice is about 70%*.

option 2, rolling 8 dice all together is the same as rolling 8 dice one at a time, or 4 dice twice. the probability of getting 5 or more focuses when rolling 8 red dice is about 3%.

You need to re-read option #2. It's 5 or more focuses not one.

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Youre contradicting yourself. In deciding between rerolling 3 or 4 dice, you state the odds of rolling a focus with 4 dice at 70% in option 1, then reword it in option 2 saying rerolling a focus is at 3%. It cannot be both.

I don't need to reread it. In the 2nd option, regardless of how he is stated it, he thinks rerolling 4 dice (after you have 4 focus results on the previous roll) will give you 1 focus 3% of the time. Not only is this wrong, he also says right above it, if you roll 4 dice, your odds of a focus are around 70%. Again, it cant be both. And spoiler, the 3% thing is the wrong one

So I see it fairly simple.

On the first roll, I have 100% chance of changing one focus to a crit.

If I reroll all 4, there is 75% chance that each dice comes up as a hit, crit or focus and there is a relatively small chance of getting blanks on all 4 of the dice - BUT - it is there.

I would take the sure thing, change one to a crit, and reroll the other 3.

option 1, To be more precise, the chance of getting at least one focus when rolling 4 red dice is about 70%*.

option 2, rolling 8 dice all together is the same as rolling 8 dice one at a time, or 4 dice twice. the probability of getting 5 or more focuses when rolling 8 red dice is about 3%.

You need to re-read option #2. It's 5 or more focuses not one.

Youre contradicting yourself. In deciding between rerolling 3 or 4 dice, you state the odds of rolling a focus with 4 dice at 70% in option 1, then reword it in option 2 saying rerolling a focus is at 3%. It cannot be both.

I don't need to reread it. In the 2nd option, regardless of how he is stated it, he thinks rerolling 4 dice (after you have 4 focus results on the previous roll) will give you 1 focus 3% of the time. Not only is this wrong, he also says right above it, if you roll 4 dice, your odds of a focus are around 70%. Again, it cant be both. And spoiler, the 3% thing is the wrong one

I can be both except that in the he as already eliminated a huge number of possible outcomes from rolling 8 dice after he's already rolled 4 of them.

Flip a coin three times the odds of all three coming up heads should be 1/8. Now if you flip it twice and it has come up heads both times the odds of having it come up head 3 time is down to 1/2 but how can that be? That's pretty simple because you've already managed the 1/4 chance of getting heads twice in two rolls and thus thrown out 3/4 of the possible 3 flip outcomes.

It's only wrong in that it is short sighted.

One time I rolled 4 natural crits and took advantage of this rare dice result by taking a photo of it.

This is hilariously bad mathematics.

Whisper rolls 4 focus results on her green dice. What is the probability that the shuttle will roll at least 1 focus result on his red dice later? 68.36%.

Whisper rolls 4 blank results on her green dice. What is the probability that the shuttle will roll at least 1 focus result on his red dice later? 68.36%. Exactly the same because dice don't give a **** what Whisper rolled earlier.

The reasoning behind option 2 is completely ignoring the concept of dependent outcomes. In this example, four foci have already been rolled. This does not magically impact the results of the next four dice.

Do *you* have a PhD in physics from Cambridge?

I'm gonna say it again because I don't think it's been pointed out enough:

The odds of Each dice roll do not change just because you've rolled something before.

But, more importantly, and this is the bit that can't be repeated enough; the dice are sentient, they are spiteful and cruel sprites who will give you all blanks when you have focus and all eyeballs when you have target lock (followed by all blanks on a reroll).

The reasoning behind option 2 is completely ignoring the concept of dependent outcomes. In this example, four foci have already been rolled. This does not magically impact the results of the next four dice.

what dependent outcomes? the dice do not know you've stopped after 4 results to consider. all 8 results are independent rolls. the 4 dice you roll do not depend on the 4 dice before. the first 4 dice results do not impact the results of the next four dice. if it were so, you could not apply the binomial distribution to all 8, for example, as the binomial distribution applies to independent outcomes.

option 1, To be more precise, the chance of getting at least one focus when rolling 4 red dice is about 70%*.

option 2, rolling 8 dice all together is the same as rolling 8 dice one at a time, or 4 dice twice. the probability of getting 5 or more focuses when rolling 8 red dice is about 3%.

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Youre contradicting yourself. In deciding between rerolling 3 or 4 dice, you state the odds of rolling a focus with 4 dice at 70% in option 1, then reword it in option 2 saying rerolling a focus is at 3%. It cannot be both.

it is not both of course. I'll try to explain with a slightly different example: the chance of rolling 4 focuses in 4 dice is 0.4%. you can roll one die at a time or all 4 together, it doesn't matter. so imagine you roll one at a time. imagine you're rolling the 4th dice. somebody jumps in and says, oh you have a 25% chance of rolling a focus there. but it's your 4th dice and you rolled 3 focuses. the chance of rolling one focus on one die is 25%, the chance of rolling 4 focuses in 4 dice is 0.4%. so who's right? in a way, both statements are right. there is no contradiction in the sense that you're measuring the probabilities of different events. one is the chance of one result with one die, the other is the chance of 4 results with 4 dice. you're not choosing the chance you prefer, you're just saying, OK, of course I know that the chance of getting a focus with a single dice, even the 4th dice in this example, is 25%. However, I also know that the chance of this different event, of having 4 consecutive focuses, is only 0.4%, so I'm not holding my breath to get a 4th focus. it can and does sometimes happen, but not very often.