How many tech rolls to roll?

[axis_roll]

In a game where you need a specific tech that would be 'HUGE' to get (possible game breaker)... how many dice should you roll?

lets use the assumption you have lots of cash, and there is no need to buy any units.

I guess I am asking, can anyone post the odds for getting a specific number given that you roll n number of dice?

For example, 1 dice for 1 number is 1/6, or 16%, but 2 dice does not statistically double your chances, if I remember my stats correctly probably more like 30%, not 32%. I am not a huge stats guy.

Who ever posts this answer, can you also explain how you got your numbers?

THANKS!

[TomJag2]

That's an easy one. None. If you have lots of cash, don't need more units, you've got the game won. The better players usually don't use tech roles unless they get far behind and are desperate. They prefer winning with solid strategy than trusting to luck.

[pagan]

1 in 6 chance on a single die roll to get any ONE specific number.

This equates to:

1 die roll = 16.7%

multiple dice rolls it becomes a bit different in that you only need a single successful roll of a specific 16.7% on two dice. answer is NOT 33% !

binomial distribution:

probability of zero rolls of a specific number
F>b = n!p^x(1-p)^n-x / x!(n-x)!

probability of At Least One roll of a specific number
f(x>=1) = 1-f(0)

.................Zero - @least 1
2 die rolls: 25.0% _ 65.1%
3 die rolls: 29.6% _ 65.4%
4 die rolls: 31.6% _ 65.6%
5 die rolls: 32.8% _ 66.0%
***6 die rolls: 33.5% _ 66.5%
7 die rolls: 34.0% _ 67.2%
8 die rolls: 34.4% _ 68.4%
9 die rolls: 34.6% _ 70.4%
10 die rolls: 34.9% _ 75.0%

Now to further confuse youI will not post the ACTUAL numbers except to say that the 6-DIE is correct.

[ April 20, 2004, 09:51 AM: Message edited by: PAGAN ]

[axis_roll]

Originally posted by TomJag2:
That's an easy one. None. If you have lots of cash, don't need more units, you've got the game won. The better players usually don't use tech roles unless they get far behind and are desperate. They prefer winning with solid strategy than trusting to luck.You're missing the point Tom. The amount of cash is a hypothetical set up.

I was trying to find where the number of dice added to the number of rolls does not greatly increase your chances of getting that tech... the law of diminishing returns.

[raveman1000]

Hi,

The percentage of getting the tech you want using different number of dice are shown below:

Dice Percentage
1 16,67%
2 30,56%
3 42,13%
4 51,77%
5 59,81%
6 66,51%
7 72,09%
8 76,74%
9 80,62%
10 83,85%

The formula I used is as follow:

Probability of getting none (i.e. all missing)=
f(0) = (5/6)^(number of dice)

Probability of getting at least one = 1-f(0)

There you go.

I hope this helps.

[DY]

It's late and I'm too tired to work out what PAGAN is talking about. But Woody's chart is the one I'm familiar with and as a graduate in Mathematics, I can safely say he is correct.

PAGAN may be trying to work out the optimal number of dice to roll to give the largest expected payoff, but like I said, my eyes are hurting...

[holywolfman]

I thought that was a formula for making "baby food" (lol)- Good to know someone is really good at math!

Now- what are the odds if you change the value of certain techs to roll from a 1d6 to a different side die?

ie: (you still choose # tech desired!)

1) Jet Fighters:......Roll 1d6 (16.7%)
2) Rockets:...........Roll 1d8 (12.5%)
3) Super Subs:........Roll 1d6 (16.7%)
4) Long Range Air:....Roll 1d12 (8.3%)
5) Combined Bombard:..Roll 1d6 (16.7%)
6) Heavy Bombers:.....Roll 1d12 (8.3%)

(WE also tried limiting the "allowed"/amount of dice that can be bought to '2' per turn!)

[Note]: Since 'Long Range' and 'HB's' are clearly the favored techs- just make them harder to obtain but still NOT IMPOSSIBLE!

-Nick- smile.gif

[ April 20, 2004, 12:38 PM: Message edited by: holywolfman ]

[AxisRoll]

With the new game, I disagree with the comment "A good player does not need dice"

Tech is easier to get and now we are working on plans to position yourselves for a round or 2, so in the 3rd round, you go for the tech to open pandora's box and blindside your opponent.

This works best with long range. Battles you could not do are now available to you.

So as the defender when you are placing units, should you consider this? It is a little much to deal with. But for $20 and 4 dice, I can hit a 4!

[squirecam]

Originally posted by AxisRoll:
With the new game, I disagree with the comment "A good player does not need dice"

Tech is easier to get and now we are working on plans to position yourselves for a round or 2, so in the 3rd round, you go for the tech to open pandora's box and blindside your opponent.

This works best with long range. Battles you could not do are now available to you.

So as the defender when you are placing units, should you consider this? It is a little much to deal with. But for $20 and 4 dice, I can hit a 4!This is the big problem. Because you can "get any tech", the game ends much sooner and is tilted towards the allies more than the prior game. The US can have 5-6 LRA HB to attack Germany on turn 4. Germany now has no income. I dont care where they are in the USSR, with no more income, Germany loses.

The techs are not balanced and that was a prerequisite to "choosing" techs. It needs fixing badly.

Squirecam

[ April 20, 2004, 02:51 PM: Message edited by: squirecam ]

[axis_roll]

Originally posted by squirecam:
This is the big problem. Because you can "get any tech", the game ends much sooner and is tilted towards the allies more than the prior game.
SquirecamWhoa...

Why do you assume that it helps the allies more? The axis has more units to take better advantage of said weapons (for example, rockets are a great investment for Germany).

I also think long range for Germany when necessary can be a game winner too.

I just don't understand why you think directed tech automatically helps the allies more....

[squirecam]

Originally posted by axis_roll:
</font><blockquote>quote:</font><hr />Originally posted by squirecam:
This is the big problem. Because you can "get any tech", the game ends much sooner and is tilted towards the allies more than the prior game.
SquirecamWhoa...

Why do you assume that it helps the allies more? The axis has more units to take better advantage of said weapons (for example, rockets are a great investment for Germany).

I also think long range for Germany when necessary can be a game winner too.

I just don't understand why you think directed tech automatically helps the allies more....</font>[/QUOTE]When Germany can afford 6 HB to bomb the US, then it will be even.

As it stands, The US can get LRA and HB. Germany and Japan must use their money on units to conquer territory.

And rockets are not even close to being as deadly as HB are.

[holywolfman]

(True)-BUT, 'Rockets' can do thier damage as well! Especially when they CAN NOT be blocked by any means!

-Nick- smile.gif

[Samurai]

We've always played that you roll the tech dice 1 at a time, announcing before each roll which tech you are going for. You must determine beforehand the number of tech dice you are buying, though. So let's say you really want HB, and you buy 4 dice. On the very first roll, you get lucky and acquire HB! You still have 3 tech dice left, and you can't sell them back to the bank, but these are not wasted. You may now declare another technology before each die, like Long Range Aircraft or Super Subs. The rational is that, if you get lucky and get another tech, its because either a) something about the 1st advancement was helpful in discovering the 2nd, or b) the quick discovery allowed alloted funds to be diverted to other research.

I'm guessing from the descriptions here that most people required the dice to be earmarked for a single tech before any dice are rolled, and then all dice are rolled together?

[ April 20, 2004, 11:50 PM: Message edited by: Samurai ]

[holywolfman]

We have been rolling tech/dice together BUT we also limit alloted dice to 2 per turn for 1 possible tech per turn! (We also tried using the 'ODD' chart by uping the sides of the die for different techs: 1d12 for HB's and Long Range/ 1d8 for Rockets; etc.

(works pretty good!)- still can get 'Lucky' rolls!

-Nick- smile.gif