Probability question for the math Wizards...

[webhead817]

I'm trying to figure out the odds of rolling successfully for leadership, with these variables.

First, I have two characters with leadership. I also have one character with probability control that can affect one of their rolls.

So, that's two chances to begin with, with a second chance on one of them.

How well does that work? I'm trying to figure out the lowest cost to achieve near guaranteed leadership rolls.

[Tsannik]

It's 50%. Either you will or you won't!

LOL HAHA..... I... I'll just go sit in the corner now....

:p

[webhead817]

I asked for math wizards, not math wise guys! ;) Seriously though, it's better than 50/50, right?

[bjmc1975]

One guy with leadership: 50%
Two guys: 75%
Three guys: 87.5%
Four Guys: 93.75%
etc.

Essentially, the odds are always ([x^2]-1)/(x^2). Thus, 1/2, 3/4, 7/8, 15/16, etc. To not get leadership means missing every roll, wheras you only need one success. This is for straight leadership. If you throw probability control into the mix, that simply is the same as adding another guy with leadership - therefore, one leadership and one PC'er is the same as two leadership guys for purposes of this equation.

I knew that Physics degree would come in handy eventually......

[Spiritual_Ex]

87.5% I believe, although I could be wrong.

[cyberdragon]

First, let's establish that each roll is independant form one another.

If you have 2 rolls for Leadership, then you get:

3/6 of success on the first roll and 3/6 on the second roll.

If you roll them together, you get 36 different possible results. Among those 36 results, only 25% is a fail as the little matrix below demonstrates. 9 couples out of 36 possible couples is a fail. That is expressed by 3/6 * 3/6 = 9/36. Probability of success: 27/36 = 75%.

1 2 3 4 5 6
1 X X X
2 X X X
3 X X X
4
5
6

Let's say you take your reroll (Probability Control) at the same time. We would have a probability of failure : 3/6 * 3/6 * 3/6 = 27/216 = 0.125%. Probability of success: 87.5%.

ANSWER:

Two leadership rolls: 75%
Probability Control: 87.5%

Can someone validate this please? :)

[cyberdragon]

Three posts with the same answer. I gues it's right then.

Sly.

[Styrix]

Probability Control can't work with Leadership, I think. Can I get a judge to confirm?

[Xanth]

I don't know the math but I do know it works on Leadership. It actually works on any dice roll.

[webhead817]

bjmc, I tried the math myself, and came up with the same answer. Seems right to me. Thanks all!

So, you can get an almost 9 out of 10 chance at leadership for a minimum of 57 points, with Gabriel Jones, Operative #128, and rookie Kingpin. That might be usable in a three hundred point game.

[A_Higher_Level]

Q:
A coin hads two sides... You are going to flip the coin 100 times. The first 50 times you flip it, it turns up heads. On what side will the coin land when you flip it that 51st time.

...

A:
It's STILL 50%! The results of the last 50 times the coin was flipped does not influence the result of the 51st time the coin will be flipped. ***Not unless one wants to take in the other variables of gravity, wind resistance, distance, inertia, and the wear and tear of the actual quarter in direct relation to the skill factor of the individual actually flipping the coin***

[Mr. Pilkington]

I haven't seen a specific ruling on PC not working for Leadership, and by the wording of PC on the PAC it is fine. PC allows a reroll of any die roll initiated by a figure within 10 squares and clear LOF to the PCer. You can pretty much reroll any type of roll (attack, B/C/F, Super Senses, Shape Change, Skrull team, Impervious check, Support, Regeneration, Breakaway, Leadership).

[Xian]

Originally posted by A_Higher_Level
The results of the last 50 times the coin was flipped does not influence the result of the 51st time the coin will be flipped.

Yes, the result of each individual die roll (or coin flip) is not at all related to any other roll of the die (or coin flip). Statistically speaking, your chances of rolling a 4, 5, or 6 are 50% any time you roll the die, for any given die.

However, the probability of rolling 4, 5, or 6 on one die (among multiple dice) is greater than 50%.


Xian

[A_Higher_Level]

It really sux to use your probability on leadership only to have your character roll a critical miss when they attack.

[cyberdragon]

Yep.

Those principles illustrate why I always randomly choose numbers when - and that's rare - I buy a lottery ticket.

And it also makes it worthwhile to have 2 clix with leadership on your team. Especially on high point teams.

:)

[cyberdragon]

If your probability to be successfull on leadership goes from 75% to 87% when using probability control with 2 leadership rolls, does it pay more than reducing the odds of snake eyes during combat when the probability goes from 3% to .0007%?

Your pick.

[webhead817]

Well, I'm looking at it from the point of view where I have a team that NEEDS 4 actions in a 300 point game. If you pick rookie Scarlet Witch for 5 more points than the rookie Kingpin, you get the flexibility to either re-roll leadership, or an attack roll.

[Mr. Pilkington]

Webhead - what are you building out of now 238 points (300 - 62 for 2 leadership and one PC) that has to have 4 actions? I'm just curious. :D

[cyberdragon]

Right. I find that in most 300 point games,
maybe with the exception of the first round, I don't have the opportunity to use Leadership very often.

Often half your team has played the turn before and unless you push some of them leadership is not required.

On the other hand, if for some reason you really need that extra action, then you'll be glad to have a good crack at it. I just think that the opportunity may not present itself that often.

[Earnan]

The one thing I can come up with is a team that has enough figs to need 3 activations, and then needs a SHIELD boost on top of that... I had one of them once. It used Firelord, and before you all jump me it was because I wanted his high attack and EE. :) It was a metagame team to take out IG teams, and it worked. I think I made and RCE attack twice in 5 rounds....

WarlordEarnan

[Melkoloran]

I am utterly amused that people have to plan their defenses of using Firelord -before- posting about it these days ;)

[Styrix]

A team heavy on WillPower would need the extra actions, like Kingpin, Operative 138 (or whatever), Scarlet Witch, and the rest in Doc Ocks.

101 Doc Ocks.... : drool : :p

[the itsy bit]

never tell me the odds !

2 figs with leadership will give you 1 extra action per turn on average.
If you put 8 figs with leadership in that army however, the laws of probability will turn against you and give you nothing !:D

percentage,schmercentage % are never there when you will need them so don't go counting on the numbers !

[EVIL CAP]

If memory serves me correctly you only get to roll Leadership once no matter how many characters you have got it

[webhead817]

EVIL Cap, you can only get the benefits once, but you can roll for it as many times as you have it.

Mr. Pilk, I'm working on some "first strike" teams, a lot of it has to do with double TK and stuff like that, but essentially making it so I can attack the far side of the board on turn 1. Basically looking for the elusive "anti-turtle".

[Styrix]

My use for multiple leadership:

Doctor Sextavius:
http://www.hcrealms.com/forum/showthread.php?s=&postid=237463#post237463

[CyberVenom]

Head....am.....hurt.....stupid numbers. :D

[webhead817]

Well, here's one example. If you use three TK's, and say Spiral, with leadership, you can TK up a TK'er and Spiral, then TK Spiral up to your opponents front line and go for an early KO. So, 4 actions, 3 TK's and one attack.

[cyberdragon]

Hmm. This could be interesting. I can imagine the other guy's face. Even more so if you're lucky enough to get rid of one fig in the first flurry attack and then you can target another.

Like those Master Card adds:

3 SHIELD Mandroids: 3.00
1 Spiral Unique: 15.00
The look of surprise on the other guys' face: priceless. :D

[Mr. Pilkington]

You would *have* to have 3 TKers in that
situation though, would you? I mean, you *could* get by with 2 TK figures and a long-range taxi (Taxi TKer up, Tk Spiral to him, TK Spiral further up with him). And you might be able to squeeze a free move onto said taxi... Thus you could get by with 3 regular actions (TK, TK, and slice-n-dice) and a free move.

Just thinking out loud here.

[webhead817]

Yes, if you played DC and Marvel together. So far, the Avengers fliers are too expensive/don't have enough range, depending. (If I'm wrong on this, someone please point out to me who I'm missing.)

Plus, with the TK "chain" in place, you can send in reinforcements from your starting area.

[Styrix]

Vision, Quasar, and Vet Magneto all have the free move taxi 9 movement necessary. And they would probably all be worth more the points than 2 superfluous leadership figs. Vet Magneto could move for free, be one of the TKers if needed, and brings leadership himself. And Magneto is only 6 points more expensive than the Operative 128, Kingpin, Mandroid, and Scarlet Witch he replaces. Probably worth the points for this tricky pony.

My version thus far:
Magneto Veteran 103 (free move, TK, Leadership if needed)
Mandroid Armor Rookie 28 (TK)
Mandroid Armor Rookie 28 (TK, and enhance Magento's already great damage).
Spiral Unique 56 (The whole point(s))
Doctor Octopus Veteran 66 (Perplex Spiral's AV up for first strike insurance, and later actually useful).
A.I.M. Medic Veteran 17 (duh)
298 points

[Mr. Pilkington]

Something like:

E Ultron (139)
U Spiral (56)
R Mandroid (28)
R Mandroid (28)
R Quicksilver (18)
LE Operative #128 (16)
E Hydra Medic (15)
--------------------------------
300 points

Ultron taxis a Mandroid for free due to BoEM team. The other Mandroid TKs Spiral up to the first one. The first one then TKs her up to the other team for real ginsu action. Plus you have Leadership in Op 128 50% of the time.

Granted, this is an extreme case. I wanted a wildcard taxi with 10 movement. You could use V Magneto and drop Ultron and Quicksilver and have a free move taxi with 9 movement with more flexibility for only 103 points. So for 215 points you get the free move taxi, with Leadership and TK, 2 rookie Mandroids and Spiral. This leaves 85 points for support staff, gives you one Leadership already and give Spiral a free move if you need it.

[Edit: Heh. It took me so long to finish that post the the V Magneto team got mentioned before me. Oh well. That's the price of posting from work! :D]

[Styrix]

Originally posted by Mr. Pilkington
Heh. It took me so long to finish that post the the V Magneto team got mentioned before me. Oh well. That's the price of posting from work! :D Hah! Everything goes to the quick and the cute. And buddy, I ain't cute! ;) And yeah, I work too (sorta, copier's borken).

[webhead817]

Here's what I've got,

vet. Ultron 188
le Adrian Toomes 30
rook Mandroid Armor 28
le Gabriel Jones 17
le Operative #128 16
rook Quicksilver 18

I just can't fit in the third leadership or probability control.

[Mr. Pilkington]

Whoa. That one threw me a curve. Are we still in the same thread? Oh wait, he mentioned needing 3 Leadership (or 2+PC).

Now my head is trying to wrap itself around your team. You have beastly Ultron (MoE), kickin' Vulture (no team), cheap TK Mandroid (SHIELD), cheap Leader Gabe (SHIELD), cheap leader Op (Hydra) and all-around bargain harasser rookie Quicksilver (BoEM). Lots of team abilities, no wildcards. Only one real damaging piece (Ultron) and not a whole lot of support.

I give. What in the blue hell does this team do? :D

[webhead817]

Well, most people I play in a three hundred point game put their six figs in a group, three in the front, three in the back behind them.

With this team, Toomes taxis up Ultron, Mandroid TK's up Gabe Jones, and Ultron beems the other team with a triple energy explosion that should do between 2 and 6 damage to each character on turn one.

It wouldn't always work, but when it did...

I just wish I could fit that extra leadership in there to more guarantee the fourth action I need to activate the SHIELD team ability to double the damage.

[Mr. Pilkington]

If you swap out Toomes for a cheaper taxi you could get a free move (say a doombot). But you lose the 10 movement on the taxi.

The only parts of the team that I see as variable are Toomes and Quicksilver. Everything else is needed for the EE combo. You could use a Wasp or a Doombot and TK Ultron instead of the SHIELD weenie. An 8 movement should still get the SHIELD person taxied up behind Ultron. If I tallied right you have 3 points unused. An E Wasp would fit in place of Toomes. granted you wouldn't have a taxi adjacent to Ultron for a turn 2 evac if you needed it. This is tough!

[Styrix]

That's one tricky pony! Beautiful!

[Mr. Pilkington]

Nevermind. The range won't work without a 10 move taxi. You have to place Ultron in front of the 10 move taxi to get him within range of the enemy, then you need to TK the SHIELD guy up, again behind Ultron. My Wasp scenario would be one range away from hitting the opposing starting zone.

[Styrix]

I'm right in thinking this can't hit the very back row, only the second to back row? Remind me to change my set-up position.

[webhead817]

I'm right in thinking this can't hit the very back row, only the second to back row? Remind me to change my set-up position.

Right, that's kind of the idea. I figure once I burn a few people with this, they'll start playing a little more coy, and shy away from turtle strategies.

Quicksilver is only there to tie up survivors on turn two, he can get about anywhere on the board if he's tk'd up 10 squares.