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Subject: Tell Me The Odds - What are the relevant probabilities? rss

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David H
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"Never Tell Me The Odds"

I'm not a mathematician and not really a card counter, but I still find knowing the odds interesting, enlightening, and occasionally useful. Without getting into the math itself at this point...

What are some odds-based questions that would be useful to answer within the context of this game? I'll start and after we've compiled what's relevant maybe we can solicit commentary from someone equipped to answer?

Objectives and Resource Lockout
• I have X copies of an objective in my Y sized deck, how likely am I to see 1 copy if I draw four and discard 1? Useful to know how often you get an objective you like to see or avoid.
• To see 2 copies? Useful to know how often the objectives will stack or be stuck playing one.
• How likely are objective combos? Likelihood of seeing two (or three) objective all together.
• How often will I be resource locked out on draw?
• How likely is a resource lockout after a damaged objective?

Opening Hand and Discard
• I have X copies of a card in my Y sized deck, how likely am I to see at least 1 copy if my opening hand is Z? If I do not see 1 copy in my opening hand of Z cards, how likely am I to see it if I discard W times?
• How do these odds change with the mulligan rule (prior to discard)?
Obviously, this is useful to know how likely you are to draw into resources, mains, etc. The main calculation twist is triggering the draw mechanic repeatedly- whether based on the framework event, Fall of the Jedi, playing 0-cost events, etc.- the issue is: What are the odds of seeing the card I want to see by discarding these known quantities in my hand? Is a 2% better chance of seeing a main worth tossing a decent event? Putting an empirical value on digging basically...
• Similar inquiry as above, except, instead of the probability of seeing 1 of X copies in your opening hand, what about at least 1 of two (or more) populations in your opening hand: concretely, 1 main (out of X mains) and 1 resource (out of V resources)... and then with the one mulligan and with the variable discard mechanics.Useful for that basic 1 main and 1 resource opening; or other combo probabilities.
• I assume subsequent hands are just a tweaking of the above variables but could be totally wrong.

Draw Mechanic
• Probabilities surrounding "Holding All the Cards"... LS is playing it to obtain some advantage, but what is DS's chances of drawing into a Choke (or whatever)? Essentially the same calculations as above or is there a different equation?
• Probabilities surrounding Attack Pattern Delta, Vader's Advance Tie, & Last Defense of Hoth. This one is basic, right?

Edge Battle
• Can't think of any questions...
---

Relevant Threads:
Mathematics Behind Drawing Objectives
Why I think multi-faction decks should work just fine
Things unhealthy for the game - Protectors, Chokes, Swindled...
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Michael Schwarz
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In a 10 card deck, you're looking at something like a 54% chance of seeing a specific card if it appears twice.

I think it's 15%, again in a 10 card deck, but it's been awhile since I bothered to crunch that.

To plan for a specific combo? Not great. If it's a two card combo, that's doable, if both are doubled, but you're much better off looking for synergies, rather than actual combos.

Depending on your deck construction, this should be very rare to never. Having < 7 (out of ten) off Affiliation Objectives will make it a legitimate risk, though.

This is going to depend on your deck. If you have 6 off affiliation objectives, and you end up with 3 on affiliation objectives, your risk of the replacement objective being off affiliation is 1:7...

Chance of drawing a specific card, in a 50 card deck is going to be 1:50 for a single copy, 1:25, for two, and 2:25 for four. Obviously, once you start drawing cards, and get something else, your odds do go up (as the deck's population declines. (Note, this is NOT the gamblers fallacy, removing cards from the deck alters the odds.))

Calculating crap like resources is a lot harder, if you've got, say, 10, you have a 1:5 of getting one. With the odds diminishing as you draw resources, and increasing as you draw non-resources.

Already covered this.

Each card is a separate random chance. Like I said, when you draw a card other than the specified, your chances of drawing the specified card go up, drawing the specified reduces your chances of drawing another.

Drawing for advantage isn't really statistical. At least not in a conventional sense. Star Wars offers you a lot of tools to draw large amounts of cards from turn to turn (by dumping a lot of cards.) That's going to overshadow statistics on your ability to get the cards you want over your opponent. If you're doubling up on key objective sets, and your opponent is not, you'll have a critical advantage, otherwise, you won't.

Yeah, it is.

Edge Battles are more about poker than statistics, and I know I'm pissing someone off here.
 
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David H
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Quote:
In a 10 card deck, you're looking at something like a 54% chance of seeing a specific card if it appears twice.
No, that's the probability of seeing the card exactly once, by using the hypergeometric distribution for (k=1,n=4,K=2,N=10), but the probability for seeing a specific objective includes the probability of drawing exactly two H(2,4,2,10) which, for the purposes of this is a mutually exclusive probability and is added. The other way you can think about it is to calculate for probability of NOT seeing the objective H(0,4,2,10), then subtract that from 1 to get the probably of seeing (at least 1 = either 1 or 2) a specific objective.

Thus, for a 10 objective deck with 2 copies of an objective, you have a 66.67% chance of seeing that objective in your initial draw of 4.

In an 11 objective deck, your chances drop 4.85% to 61.82% of seeing that objective.

As long as we're dumping probabilities...

In a 10 objective deck with 2x Trust Me and 2x Life Debt, you have a 44.44% chance of seeing both in your initial draw of 4 (again, can draw 1 or 2 of either).

With the same composition as above, drawing 2x Trust Me, is 13.3% (1 to 6.5 odds)... which drops to 10.9% (1 to 8.2) with 11 objectives. Drawing 2x Trust Me and at least one Life Debt is 8.89% (1 to 10.25).

If you're running a multi-affiliation 10 objective deck with a 6/4 split, the probability of drawing all four of your minority affiliation are only 0.48% (1 to 209).

....

I'm curious what people want to know so we can figure out the appropriate tools to answer.
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Adam Howland
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David has it; you need to use hyper-geometric probabilities to get the right answers. There of plenty of these online, and even excel has the function already programmed.
 
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