Deck size & Probability - A case for (slightly) bigger deck

[Atomzed]

(Ooops, not for me)

Anyway the rest of the inclusion-exclusion calculations are this: P() stands for probability

P(KPAJR) = 1 - P(nK) - P(nP) - P(nA) - P(nJ) - P(nR)
+P(nK,nP) + P(nK,nA)+P(nK,nJ)+P(nK,nR)+P(nP,nA)+P(nP,nJ)+P(nP, nR)+P(nA,nJ)+P(nA,nR)+P(nJ,nR)
-P(nK,nP,nA) - P(nK,nP,nJ) - P(nK,nP,nR) - P(nK,nA,nJ) - P(nK,nA,nR) - P(nK,nJ,nR) - P(nP,nA,nJ) - P(nP,nA,nR) - P(nP,nJ,nR) - P(nA,nJ,nR)
+P(nK,nP,nA,nJ) + P(nK,nP,nA,nR) + P(nK,nP,nR,nJ)+P(nK,nA,nR,nJ)+P(nP,nA,nR,nJ)
-P(nK,nP,nA,nJ,nR)

I'm afraid there is no easier way to get an exact answer.

Yah, not for u.

Just so that ppl can understand why i included assumption 7, Ringel, do you agree that for sake of simplicity, the assumption 7 is actually a valid assumption?

[kamman13]

So you have 4 SoV in a 29 card deck, your opponent has 4 wbt in a 39 card deck. You will draw more shrieks than they will get wbt, statistically speaking.

So the wolf adds 2 JD, increasing his odds of drawing a weapon. Most DC decks already have this in their 40 cards. And you still haven't dealt with the lone wolf healing problem, which SoV only amplifies by reducing your resource pile, making you able to deal less damage per turn, and increasing the efficiency of lone wolf. Without allies or SS, DC should have no problem milling Majiya to death.

[MistahBoweh]

Looking at T2 only, bec i have already played Kris, and sac a card, the chances of me drawing a Puwen:-
a) Hand size = 4 from previous hand + 1 new drawn card
b) Deck size = 37

This is what I'm saying is incorrect. You're forgetting that you looked at one more card from your deck, the unknown sacced card.

You looked at six cards, not five, and picked an unnecessary card to sac.

Thus all of your calculations are much worse than they should be because you're reducing the number of cards the player has actually seen. I recognize that you're not stopping to calculate exactly what each card in the opening hand. That doesn't mean that you have access to fewer cards in your deck when actually playing. I am trying to give you your alternative now and you aren't taking it.

[MistahBoweh]

So the wolf adds 2 JD, increasing his odds of drawing a weapon. Most DC decks already have this in their 40 cards. And you still haven't dealt with the lone wolf healing problem, which SoV only amplifies by reducing your resource pile, making you able to deal less damage per turn, and increasing the efficiency of lone wolf. Without allies or SS, DC should have no problem milling Majiya to death.

I never said my deck has no allies, I actually said the opposite. Why do you keep saying I play no reusable sources of damage?

[kamman13]

This is what I'm saying is incorrect. You're forgetting that you looked at one more card from your deck, the unknown sacced card.

You looked at six cards, not five, and picked an unnecessary card to sac.

Thus all of your calculations are much worse than they should be because you're reducing the number of cards the player has actually seen. I recognize that you're not stopping to calculate exactly what each card in the opening hand. That doesn't mean that you have access to fewer cards in your deck when actually playing. I am trying to give you your alternative now and you aren't taking it.

@Atomzed, DND is correct here- you would never sac a card you needed for a later turn, so your assumption 7 is incorrect. To explain it a different way,if you're looking for a T2 Puwen, you started with 6 cards, and drew 1 extra. One of those was a kris that you played, giving you effectively 6 (not 5) cards to chose a puwen from. This should increase your probabilities significantly.

[kamman13]

I never said my deck has no allies, I actually said the opposite. Why do you keep saying I play no reusable sources of damage?

Well, you've only talked about burn accumulating 40 damage thus far, and the 1.27 majiya noobtube only features burn. So I assumed that's what you were talking about.

[MistahBoweh]

As for mage vs dc, I told you, did I not? You need burn for 40 damage minimum plus 5 cards at least to sac for resources. DC does not have 40 health. Assuming you're not completely allyless, the gain can be pushed through, and you can safely have a set of Shriek of Vengeance slipped in as some cards you'd be saccing in other matchups.

I can see the deck with 2x SK. After the shrieks kill the WBTs, you can keep a full hand and loop the pair indefinitely until DC loses.

[Ringel]

I agree, assumption 7 is too strong. For a quick estimate I would use the hypergeometric calculator, but reduce deck size by 1 each time, and keep draw fixed at 6 cards (You draw 1 new card but put aside the card you needed)

P(picking one of 4 Kris in 6 cards in a 39 card deck)*P(picking one of 4 Puwen in 6 cards in a 38 card deck)*P(picking one of 8 Aldon/Jasmine in 6 cards from a 37 card deck)*P(picking one of 4 Jewelers in 6 cards in a 36 card deck)*P(picking one of 4 Ravens in 6 cards in a 35 card deck)

Repeat, starting at 41 cards.

It wont be right, but I think it will be a better eyeball estimate.

Eyeball estimates: 39 cards: Perfect hand, probability 0.0599
41 cards: Perfect hand, probability 0.0495

I want to state this again. Even if we calculate the exact probabilities, I expect they will be small, and that they will be close together.

[kamman13]

I can see the deck with 2x SK. After the shrieks kill the WBTs, you can keep a full hand and loop the pair indefinitely until DC loses.

Ah, I missed that clause. Well, I do still see problems with 2x SK, but I see that the deck is not a complete auto-loss. In any case, I don't see any point to belaboring this example further.

[kamman13]

I agree, assumption 7 is too strong. For a quick estimate I would use the hypergeometric calculator, but reduce deck size by 1 each time, and keep draw fixed at 6 cards (You draw 1 new card but put aside the card you needed)

P(picking one of 4 Kris in 6 cards in a 39 card deck)*P(picking one of 4 Puwen in 6 cards in a 38 card deck)*P(picking one of 8 Aldon/Jasmine in 6 cards from a 37 card deck)*P(picking one of 4 Jewelers in 6 cards in a 36 card deck)*P(picking one of 4 Ravens in 6 cards in a 35 card deck)

Repeat, starting at 41 cards.

It wont be right, but I think it will be a better eyeball estimate.

Eyeball estimates: 39 cards: Perfect hand, probability 0.0599
41 cards: Perfect hand, probability 0.0495

I want to state this again. Even if we calculate the exact probabilities, I expect they will be small, and that they will be close together.

Also, is it accurate in this case to just multiply the probabilities together to get the "ideal" hand probability? My recollection of stats is that technique is only allowed when the tests are completely independent from one another, which they don't seem to be in this case. Is that what your formula takes into account?