Turn 4 wins:
Mt Mt ST - KF - LB SS - TH
ST ST - KF GG - LB - ITR ITR
Is ST - KF - LB - P - ITR ML
Mt Mt Mt Is - KF GG - TH
Mt Is Is ST - KF - SS - P
Mt - KF GG - LB - TH - ML ML
Mt Mt ST - GG - SS - P - ML (drew GG off T2 preordain)
Mt Is - KF - BL SS - ITR ML
Mt Is Is HD - KF GG - LB
Is HD ST - GG GG - BL BL
Turn 5 wins:
Mt Is Is - GG - P - ITR CTM
Mt Mt - GG - LB BL SS - P
Mt Is - KF - BL BL - ITR ML (drew another KF)
Mt Is Is HD - KF - BL - ITR(I think i just messed this one up, it should be a T4 kill)
Mt Is Is - GG - LB - TH - CTM
Turn 6 wins:
M - KF GG - P P - 2ITR
It does not look like any of these hands were particularly color-screwed, which is a problem I thought might occur with only eleven turn 1 red sources. We'll see whether this problem creeps up in the mulligan hands.
The KF hands just drew a bit badly to be five turn kills instead of four. The GG hands tended to play out as 5 turn kills. 10 from GG plus 10 from other (with 5 turns of draw/mana) is more reasonable than 8 from GG plus 12 from other (in 4 turns of draw/mana)
If we mulliganed all the 5 + 6 turn kill hands (6), we'd expect to see similar results to the 6 card and worse mulligans, which are:
4 turn win: 4
5 turn win: 5
6+ turn win: 5
Which may or may not be worth the risk. 9/15 (60%) you're even or better. 11/15 (73%) you're even or worse. 40% you're worser, 27% you're better. I'm not sure which of these four numbers is the one I should be basing this decision on.
The one land hands resulted in a turn 4, and a turn 6 kill. The one that was a turn 6 looks slightly better to me at this time, but it really came down to whether they drew a land in the first two turns or not. (T3 KF is often a T4 kill) The T4 kill drew its land off the top, but still would have killed if it had drawn the second land t3. The T6 kill didn't draw a land until T4. (and I got a bit impatient with burn, if I'd held it I'd have taken them to 1 life or killed on turn 5?) The chance of not drawing a land in the top two (HD on the second turn doesn't help) is (30/53 * 33/52) = 35%, so the chance of drawing a land is 65%, which seems like it makes this a good keep.
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6 Card Keeps:
Turn 4 wins:
Mt HD ST - KF - SS - TH
Mt HD - KF - P TH - ML
Mt Mt ST - KF GG - LB
Turn 5 wins:
Mt Is Is ST ST - KF GG (Drew 3 land)
ST - GG GG - P - CTM
Mt Mt Is HD - GG - SS
Turn 6+ wins:
Mt Mt ST - KF - P TH (Drew land or orange spells)
Here the one land keep didn't have a KF, so it seems like a good keep even now. Worst case this is a T6 kill, and if I draw any burn spell in 4 draw steps it is a t5 kill.
Most of the delays in kill turn here involved keeping a hand of many land, with some action, and drawing more land. With 3 land in hand, the odds of the first two draw steps being land are (21/53 * 20/52) = 15%. If you have 4 land (or ST + 2 land, and agressively sac, which is what I was doing), it goes down to 14%. Not as much of a drop-off as you'd think. 12.4% for 5 land (or 1 land + 2 ST, or 3 + ST). You can't play around this 15% chance, but it can be discouraging. It doesn't help that I have ~6 more cards that are just as good/bad as a land, so if you factor those in, it is more like 25% of drawing a 0-impact card in both of the first two draw steps. That's pretty encouraging.
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5 Card Keeps:
Turn 4 wins:
Mt - KF GG - TH - ML
Turn 5 wins:
HD - KF KF KF - TH
Turn 6 wins:
Is Is Is - KF - SS (drew 3x KF)
Is HD ST - KF - ITR
50% turn 5 or better here, which is something. But going to 5 is not great, because you have to include the 4 carders as well. so going to 5 gives you
Turn 4: 1
Turn 5: 2
Turn 6+: 4
Which is only 42% turn 5 or better.
Obviously, these 5 card keeps are all pretty speculative. They either have one land, and KF, or 3 land + KF. Neither of those are very good times, and we see 2 additional 0-impact cards across these 25 cards. (better than the 6/60 ratio at least?) The turn 5 wins hit turn 2 and 3 KFs. The turn 4 win was t2 KF (hit the land) The T6 wins had either no action, or no land. (emphasizing what the hand already lacked)
Still, it could be much, much worse than 42% T5 or better going to 5.
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4 Card Keeps:
Turn 5 wins:
KF - LB - P - ML
Turn 6+ wins:
Is - SS - P TH
KF - LB - TH - ML
Obviously these are extremely speculative hands. Two have no land!
I never went to three, but it is not terribly hard to imagine a turn 4 kill off Land + KF + something. (which none of these hands are) T2 KF, (one card in hand), T3 preordain, DD spell (1 cards in hand, opponent at ~11), 2 draw + burn, or 2 burn and opponent is dead.
Probably better odds than the KF + LB + TH + ML hand had... (plan = draw two lands (25%) to get a t3 KF, then draw another land off the TH (~50%) to cast the LB (50%) and get in for 10 on turn 4. Then draw draw spell (<20%) into burn spell (~50%) into opponent dead turn 5! Overall, thats probably 0.5% to kill on T5 or better.
KF + 2 Land + non-land-non-terrible is ~(4/60 * 24/59 * 23/58 * 26/57) * 4* 3*2*1/2(order irrelevant) ~= 4% You probably need to get lucky again on the T3-4 draw step, but a HD as one of the lands, or a preordain as the something could substantially improve your chances there. Perhaps up to as high as 6-8% overall! That's probably better than the KF-LB-TH-ML hand had.
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Mulligans:
7 Card Mulligans:
6 land - BL
Mt Mt - LB BL BL - TH - ML
Is HD - GG - LB SS - P - ITR
Mt Is ST ST - BL - P TH
Is ST ST - BL - ITR ITR ML
Is Is Is Is Mt - BL - TH
Mt Is HD - BL SS - P - ITR
Mt Mt Is - BL BL SS - CTM
Mt Mt Is Is - LB BL SS
Is Is - KF KF GG - TH - ML
Mt - GG - BL SS SS - P - ML
Is - GG - BL SS - TH TH - CTM
Is ST - LB - P TH TH - ITR
Is Is - GG - LB LB BL - ML
6 Card Mulligans:
3Land - LB - 2ITR
No Land (reporting was lax in the first few hands)
Mt ST HD - BL - TH - ML
Is ST - LB LB SS - CTM
KF - BL SS - P - CTM
Is Is HD HD - SS - P
Mt Mt Is ST - SS - ITR
5 Card Mulligans:
Mt Is HD - LB - CTM
BL BL SS - ITR ML
Mt - SS - TH TH - ML
The chance of not drawing a KF in the top two (if you don't have one) is (49/53 * 48/52) = 85%, so a 15% chance of drawing at least one KF if you don't have one, in the first two turns.(21% in the first three, since that could be still fast enough). So a no-draw, no-KF hand seems like a good ship. Halimar Depths turn 1 basically gives you the first three draws in one step, but you also only get those draws for the first four turns, so it just gives you the 21% on turn 2, instead of across turns 2, 3, and 4. (aka it makes you no less likely to be 100% screwed)
If you have a hand like Island-RedSource-Preordain, and want to see what your chances of aggressively hitting a KF turn 2 is (ship both if not KF to get a random card), you again have the 21% chance of hitting it on the turn 1 Preordain, but unlike Halimar Depths, you actually have your draw step turn 2 to hit it, and your draw step turn 3 may not be too late. Also, unlike HD, you get new cards on T2, T3, not cards you already know won't help you. (Like the "Sage Owl, see 4 lands, scoop" problem).
Therefore, if we have the P + U + R hand, and want to figure our KF chances, we have the top 3 (preordain pushes two + random draw), plus the next card (T2 draw) plus probably the next card (T3 draw) to try to hit the KF. The odds of hitting a KF T2 become (49/53 * 48/52 * 47/51 * 46/50) = 72%, so a 28% chance of it working by T2 (34% by turn 3)
If you have double-Preordain + U + R, you're really hoping to hit the KF by turn 3, but then you have your 3 other cards, plus one preordain draw, to try to kill them on turn 4.
You have your same shot of hitting the KF on your first preordain + draw phase (28%). If that doesn't work, you bring your total up to 50% of hitting the KF with the second preordain + third draw phase.
So, the double-Preordain + good mana + good instant+sorcery hand may be worth keeping. Treasure Hunt math is harder, so I'm not sure how good those hands are, or how risky. Some of those 7 card hands, with 2+ land, and 2+ draw spells might have been keepers, but it's so random.
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Key: (and general order)
Land:
Is = Island
Mt = Mountain
ST = Scalding Tarn
HD = Halimar Depths
Creatures:
KF = Kiln Fiend
GG = Goblin Guide
Damage:
LB = Lightning Bolt
BL = Burst Lightning
SS = Staggershock
Draw:
P = Preordain
TH = Treasure HuntOther:
ITR = Into the Roil
ML = Mana Leak
CTM = Call To Mind
Call to mind gets an "other", even though it is similar to Staggershock:
-It does 2-4 damage, compared to SS's 4.
-It costs 3 mana, of lax color requirements
-It can give you the "rebound" on the same turn you cast it, instead of next turn
Because:
-It does 0 damage up front (though often 2-3 on the "rebound")
-It requires 4 mana to cast two spells in the same turn
-You have to pay for the "rebound" the next turn, which can interfere with casting another 3cc spell, or just from colored mana troubles going double-bolt, or double-blue spell.
It is definately better than ITR or ML for goldfishing purposes. ITR could have infinite value, bouncing a wall or KHE (Time walk, as an instant?), or could have 0 value.
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