Edit - Thanks for the feedback, I realize it was unedited and rough - I was submitting it for feedback on the content, obviously if anything was going online it would need serious tuneups (probably even a rewrite of the english parts). Anyways I haven't seen any support for the maths so for the time being I'll satiate my need to write with drafting/standard articles, which are usually far easier and faster to write.
Statistics and Magic The Gathering Quick aside - if anyone's interested in this type of content please let me know, and I'll cover the topics of curving out and mulligans in more depth. Sorry index 1 came out kinda chunky - don't know how to fix it in mtgsalvation
Maths is hard (for some of us). Magic the gathering is at its core a highly mathematical game. Deck building has no psychology, the best deck for you is the deck that gives you the highest % chance of winning. This article is about the basics of maths and deck building. I will post quick excel instructions beneath each segment so people can create their own statistics charts (and hopefully input their own decks into them). I am no expert and my formulae’s do not cover everything, however hopefully there is something that can be learned or copied from this article.
The odds of a card being in your top card is 1/60. The problem always arises at the second card. Say you run 2 copies of a card. You have to calculate the odds of drawing that card in the first draw only, on the second draw only, on both draws and on neither. Move it up to 3 and we have 9 spot calculations. Personally, I use the hypgeomdist formulae (Index 1) to determine the odds. It’s a bit complicated but essentially, it allows you to calculate multiple draws.
Starting Hands odds – See Index 1 • Determine the number of copies you want to draw (a)
• Determine the number of cards drawn (opening hands 7) (b)
• Determine the number of cards you want to draw (total) (c)
• Determine the number of cards in your deck (d)
• Punch into excel =Hypgeomdist(a,b,c,d)
Using this formulae we can already punch in some mulligan statistics for various decks. The difference between 25 and 24 land in the opening 7 increases your odds of drawing 5-6-7 (often mulligan) hands by 1.64% and decreases 0-1 landers by 2.02% (see index 1 for numbers). You must factor in the skewing of future draws as well towards drawing more land. This will be covered shortly and is the bulk of this article.
See index 1 for a quick mulligan statistics guide.
Deckbuilding Odds - Starting hands Continued Skewing - See Index 2
The skewing odds are a little complicated however are very useful in determining the exact number of lands you want to run. For our formulae, we will only look at the effects of skewing on hands we keep. If you just need a land in the next 3 cards just use the formulae = Hypgeomdist(1,3,cards wanted, cards in deck)+ Hypgeomdist(2,3,cards wanted, cards in deck)+ Hypgeomdist(3,3,cards wanted, cards in deck)
• Determine the number of land you want to run (25 example)
• Find the hands you are willing to keep (landrange is simple)
• Turn them into 100% (if your only counting keepable hands)
• Multiply that by the good land figures for hypgeomdist 5/53/23/(1 or 2)
• The residual is negative skewing
• Multiple this by the % of hands kept
• Repeat for the other figures and compare
• If you want to get really technical, repeat this figure for 6 cards and multiply it by the odds of you having to mulligan (1-odds of keeping opening hand)*100 =X%. Then add this figure to the positive hands.
1. First we need to determine the number of lands we run and the range we are winning to keep. For this example we shall use 25 lands and keeping 2-4 lands.
2. Secondly we will need to turn the 3 figures we get (for 2, 3 and 4) by using the index 1 formulae into % figures so that the 3 add up to 100%. This is easily done by adding the 3 together, dividing 100 by them. Then you multiply this new figure by the old figures for 2, 3 and 4 cards. They should total 100%
3. Thirdly we shall multiply one figure by (hypgeomdist 5 (see step 3/4) for the odds of 0, 1, 2, 3, 4, 5 copies drawn. These should total the initial figure. You can shorten this by only calculating the positive no of drawn (say 1, 2 or 3 lands), and just marking the rest off as negative. To keep this simple, we shall be comparing hands with between 4 and 6 lands.
Alternately, you can play with the positive number of lands drawn depending on your acceptable number of lands. For example, in a 2land hand, drawing 1 may be unacceptable in the top 5 however drawing 3 may be fine. We shall not discuss this here since it would involve more lengthy formulae, however feel free to play around with it if you want more accurate figures.
4. Repeat this for the other 2 figures in step 2, here being 3 lands in the opening hand and 4 lands in the opening hands
5. Multiply these figures into the % figures found in 2. This will give you a % of hands that draws well that you keep. Then multiply that into the %you keep for a total
6. We then repeat this process for the figures we want to compare our skewing to, here would be 24 and 26 land.
7. Since we are looking at the good figures, compare them to each other, the higher the better.
Lets try this out for 24-26 lands. I use excel since I find that faster than doing the numbers manually. The only formulae used is hypgeomdist which is explained in index 1 if you'd rather follow manually. You can see the working used in Index 2.
Summary - 24 lands is best if you need 4/6 lands by t5 since it skews the most positively - despite having the lowest % of opening hands kept Statistics and Magic The Gathering
Maths is hard (for some of us). Magic the gathering is at its core a highly mathematical game. Deck building has no psychology, the best deck for you is the deck that gives you the highest % chance of winning. This article is about the basics of maths and deck building. I will post quick excel instructions beneath each segment so people can create their own statistics charts (and hopefully input their own decks into them). I am no expert and my formulae’s do not cover everything, however hopefully there is something that can be learned or copied from this article.
The odds of a card being in your top card is 1/60. The problem always arises at the second card. Say you run 2 copies of a card. You have to calculate the odds of drawing that card in the first draw only, on the second draw only, on both draws and on neither. Move it up to 3 and we have 9 spot calculations. Personally, I use the hypgeomdist formulae (Index 1) to determine the odds. It’s a bit complicated but essentially, it allows you to calculate multiple draws.
Starting Hands odds – See Index 1
• Determine the number of copies you want to draw (a)
• Determine the number of cards drawn (opening hands 7) (b)
• Determine the number of cards you want to draw (total) (c)
• Determine the number of cards in your deck (d)
• Punch into excel =Hypgeomdist(a,b,c,d)
Using this formulae we can already punch in some mulligan statistics for various decks. The difference between 25 and 24 land in the opening 7 increases your odds of drawing 5-6-7 (often mulligan) hands by 1.64% and decreases 0-1 landers by 2.02% (see index 1 for numbers). You must factor in the skewing of future draws as well towards drawing more land. This will be covered shortly and is the bulk of this article.
See index 1 for a quick mulligan statistics guide.
Deckbuilding Odds - Starting hands Continued Skewing - See Index 2
The skewing odds are a little complicated however are very useful in determining the exact number of lands you want to run. For our formulae, we will only look at the effects of skewing on hands we keep. If you just need a land in the next 3 cards just use the formulae = Hypgeomdist(1,3,cards wanted, cards in deck)+ Hypgeomdist(2,3,cards wanted, cards in deck)+ Hypgeomdist(3,3,cards wanted, cards in deck)
• Determine the number of land you want to run (25 example)
• Find the hands you are willing to keep (landrange is simple)
• Turn them into 100% (if your only counting keepable hands)
• Multiply that by the good land figures for hypgeomdist 5/53/23/(1 or 2)
• The residual is negative skewing
• Multiple this by the % of hands kept
• Repeat for the other figures and compare
• If you want to get really technical, repeat this figure for 6 cards and multiply it by the odds of you having to mulligan (1-odds of keeping opening hand)*100 =X%. Then add this figure to the positive hands.
1. First we need to determine the number of lands we run and the range we are winning to keep. For this example we shall use 25 lands and keeping 2-4 lands.
2. Secondly we will need to turn the 3 figures we get (for 2, 3 and 4) by using the index 1 formulae into % figures so that the 3 add up to 100%. This is easily done by adding the 3 together, dividing 100 by them. Then you multiply this new figure by the old figures for 2, 3 and 4 cards. They should total 100%
3. Thirdly we shall multiply one figure by (hypgeomdist 5 (see step 3/4) for the odds of 0, 1, 2, 3, 4, 5 copies drawn. These should total the initial figure. You can shorten this by only calculating the positive no of drawn (say 1, 2 or 3 lands), and just marking the rest off as negative. To keep this simple, we shall be comparing hands with between 4 and 6 lands.
Alternately, you can play with the positive number of lands drawn depending on your acceptable number of lands. For example, in a 2land hand, drawing 1 may be unacceptable in the top 5 however drawing 3 may be fine. We shall not discuss this here since it would involve more lengthy formulae, however feel free to play around with it if you want more accurate figures.
4. Repeat this for the other 2 figures in step 2, here being 3 lands in the opening hand and 4 lands in the opening hands
5. Multiply these figures into the % figures found in 2. This will give you a % of hands that draws well that you keep. Then multiply that into the %you keep for a total
6. We then repeat this process for the figures we want to compare our skewing to, here would be 24 and 26 land.
7. Since we are looking at the good figures, compare them to each other, the higher the better.
Lets try this out for 24-26 lands. I use excel since I find that faster than doing the numbers manually. The only formulae used is hypgeomdist which is explained in index 1 if you'd rather follow manually. You can see the working used in Index 2.
Summary - 24 lands is best if you need 4/6 lands by t5 since it skews the most positively - despite having the lowest % of opening hands kept
Index 1
Index 1
Starting Hand Odds
Excel
Hypgeomdist(the number of copies you want to draw, no of cards drawn, no of cards in your deck you want to draw, cards in deck)
Maths
For those of you mathematically inclined, here is the simplest explanation of the formulae I could find, many thanks to Jon Prywes
H (n) = C (X, n) * C (Y - X, Z - n) / C (Y, Z)
X standing for the number of a certain card that you have in the deck.
Y is the number of cards in the deck.
Z is the number of cards you are drawing.
N is the number you are checking for.
Index 2
All figures will be rounded to 3 decimal places
24 lands
Step 1
24 Lands -
Odds of drawing 2 land = hypgeomdist (2,7,24,60) =0.269
Odds of drawing 3 land = hypgeomdist (3,7,24,60) =0.309
Odds of drawing 4 land = hypgeomdist (4,7,24,60) =0.196
Step 2
Total =(sum 0.269+0.309+0.196) =0.775 or 77.5%
=100/77.5= 1.290...
1.29*0.269=0.347...
1.29*0.309=0.399... (round up to .4 so they equal 100%)
1.29*0.196=0.253...
Step 5?
0.691*0.347= 0.24
0.865*0.4= 0.342
0.729*0.253=0.184
240+.342+.184=.766
=.766
.776*.775
=.6014
60.14% of hands end up keepable with between 4/6 lands by t5
25 Lands
Step 1
25 lands
Odds of drawing 2 land = hypgeomdist (2,7,25,60) =0.252
Odds of drawing 3 land = hypgeomdist (3,7,25,60) =0.312
Odds of drawing 4 land = hypgeomdist (4,7,25,60) =0.214
Step 2
total =( sum 0.252+0.312+0.214)=0.718 or 77.8%
100/77.8=1.285
1.285*0.252=0.324
1.285*0.312=0.401
1.285*0.214=0.275
Step 5
719*.324 =.233
853*.401=.342
.696*.275 =.191
=.233+.342+.191=. 766
.766*.778 =.5959
=59.59% of hands end up keepable with between 4/6 lands by t5
26 lands
Step 1
Odds of drawing 2 land = hypgeomdist (2,7,26,60) =.234
Odds of drawing 3 land = hypgeomdist (3,7,26,60) =.312
Odds of drawing 4 land = hypgeomdist (4,7,26,60) =.232
Step 2
total =(.234+.312+.232) =.778
100/77.8=1.285
1.285*.234=.301
1.285*.312=.401
1.285*.232=.298
Step 5
=.744*.301 =.224
=.838*.401 =.336
=.662*.298 =.197
.224+.336+.197=.757
.757*.778=.589
=58.9% of hands end up keepable with between 4/6 lands by t5
I'm sorry, the only thing I came to give was advice;
You need better editing. You have missed punctuation marks, ' claims possession, etc.
% should never be used unless it's after a number, if that's not the case, always write it out.
Writers are often told not to seek publishing until they have edited it enough. If I were a publisher I would reject it, you didn't even edit your first sentence correctly!
I wish you better luck in the future, and remember, ****ing edit it until you can't, then give it to someone else to edit some more.
Thanks for the feedback, it's been really useful. Honestly when I submitted this it was with an email asking whether the content was ok (and in there I admitted I may need to rewrite the english). So far I've had no comment on the content whatsoever. Whether this is because of the bad english, I don't know, but in future, it'll just be easier to write something generic and easy to follow than stuff like this. It's good to know the punctuation is turning people away (all feedback is good feedback), but at the same time its a tad disheartening nobody has made any feedback on the content (and yes I know the issues are linked). Therefore from here on I plan to stick to more generic articles with perhaps a sprinkling of maths or just the end result from these formulae rather than the poorly punctuated block you see before you.
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Statistics and Magic The Gathering
Quick aside - if anyone's interested in this type of content please let me know, and I'll cover the topics of curving out and mulligans in more depth.
Sorry index 1 came out kinda chunky - don't know how to fix it in mtgsalvation
Maths is hard (for some of us). Magic the gathering is at its core a highly mathematical game. Deck building has no psychology, the best deck for you is the deck that gives you the highest % chance of winning. This article is about the basics of maths and deck building. I will post quick excel instructions beneath each segment so people can create their own statistics charts (and hopefully input their own decks into them). I am no expert and my formulae’s do not cover everything, however hopefully there is something that can be learned or copied from this article.
The odds of a card being in your top card is 1/60. The problem always arises at the second card. Say you run 2 copies of a card. You have to calculate the odds of drawing that card in the first draw only, on the second draw only, on both draws and on neither. Move it up to 3 and we have 9 spot calculations. Personally, I use the hypgeomdist formulae (Index 1) to determine the odds. It’s a bit complicated but essentially, it allows you to calculate multiple draws.
Starting Hands odds – See Index 1
• Determine the number of copies you want to draw (a)
• Determine the number of cards drawn (opening hands 7) (b)
• Determine the number of cards you want to draw (total) (c)
• Determine the number of cards in your deck (d)
• Punch into excel =Hypgeomdist(a,b,c,d)
Using this formulae we can already punch in some mulligan statistics for various decks. The difference between 25 and 24 land in the opening 7 increases your odds of drawing 5-6-7 (often mulligan) hands by 1.64% and decreases 0-1 landers by 2.02% (see index 1 for numbers). You must factor in the skewing of future draws as well towards drawing more land. This will be covered shortly and is the bulk of this article.
See index 1 for a quick mulligan statistics guide.
Deckbuilding Odds - Starting hands Continued Skewing - See Index 2
The skewing odds are a little complicated however are very useful in determining the exact number of lands you want to run. For our formulae, we will only look at the effects of skewing on hands we keep. If you just need a land in the next 3 cards just use the formulae = Hypgeomdist(1,3,cards wanted, cards in deck)+ Hypgeomdist(2,3,cards wanted, cards in deck)+ Hypgeomdist(3,3,cards wanted, cards in deck)
• Determine the number of land you want to run (25 example)
• Find the hands you are willing to keep (landrange is simple)
• Turn them into 100% (if your only counting keepable hands)
• Multiply that by the good land figures for hypgeomdist 5/53/23/(1 or 2)
• The residual is negative skewing
• Multiple this by the % of hands kept
• Repeat for the other figures and compare
• If you want to get really technical, repeat this figure for 6 cards and multiply it by the odds of you having to mulligan (1-odds of keeping opening hand)*100 =X%. Then add this figure to the positive hands.
1. First we need to determine the number of lands we run and the range we are winning to keep. For this example we shall use 25 lands and keeping 2-4 lands.
2. Secondly we will need to turn the 3 figures we get (for 2, 3 and 4) by using the index 1 formulae into % figures so that the 3 add up to 100%. This is easily done by adding the 3 together, dividing 100 by them. Then you multiply this new figure by the old figures for 2, 3 and 4 cards. They should total 100%
3. Thirdly we shall multiply one figure by (hypgeomdist 5 (see step 3/4) for the odds of 0, 1, 2, 3, 4, 5 copies drawn. These should total the initial figure. You can shorten this by only calculating the positive no of drawn (say 1, 2 or 3 lands), and just marking the rest off as negative. To keep this simple, we shall be comparing hands with between 4 and 6 lands.
Alternately, you can play with the positive number of lands drawn depending on your acceptable number of lands. For example, in a 2land hand, drawing 1 may be unacceptable in the top 5 however drawing 3 may be fine. We shall not discuss this here since it would involve more lengthy formulae, however feel free to play around with it if you want more accurate figures.
4. Repeat this for the other 2 figures in step 2, here being 3 lands in the opening hand and 4 lands in the opening hands
5. Multiply these figures into the % figures found in 2. This will give you a % of hands that draws well that you keep. Then multiply that into the %you keep for a total
6. We then repeat this process for the figures we want to compare our skewing to, here would be 24 and 26 land.
7. Since we are looking at the good figures, compare them to each other, the higher the better.
Lets try this out for 24-26 lands. I use excel since I find that faster than doing the numbers manually. The only formulae used is hypgeomdist which is explained in index 1 if you'd rather follow manually. You can see the working used in Index 2.
Summary - 24 lands is best if you need 4/6 lands by t5 since it skews the most positively - despite having the lowest % of opening hands kept Statistics and Magic The Gathering
Maths is hard (for some of us). Magic the gathering is at its core a highly mathematical game. Deck building has no psychology, the best deck for you is the deck that gives you the highest % chance of winning. This article is about the basics of maths and deck building. I will post quick excel instructions beneath each segment so people can create their own statistics charts (and hopefully input their own decks into them). I am no expert and my formulae’s do not cover everything, however hopefully there is something that can be learned or copied from this article.
The odds of a card being in your top card is 1/60. The problem always arises at the second card. Say you run 2 copies of a card. You have to calculate the odds of drawing that card in the first draw only, on the second draw only, on both draws and on neither. Move it up to 3 and we have 9 spot calculations. Personally, I use the hypgeomdist formulae (Index 1) to determine the odds. It’s a bit complicated but essentially, it allows you to calculate multiple draws.
Starting Hands odds – See Index 1
• Determine the number of copies you want to draw (a)
• Determine the number of cards drawn (opening hands 7) (b)
• Determine the number of cards you want to draw (total) (c)
• Determine the number of cards in your deck (d)
• Punch into excel =Hypgeomdist(a,b,c,d)
Using this formulae we can already punch in some mulligan statistics for various decks. The difference between 25 and 24 land in the opening 7 increases your odds of drawing 5-6-7 (often mulligan) hands by 1.64% and decreases 0-1 landers by 2.02% (see index 1 for numbers). You must factor in the skewing of future draws as well towards drawing more land. This will be covered shortly and is the bulk of this article.
See index 1 for a quick mulligan statistics guide.
Deckbuilding Odds - Starting hands Continued Skewing - See Index 2
The skewing odds are a little complicated however are very useful in determining the exact number of lands you want to run. For our formulae, we will only look at the effects of skewing on hands we keep. If you just need a land in the next 3 cards just use the formulae = Hypgeomdist(1,3,cards wanted, cards in deck)+ Hypgeomdist(2,3,cards wanted, cards in deck)+ Hypgeomdist(3,3,cards wanted, cards in deck)
• Determine the number of land you want to run (25 example)
• Find the hands you are willing to keep (landrange is simple)
• Turn them into 100% (if your only counting keepable hands)
• Multiply that by the good land figures for hypgeomdist 5/53/23/(1 or 2)
• The residual is negative skewing
• Multiple this by the % of hands kept
• Repeat for the other figures and compare
• If you want to get really technical, repeat this figure for 6 cards and multiply it by the odds of you having to mulligan (1-odds of keeping opening hand)*100 =X%. Then add this figure to the positive hands.
1. First we need to determine the number of lands we run and the range we are winning to keep. For this example we shall use 25 lands and keeping 2-4 lands.
2. Secondly we will need to turn the 3 figures we get (for 2, 3 and 4) by using the index 1 formulae into % figures so that the 3 add up to 100%. This is easily done by adding the 3 together, dividing 100 by them. Then you multiply this new figure by the old figures for 2, 3 and 4 cards. They should total 100%
3. Thirdly we shall multiply one figure by (hypgeomdist 5 (see step 3/4) for the odds of 0, 1, 2, 3, 4, 5 copies drawn. These should total the initial figure. You can shorten this by only calculating the positive no of drawn (say 1, 2 or 3 lands), and just marking the rest off as negative. To keep this simple, we shall be comparing hands with between 4 and 6 lands.
Alternately, you can play with the positive number of lands drawn depending on your acceptable number of lands. For example, in a 2land hand, drawing 1 may be unacceptable in the top 5 however drawing 3 may be fine. We shall not discuss this here since it would involve more lengthy formulae, however feel free to play around with it if you want more accurate figures.
4. Repeat this for the other 2 figures in step 2, here being 3 lands in the opening hand and 4 lands in the opening hands
5. Multiply these figures into the % figures found in 2. This will give you a % of hands that draws well that you keep. Then multiply that into the %you keep for a total
6. We then repeat this process for the figures we want to compare our skewing to, here would be 24 and 26 land.
7. Since we are looking at the good figures, compare them to each other, the higher the better.
Lets try this out for 24-26 lands. I use excel since I find that faster than doing the numbers manually. The only formulae used is hypgeomdist which is explained in index 1 if you'd rather follow manually. You can see the working used in Index 2.
Summary - 24 lands is best if you need 4/6 lands by t5 since it skews the most positively - despite having the lowest % of opening hands kept
Index 1
Index 1
Starting Hand Odds
Excel
Hypgeomdist(the number of copies you want to draw, no of cards drawn, no of cards in your deck you want to draw, cards in deck)
Maths
For those of you mathematically inclined, here is the simplest explanation of the formulae I could find, many thanks to Jon Prywes
H (n) = C (X, n) * C (Y - X, Z - n) / C (Y, Z)
X standing for the number of a certain card that you have in the deck.
Y is the number of cards in the deck.
Z is the number of cards you are drawing.
N is the number you are checking for.
Cards wanted Opening Hands 7 cards deck of 60
1 88.3% 11.7%
2 77.9% 21.0% 1.2%
3 68.5% 28.2% 3.3% 0.1%
4 60.1% 33.6% 5.9% 0.4% 0.0%
5 52.5% 37.5% 9.0% 0.9% 0.0% 0.0%
6 45.9% 40.1% 12.3% 1.6% 0.1% 0.0% 0.0%
7 39.9% 41.6% 15.6% 2.7% 0.2% 0.0% 0.0% 0.0%
8 34.6% 42.2% 18.8% 3.9% 0.4% 0.0% 0.0% 0.0%
9 30.0% 42.0% 21.9% 5.4% 0.7% 0.0% 0.0% 0.0%
10 25.9% 41.1% 24.7% 7.2% 1.1% 0.1% 0.0% 0.0%
11 22.2% 39.8% 27.2% 9.1% 1.6% 0.1% 0.0% 0.0%
12 19.1% 38.1% 29.3% 11.1% 2.2% 0.2% 0.0% 0.0%
13 16.3% 36.1% 31.0% 13.2% 3.0% 0.4% 0.0% 0.0%
14 13.9% 34.0% 32.3% 15.4% 3.9% 0.5% 0.0% 0.0%
15 11.8% 31.6% 33.2% 17.6% 5.0% 0.8% 0.1% 0.0%
16 9.9% 29.2% 33.7% 19.7% 6.2% 1.1% 0.1% 0.0%
17 8.3% 26.8% 33.9% 21.7% 7.6% 1.4% 0.1% 0.0%
18 7.0% 24.4% 33.7% 23.6% 9.1% 1.9% 0.2% 0.0%
19 5.8% 22.1% 33.2% 25.4% 10.7% 2.5% 0.3% 0.0%
20 4.8% 19.9% 32.4% 27.0% 12.4% 3.1% 0.4% 0.0%
21 4.0% 17.7% 31.3% 28.3% 14.2% 3.9% 0.5% 0.0%
22 3.3% 15.7% 30.0% 29.4% 16.0% 4.8% 0.7% 0.0%
23 2.7% 13.8% 28.6% 30.3% 17.8% 5.8% 1.0% 0.1%
24 2.2% 12.1% 26.9% 30.9% 19.6% 6.9% 1.3% 0.1% (234)77.5%
25 1.7% 10.5% 25.2% 31.2% 21.4% 8.2% 1.6% 0.1% (234)77.8%
26 1.4% 9.1% 23.4% 31.2% 23.2% 9.6% 2.0% 0.2%
27 1.1% 7.7% 21.6% 31.0% 24.8% 11.0% 2.5% 0.2%
28 0.9% 6.6% 19.7% 30.5% 26.3% 12.6% 3.1% 0.3%
29 0.7% 5.5% 17.9% 29.8% 27.6% 14.3% 3.8% 0.4%
30 0.5% 4.6% 16.1% 28.8% 28.8% 16.1% 4.6% 0.5%
0 1 2 3 4 5 6 7
Copies Drawn
Index 2
All figures will be rounded to 3 decimal places
24 lands
Step 1
24 Lands -
Odds of drawing 2 land = hypgeomdist (2,7,24,60) =0.269
Odds of drawing 3 land = hypgeomdist (3,7,24,60) =0.309
Odds of drawing 4 land = hypgeomdist (4,7,24,60) =0.196
Step 2
Total =(sum 0.269+0.309+0.196) =0.775 or 77.5%
=100/77.5= 1.290...
1.29*0.269=0.347...
1.29*0.309=0.399... (round up to .4 so they equal 100%)
1.29*0.196=0.253...
Step 3-4
2land
=hypgeomdist (2, 5, 22, 53) =36.2%
= hypgeomdist (3, 5, 22, 53) =25%
= hypgeomdist (4, 5, 22, 53) =7.9% (total 69.1%)
3land
= hypgeomdist (1,5,21,53) 26.3%
= hypgeomdist (2,5,21,53) 36.3%
= hypgeomdist (3,5,21,53) 23% (total 85.6%)
4land
= hypgeomdist (0,5,20,53) 8.3%
= hypgeomdist (1,5,20,53) 28.5%
= hypgeomdist (2,5,20,53) 36.1% (total 72.9%)
Step 5?
0.691*0.347= 0.24
0.865*0.4= 0.342
0.729*0.253=0.184
240+.342+.184=.766
=.766
.776*.775
=.6014
60.14% of hands end up keepable with between 4/6 lands by t5
25 Lands
Step 1
25 lands
Odds of drawing 2 land = hypgeomdist (2,7,25,60) =0.252
Odds of drawing 3 land = hypgeomdist (3,7,25,60) =0.312
Odds of drawing 4 land = hypgeomdist (4,7,25,60) =0.214
Step 2
total =( sum 0.252+0.312+0.214)=0.718 or 77.8%
100/77.8=1.285
1.285*0.252=0.324
1.285*0.312=0.401
1.285*0.214=0.275
Step 3/4
2land
=hypgeomdist (2, 5, 23, 53) =.358
=hypgeomdist (3, 5, 23, 53) =.268
=hypgeomdist (4, 5, 23, 53) =.093 =.719
3Land
= hypgeomdist (1,5,22,53) =.241
= hypgeomdist (2,5,22,53) =.362
= hypgeomdist (3,5,22,53) =.25 =.853
4land
= hypgeomdist (0,5,21,53) .07
= hypgeomdist (1,5,21,53) .263
= hypgeomdist (2,5,21,53) .363 = .696
Step 5
719*.324 =.233
853*.401=.342
.696*.275 =.191
=.233+.342+.191=. 766
.766*.778 =.5959
=59.59% of hands end up keepable with between 4/6 lands by t5
26 lands
Step 1
Odds of drawing 2 land = hypgeomdist (2,7,26,60) =.234
Odds of drawing 3 land = hypgeomdist (3,7,26,60) =.312
Odds of drawing 4 land = hypgeomdist (4,7,26,60) =.232
Step 2
total =(.234+.312+.232) =.778
100/77.8=1.285
1.285*.234=.301
1.285*.312=.401
1.285*.232=.298
Step 3/4
2land
=hypgeomdist (2, 5, 24, 53) =.351
=hypgeomdist (3, 5, 24, 53) =.286
=hypgeomdist (4, 5, 24, 53) =.107 =.744
3Land
= hypgeomdist (1,5,23,53) =.212
= hypgeomdist (2,5,23,53) =.358
= hypgeomdist (3,5,23,53) =.268 =.838
4land
= hypgeomdist (0,5,22,53) =.059
= hypgeomdist (1,5,22,53) =.241
= hypgeomdist (2,5,22,53) =.362=.662
Step 5
=.744*.301 =.224
=.838*.401 =.336
=.662*.298 =.197
.224+.336+.197=.757
.757*.778=.589
=58.9% of hands end up keepable with between 4/6 lands by t5
You need better editing. You have missed punctuation marks, ' claims possession, etc.
% should never be used unless it's after a number, if that's not the case, always write it out.
Writers are often told not to seek publishing until they have edited it enough. If I were a publisher I would reject it, you didn't even edit your first sentence correctly!
I wish you better luck in the future, and remember, ****ing edit it until you can't, then give it to someone else to edit some more.