MYSQL query with ORDER BY and two LIMITs

Hello
I have DB like this

Name chance winner
a 245 0
b 154 0
c 5 0
d 12 0
e 300 0
f 40 1
g 2 0
h 30 0
i 80 0
j 250 1


- I want a qury which gives me top 4 highet chance and top 2 lowest chance
- In total the record should be 6 records
- If winner is flaged 1 then it should not be considred

In above excmple we should get result like

e
a
b
i
c
g

I am using this query but its not working
SELECT * FROM `DB_name` WHERE winner !='1' ORDER BY `chance` DESC LIMIT 4, `chance` ASC LIMIT 2