There are two problems to solve here.
1) Finding the max values per type. This will get the Max value per StakeType and make sure that we do the exercise only for the wanted events and group type.
SELECT StakeGroupTypeID, EventID, StakeTypeID, MAX(StakeValue) AS MaxStakeValue
FROM SI_STAKES
WHERE Stake.[EventID]=6
AND Stake.[StakeGroupTypeID]=1
GROUP BY StakeGroupTypeID, EventID, StakeTypeID
2) Then we need to get only one return back for that value since it may be present more then once.
Using the Max Value, we must find a unique row for each I usually do this by getting the Max ID is has the added advantage of getting me the most recent entry.
SELECT MAX(SMaxID.ID) AS ID
FROM SI_STAKES AS SMaxID
INNER JOIN (
SELECT StakeGroupTypeID, EventID, StakeTypeID, MAX(StakeValue) AS MaxStakeValue
FROM SI_STAKES
WHERE Stake.[EventID]=6
AND Stake.[StakeGroupTypeID]=1
GROUP BY StakeGroupTypeID, EventID, StakeTypeID
) AS SMaxVal ON SMaxID.StakeTypeID = SMaxVal.StakeTypeID
AND SMaxID.StakeValue = SMaxVal.MaxStakeValue
AND SMaxID.EventID = SMaxVal.EventID
AND SMaxID.StakeGroupTypeID = SMaxVal.StakeGroupTypeID
3) Now that we have the ID's of the rows that we want, we can just get that information.
SELECT Stakes.ID, Stakes.StakeValue, SType.StakeName, SProv.ProviderName
FROM SI_STAKES AS Stakes
INNER JOIN SI_STAKESTYPES AS SType ON Stake.[StakeTypeID] = SType.[ID]
INNER JOIN SI_PROVIDERS AS SProv ON Stake.[ProviderID] = SProv.[ID]
WHERE Stake.ID IN (
SELECT MAX(SMaxID.ID) AS ID
FROM SI_STAKES AS SMaxID
INNER JOIN (
SELECT StakeGroupTypeID, EventID, StakeTypeID, MAX(StakeValue) AS MaxStakeValue
FROM SI_STAKES
WHERE Stake.[EventID]=6
AND Stake.[StakeGroupTypeID]=1
GROUP BY StakeGroupTypeID, EventID, StakeTypeID
) AS SMaxVal ON SMaxID.StakeTypeID = SMaxVal.StakeTypeID
AND SMaxID.StakeValue = SMaxVal.MaxStakeValue
AND SMaxID.EventID = SMaxVal.EventID
AND SMaxID.StakeGroupTypeID = SMaxVal.StakeGroupTypeID
)