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Financial Highlights (Details) (USD $)
12 Months Ended
Dec. 31, 2014
Dec. 31, 2013
Class 0 Units [Member]    
Per unit operating performance [Abstract]    
Net asset value per unit, beginning balance (in dollars per units) $ 127.72gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 114.88gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net income [Abstract]    
Net investment loss (in dollars per unit) $ (3.39)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ (3.32)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net gain on investments $ 25.04gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 16.16gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net income (in dollars per unit) $ 21.65gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 12.84gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net asset value per unit, ending balance (in dollars per unit) $ 149.37gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 127.72gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Ratios to average members' capital and total return [Abstract]    
Total return before Incentive Allocation (in hundredths) 19.75%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
11.18%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Incentive Allocation (in hundredths) (2.80%)gaifb_EntitiesThatCalculateNetAssetValuePerShareIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
0.00%gaifb_EntitiesThatCalculateNetAssetValuePerShareIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Total return after Incentive Allocation (in hundredths) 16.95%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
11.18%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net investment loss before Incentive Allocation (in hundredths) (2.73%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(2.74%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Incentive Allocation (in hundredths) (2.75%)gaifb_IncentiveAllocationOfNetInvestmentPercentage
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
0.00%gaifb_IncentiveAllocationOfNetInvestmentPercentage
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net investment loss after Incentive Allocation (in hundredths) (5.48%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(2.74%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Total expenses before Incentive Allocation (in hundredths) 2.93%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
2.95%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Incentive Allocation (in hundredths) 2.75%gaifb_IncentiveAllocationAllocatedToExpenses
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
0.00%gaifb_IncentiveAllocationAllocatedToExpenses
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Total expenses after Incentive Allocation (in hundredths) 5.68%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
2.95%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Class 2 Units [Member]    
Per unit operating performance [Abstract]    
Net asset value per unit, beginning balance (in dollars per units) $ 98.41gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 90.29gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net income [Abstract]    
Net investment loss (in dollars per unit) $ (4.53)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ (4.47)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net gain on investments $ 19.70gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 12.59gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net income (in dollars per unit) $ 15.17gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 8.12gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net asset value per unit, ending balance (in dollars per unit) $ 113.58gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 98.41gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Ratios to average members' capital and total return [Abstract]    
Total return before Incentive Allocation (in hundredths) 17.38%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
8.99%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Incentive Allocation (in hundredths) (1.96%)gaifb_EntitiesThatCalculateNetAssetValuePerShareIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
0.00%gaifb_EntitiesThatCalculateNetAssetValuePerShareIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Total return after Incentive Allocation (in hundredths) 15.42%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
8.99%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net investment loss before Incentive Allocation (in hundredths) (4.78%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(4.75%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Incentive Allocation (in hundredths) (1.92%)gaifb_IncentiveAllocationOfNetInvestmentPercentage
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
0.00%gaifb_IncentiveAllocationOfNetInvestmentPercentage
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net investment loss after Incentive Allocation (in hundredths) (6.70%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(4.75%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Total expenses before Incentive Allocation (in hundredths) 4.98%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
4.95%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Incentive Allocation (in hundredths) 1.92%gaifb_IncentiveAllocationAllocatedToExpenses
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
0.00%gaifb_IncentiveAllocationAllocatedToExpenses
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Total expenses after Incentive Allocation (in hundredths) 6.90%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
4.95%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember