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Financial Highlights (Details) (USD $)
3 Months Ended
Mar. 31, 2015
Mar. 31, 2014
Class 0 Units [Member]    
Per unit operating performance [Abstract]    
Net asset value per unit, beginning balance (in dollars per units) $ 149.37gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 127.72gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net income (loss): [Abstract]    
Net investment loss (in dollars per unit) $ (1.04)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ (0.76)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net gain (loss) on investments (in dollars per unit) $ 11.60gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ (12.93)gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net (loss) income (in dollars per unit) $ 10.56gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ (13.69)gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net asset value per unit, ending balance (in dollars per unit) $ 159.93gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
$ 114.03gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Ratios to average members' capital and total return [Abstract]    
Total return before Incentive Allocation (in hundredths) 8.83%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(10.72%)gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Incentive Allocation (in hundredths) (1.76%)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) 7.07%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(10.72%)gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Net investment loss before Incentive Allocation (in hundredths) (0.66%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(0.63%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Incentive Allocation (in hundredths) (1.69%)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) (2.35%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
(0.63%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Total expenses before Incentive Allocation (in hundredths) 0.73%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
0.68%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
Incentive Allocation (in hundredths) 1.69%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) 2.42%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassAMember
0.68%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) $ 113.58gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 98.41gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net income (loss): [Abstract]    
Net investment loss (in dollars per unit) $ (1.41)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ (1.05)gaifb_InvestmentsEntitiesThatCalculateNetAssetValuePerShareNetInvestmentLoss
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net gain (loss) on investments (in dollars per unit) $ 8.95gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ (9.93)gaifb_NetGainLossOnInvestment
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net (loss) income (in dollars per unit) $ 7.54gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ (10.98)gaifb_IncomeLossNet
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net asset value per unit, ending balance (in dollars per unit) $ 121.12gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
$ 87.43gaifb_NetAssetValuePerUnit
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Ratios to average members' capital and total return [Abstract]    
Total return before Incentive Allocation (in hundredths) 8.33%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(11.16%)gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Incentive Allocation (in hundredths) (1.69%)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) 6.64%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(11.16%)gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalReturnAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Net investment loss before Incentive Allocation (in hundredths) (1.19%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(1.13%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Incentive Allocation (in hundredths) (1.60%)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) (2.79%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
(1.13%)gaifb_EntitiesThatCalculateNetAssetValuePerShareNetInvestmentLossAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Total expenses before Incentive Allocation (in hundredths) 1.25%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
1.18%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesBeforeIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
Incentive Allocation (in hundredths) 1.60%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) 2.85%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember
1.18%gaifb_EntitiesThatCalculateNetAssetValuePerShareTotalExpensesAfterIncentiveAllocation
/ us-gaap_CapitalUnitsByClassAxis
= us-gaap_CapitalUnitClassBMember