Surrender vs Insurance
- Thread starter uchicago
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You can only surrender if they offer early surrender. I would think surrender is the better play unless the count is huge. Lose .5 or breakeven/lose 1.5/win .5 were you lose 1.5 most often of the three until the insurance index is well below the TC. Just a guess though not from running any numbers.
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An astute pit boss will figure out you're using your brain no matter what if you're counting cards. I personally am not going to discard powerful tools like surrender and insurance because that one play will make or break my longevity!
Spreading your bets with the count will make it obvious to an astute pit boss you're smart. Should we stop doing that?
Spreading your bets with the count will make it obvious to an astute pit boss you're smart. Should we stop doing that?
When your insurance index is reached you win insurance 1/3 of the time and lose it 2/3 of the time. Of the 2/3 you would give up .5 of your bet if you surrender. 1/3*(0) + 2/3*(-.5 + -.5) = -2/3 for insure then surrender at the insurance index. That is better than only surrendering when your insurance bet wins at least half the time and only gets stronger as you win more than half your insurance bets. It should be clear that playing a hand that should be surrendered is even worse.
Best play, insure then surrender only after the insurance bet wins half the time or more, before that threshold surrender without insuring.
Best play, insure then surrender only after the insurance bet wins half the time or more, before that threshold surrender without insuring.
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I cannot follow you here. The break-even point for insurance is 1/3, not 1/2. Unless your intention is risk-averse play (which is a legit question in this situation), the pure EV-best play is to insure whenever insurance is favourable, and to surrender whenever surrender is favourable. If both are favourable, do both (assuming late surrender).
The outcome of the insurance bet has no influence on your surrender bet, as you are offered late-surrender only when the dealer doesn't have blackjack. Likewise, you can late-surrender whether or not you placed the insurance bet. From the pure EV standpoint, there is no reason to not insure your hand when 1/3 < pDBJ < 1/2. But maybe I just get you wrong.
The outcome of the insurance bet has no influence on your surrender bet, as you are offered late-surrender only when the dealer doesn't have blackjack. Likewise, you can late-surrender whether or not you placed the insurance bet. From the pure EV standpoint, there is no reason to not insure your hand when 1/3 < pDBJ < 1/2. But maybe I just get you wrong.
A look at your total action on the hand.
Let me try again.
You can simply surrender your hand for an EV of -.5 and be done with it. At your insurance index let us assume insurance is a break even proposition. That means you win one third of the time and lose 2/3 of the time an EV of 0, 1/3 you win 1 while 2/3 you lose .5 of your bet. That means your total play for the hand in aggregate is 1/3*(2*.5 - 1) (your outcome if you win your insurance bet minus the loss of your main bet that happens at the same time) + 2/3*(-.5 + -.5) (the insurance loss plus the surrender loss).
This sum is -2/3 which is less -1/2 which is surrender on its own. If you look at the insure than surrender the parts in the parentheses are always the same. The equation tips when you lose at most 1/2 of your insurance decisions or win at least 1/2 of your insurance decisions.
Total outcome of insure then surrender = win percentage of insurance times 0 + loss percentage of insurance times -1. This simplifies nicely to -1*loss percentage of insurance. This must be greater than -.5 to be a better course of action than surrender alone. At a loss rate of 1/2 for insurance the decisions of simply surrendering and insure then surrender have an equal outcome. At a smaller loss rate insuring then surrendering becomes the better course of action.
Let me try again.
You can simply surrender your hand for an EV of -.5 and be done with it. At your insurance index let us assume insurance is a break even proposition. That means you win one third of the time and lose 2/3 of the time an EV of 0, 1/3 you win 1 while 2/3 you lose .5 of your bet. That means your total play for the hand in aggregate is 1/3*(2*.5 - 1) (your outcome if you win your insurance bet minus the loss of your main bet that happens at the same time) + 2/3*(-.5 + -.5) (the insurance loss plus the surrender loss).
This sum is -2/3 which is less -1/2 which is surrender on its own. If you look at the insure than surrender the parts in the parentheses are always the same. The equation tips when you lose at most 1/2 of your insurance decisions or win at least 1/2 of your insurance decisions.
Total outcome of insure then surrender = win percentage of insurance times 0 + loss percentage of insurance times -1. This simplifies nicely to -1*loss percentage of insurance. This must be greater than -.5 to be a better course of action than surrender alone. At a loss rate of 1/2 for insurance the decisions of simply surrendering and insure then surrender have an equal outcome. At a smaller loss rate insuring then surrendering becomes the better course of action.
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With that, I fully agree. If you play insurance/surrender, your EV before peeking for BJ is -2/3.
Are we talking about late surrender ? Because then you cannot surrender before the dealer peeks for BJ. If you don't plan to play insurance, your EV before peek is still the same
1/3 * (-1) + 2/3 * (-.5) = -2/3
as insurance was a zero-EV sidebet not influencing your hand.
If you were talking about early surrender, then I must apologize, EV of early surrender is indeed always -1/2. But it is no secret that early surrender is more favourable (by 1/3 * .5 = 1/6 in this scenario) than late surrender.
But even with early surrender, there is no difference in taking / not taking insurance (besides variance).
Are we talking about late surrender ? Because then you cannot surrender before the dealer peeks for BJ. If you don't plan to play insurance, your EV before peek is still the same
1/3 * (-1) + 2/3 * (-.5) = -2/3
as insurance was a zero-EV sidebet not influencing your hand.
If you were talking about early surrender, then I must apologize, EV of early surrender is indeed always -1/2. But it is no secret that early surrender is more favourable (by 1/3 * .5 = 1/6 in this scenario) than late surrender.
But even with early surrender, there is no difference in taking / not taking insurance (besides variance).
I see your point. I missed a step in the LS only EV.
LS EV = 1/3*(-1) + 2/3*(-.5) = -2/3 the same as insure then surrender at the insurance index.
So I stand corrected insure at your index. Thanx MangoJ! It didn't feel right in my gut that it would be that way but I had guessed the same earlier so I didn't look for a mistake.
LS EV = 1/3*(-1) + 2/3*(-.5) = -2/3 the same as insure then surrender at the insurance index.
So I stand corrected insure at your index. Thanx MangoJ! It didn't feel right in my gut that it would be that way but I had guessed the same earlier so I didn't look for a mistake.
Hey I know this feeling. It helps to think in terms of "who's paying the bill". There is simply no way you can gain EV by making (or not making) a zero-EV bet. If you still do, either the bet is not zero-EV - or you won't gain that advantage :laugh:
A related question would be, if you cannot make both plays (for whatever reason), which one to chose for less variance if both are zero-EV ?
Variance Surrender: 1/3 * (-1)² + 2/3*(-.5)² + 4/9 = 10/9
Variance Insurance: 1/3* (0)² + 2/3*(-.5 + X)² + 4/9 > 10/9
Here, X is the hand after Dealer peeks. Since surrender is zero-EV, EV(X) = -.5. For X identical to -.5 (neglecting variance on X), one gets the same 10/9. As X does fluctuate, variance on insurance decision will be higher.
So, if both bets have zero-EV, and you cannot (or don't want to play insurance/surrender), you should surrender.
A related question would be, if you cannot make both plays (for whatever reason), which one to chose for less variance if both are zero-EV ?
Variance Surrender: 1/3 * (-1)² + 2/3*(-.5)² + 4/9 = 10/9
Variance Insurance: 1/3* (0)² + 2/3*(-.5 + X)² + 4/9 > 10/9
Here, X is the hand after Dealer peeks. Since surrender is zero-EV, EV(X) = -.5. For X identical to -.5 (neglecting variance on X), one gets the same 10/9. As X does fluctuate, variance on insurance decision will be higher.
So, if both bets have zero-EV, and you cannot (or don't want to play insurance/surrender), you should surrender.