Hey. Does anybody know what the tc index would be (hilo) to insure a BJ against a T if the payout is 10:1. Thanks.
That sounds way too low to me. You're betting that the dealer has an ace in the hole, so the bet breaks even if more than 10% of the deck is aces. With a single deck, you need to remove 12 non aces in order to get to break even (4 aces out of 40 cards). With an ace neutral level 1 count, it would break even at +12. With Hi Lo, it should be even higher than that because you're only counting aces as -1, and they should be -12.Originally Posted by Cacarulo
The Cash Cow.
Assume n decks, x non-aces already seen excluding the 2 tens, and y aces seen excluding the player's ace.
P(dealer has ace downcard) = (4n-y-1)/(52n-x-y-3)
P(dealer has no ace downcard) = (48n-x-2)/(52n-x-y-3)
E(insurance|dealer has ace downcard) = 10 (paid 10 to 1 on insurance bet, push on natural 21).
E(insurance|dealer has no ace downcard) = 0.5 (lose insurance bet, paid 3-to-2 on natural 21).
E(no insurance|dealer has ace downcard) = 0
E(no insurance|dealer has no ace downcard) = 1.5
E(insurance) = (4n-y-1)/(52n-x-y-3)*10 + (48n-x-2)/(52n-x-y-3)*0.5 = (64n-10y-0.5x-11)/(52n-x-y-3)
E(no insurance) = (4n-y-1)/(52n-x-y-3)*0 + (48n-x-2)/(52n-x-y-3)*1.5 = (72n-1.5x-3)/(52n-x-y-3)
We require E(insurance) > E(no insurance), so that 64n-10y-0.5x-11 > 72n-1.5x-3, or x-10y > 8+8n.
For n=1 and y=0, we have x>16, so that taking insurance is preferred after seeing 17 or more non-aces and 0 aces.
In this case, if x=17, then E(insurance) = (64-8.5-11)/(52-17-3) = 1.390625 and E(no insurance) = (72-25.5-3)/(52-17-3) = 1.359375.
This is a net gain in EV of 1.390625-1.359375 = 0.03125, or 3 and an eighth cents per dollar wagered.
Thus, this side bet is exploitable under the right circumstances. You may or may not consider an extra +3.125% in EV to be worth the extra effort involved in tabulating indices for different values of n, x, and y, as well as in learning the corresponding side count. Note as well that the gain in EV (defined as E(insurance)-E(no insurance)) steadily increases with increasing x, but dramatically decreases with increasing y and increasing n.
Glad to know it. In that case, the analysis I just posted can be modified to include insuring a hand other than a natural, and will most likely indicate much different indices for non-naturals compared to those needed for insuring naturals.
Alright, that's what I had interpreted. The calculated index is correct. For 1D, 2D, 4D, 6D, 8D, the indices for Hi-Lo are as follows: +5, +6, +7, +7, +7.
But there is an issue, Hi-Lo and most existing counting systems have a very low correlation for this type of insurance (32.91% for Hi-Lo) compared
to traditional insurance (76.01%). Instead, an Ace count correlates 100% same as a ten count correlates 100% with traditional insurance.
Hope this helps.
Sincerely,
Cac
Luck is what happens when preparation meets opportunity.
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