Hit/double HiLo index for Spanish 21 hand 9vs6

[aceside]

Weird! I must have said something wrong? Let me show you how I got this hit/double at Kat TC=-3.7 for the hand 9v6.
The Wizard’s basic strategy for an 8-deck SP21 shoe for 9v6 is double. We consider this particular situation only, player (4,5)v6. The Kat HiLo TC calculation is:

TC=(-32+3)/[(384-3)/48]=-3.7.

This is the critical hit/double point because I’ve checked it. That means the hit/double index is TC=-3.7. Is there a problem with this calculation?

[Norm]

Is there a problem with this calculation?

Yes.

We consider this particular situation only, player (4,5)v6.

That.

[aceside]

But this particular situation, player (4,5)v6, is the most likely event that represents all these events. Therefore, the particular result is already statistically averaged.

Now, we consider another particular 4-card situation, player (2,2,2,3)v6. Basic strategy says Hit it because it is possible to make a 6-card 21, but I would Double it if the TC count is high enough. But, what is the critical point TC for Double then?

[Norm]

But this particular situation, player (4,5)v6, is the most likely event that represents all these events.

(4,5)v6 represents (4,5)v6. Nothing else.

[aceside]

I've done some rough calculation. Consider the player starting hand (3,2,2,2)v6. To reach a 6-card 21 for a 2:1 bonus payout, we have three channels for it, and the resulting player hands and their probabilities are:

(3,2,2,2,2,T), probability=(1/12)*(3/12);
(3,2,2,2,3,9), probability=(1/12)*(1/12);
(3,2,2,2,4,8), probability=(1/12)*(1/12).

The total probability is 5/144 on top of this 4-card hand. For the Spanish 21 hand of 9v6, the Hit EV without bonus is 0.156 and the Double EV is 0.161. If we include the 6-card 21 bonus, the total Hit EV becomes,

EV=0.156x(1+5/144)=0.161.

This means that the critical point TC for the n-card decision is TC=-4. If Kat TC>-4, we double down on a 4-card 9v6; if Kat TC<=-4, we hit on a 4-card 9v6.

[Gramazeka]

8 deck. H 17, Sur after double

9vs 6. Hit or double, without bonus, 4 cards in hand. Index -6.7

[aceside]

8 deck. H 17, Sur after double

9vs 6. Hit or double, without bonus, 4 cards in hand. Index -6.7

You have a very powerful program. It may calculate all these SP21 bonus rules. After further consideration, I believe that as a card counter, we should neglect all these 3-card conditional plays and worry only about 4-card or more situations.

[aceside]

According to WOO’s basic strategy online, there are only four hands you need to worry about the 3-card double/hit conditional play. These hands are 11vT, 11vA, 10v8, and soft 17v4. A HiLo count will easily override the 3-card decisions because the 5-card bonus is a long shot and thus should not be accounted into advantage plays.

[aceside]

Somebody disagreed with what I just said. Upon further consideration, I find that for a card counter, you only need to worry about the 3-card double/hit conditional play for these two hands, 11vT and Tv8. Actually only this one hand 11vT for HiLo counters.

[aceside]

I've done some rough calculation. Consider the player starting hand (3,2,2,2)v6. To reach a 6-card 21 for a 2:1 bonus payout, we have three channels for it, and the resulting player hands and their probabilities are:

(3,2,2,2,2,T), probability=(1/12)*(3/12);
(3,2,2,2,3,9), probability=(1/12)*(1/12);
(3,2,2,2,4,8), probability=(1/12)*(1/12).

The total probability is 5/144 on top of this 4-card hand. For the Spanish 21 hand of 9v6, the Hit EV without bonus is 0.156 and the Double EV is 0.161. If we include the 6-card 21 bonus, the total Hit EV becomes,

EV=0.156x(1+5/144)=0.161.

This means that the critical point TC for the n-card decision is TC=-4. If Kat TC>-4, we double down on a 4-card 9v6; if Kat TC<=-4, we hit on a 4-card 9v6.

I re-examined this part and found a problem here. If we play basic strategy for the above hand, there are four channels to reach a 6-card 21 for a 2:1 bonus payout. The fourth channel hand is (3,2,2,2,5,7) and the probability is (1/12)*(1/12).

The total Hit EV that includes the 2:1 bonus payout becomes,

EV=0.156x(1+6/144)=0.163,
which is greater than the double EV of 0.161.

Therefore, the final strategy for a 4-card 9v6 should be Hit.

[DSchles]

With six cards removed from 48, why are you too lazy to calculate the probabilities the correct way? Why do you assume infinite deck and no depletion? Who calculates probabilities that way, when your answers differ by only 0.005? You might get a different result if you do it the right way.

Don

[aceside]

All of the Spanish 21 games I have are 8-deck shoes. Their probability numbers are very close to infinity deck ones, so I approximate them. It’s clear that at a higher HiLo count above neutral deck, these low card probabilities will drop; therefore, the 6-card 21 bonus probability will drop too. My practice at this game is that at a high HiLo count, I neglect all these n-card conditional play decisions. Just to make sure this is the correct strategy.

I just noticed a No helpful comment and thus realized that the above calculation of mine is incorrect. Let me revise this calculation a third time. The total Hit EV that includes the 2:1 bonus payout becomes,

EV=0.156+6/144=0.198,
which is greater than the double EV of 0.161.

Therefore, the final strategy for a 4-card 9v6 should be Hit.

If each rank of the low cards, 2,3,4,5 and 6, is removed by one in a 48-card deck, the above EV calculation becomes,

EV=0.156+6*(3/48)*(1/12)=0.187,
which is still greater than 0.161.

However, the double EV increases because of the higher HiLo count, so the strategy decision for a 4-card 9v6 hand should be somewhere between Hit and Double.