Code:
Rounds
SPL1 MGP Eric
xx 2*EV(x) 2*EV(x)
SPL2 MGP Eric
Pxxx 3*EV(x-P) 3*EV(x-P)
NN EV(N) + EV(N-N) 2*EV(N-N)
NPxx EV(N) + 2*EV(x-PN) EV(N-P) + 2*EV(x-PN)
Everyone's talking in circles and their own language lol. Eric, let's see if I can try and restate your question:
Is that what you're asking?
iCountNTrack sounds like he can have it play perfect strategy based on every card played, so yes, if you want perfect play.
What if you want something in-between perfect play and a CDZ- (composition dependent playing pre and post-split hands the same way but ignoring post-split hand evs) strategy?
That's what I call a CDPN (composition dependent including knowledge of whether a paircard or non-paircard has been dealt) strategy.
Let's look at SPL1. When looking at any-post-split hand, note that a paircard has been removed from the deck. So when we say EV(x) and are let's say looking at 8, 8 vs 5. Now let's say a 2 is dealt to the first 8. The EV for this hand is 8,2 vs 5 with an 8 removed from the deck.
With a CDPN knowledge for SPL1, you would:
1) Remove 1 paircard
2) Figure out the EVs for the possible hands/strategies against that upcard removing one paircard
3) Determine for the post-split hand the best composition dependent strategy for each hand
4) Play out both hands the same composition dependent way
NOTE: You are using the knowledge that this is a post-split hand and possibly changing your strategy based on that.
If you are doing a full CD+ (plus simply means composition dependent PLUS composition dependent post-split) strategy as iCountNTrack does you would:
1) Remove one paircard
2) Play out the first hand optimally
3) When that hand plays out, play out the second hand optimally based on the current deck composition
Also note that if you are trying to find a TDPN (Total dependent strategy that takes into account pair and non-pair card post-split hands) strategy (which was another question - i.e. does basic (TD - total dependent) strategy change if you take into account post-split hands), you would do the following:
1) Remove 1 paircard
2) Figure out the EVs for the possible hands/strategies against that upcard removing one paircard
3) Weight the outcomes of each hand in the usual TD calculation BUT include the EV(x) calcs given their probability of occuring
4) Play out both hands the same way as the calculated net TD strategy.
Now, let's look at SPL2. Here there are 3 possible hand types.
A) Pxxx: This is calculated the exact same way as SPL1. Again note that all 3 hands are played the same way and all 3 take into account that 2 paircards are removed before playing out a hand optimally.
B) NN: Let's play this hand out.
1) First you get a non-paircard and play out your hand. So you play this hand after removing 1 paircard. You have no idea what the next card will be but that's ok. You know you didn't get an 8.
2) Figure out the optimal play for this hand and play it. Note that I'm pretty sure this will be the same as SPL1 (x).
3) Now you get another non-pair card. Here you use the (N-N) calculations for the strategy calculations. You know you didn't get a third paircard on the first paircard.
4) Play out that hand optimally for (N-N)
C) NPxx
1) First you get a non-paircard and play out your hand. So you play this hand after removing 1 paircard. You have no idea what the next card will be but that's ok. You know you didn't get an 8.
2) Figure out the optimal play for this hand and play it.
3) Now you get a paircard P.
4) Now you calculate the optimal strategy given that an N and P were removed (x-PN)
5) Play both remaining hands the same way using the knowledge of the current shoe state.
NOTE: If you want to use the above for a TDPN strategy then you need to take the weighted probabilities of each possible round and hand in aggregate based on the total, given that the proper move is to split for the pair and add those in to the regular TD strategy calcs.
NOTE: For a CDZ+ (composition dependent playing post-split and pre-split hands the same but including the EVs from post-split hands), you need to take the weighted probabilities of each possible round and hand in aggregate based on the composition of the hand, given that the proper move is to split for the pair and add those in to the regular CD strategy calcs.
Anyways, my point is that you can indeed use knowledge from split hands to calculate a more optimal strategy as the hand is being played out, which I thought was the original question Eric posed. The column labelled Eric won't work for the reasons that led to the question, they assume that the N and P cards are all played out first which they are not. That's why it fascinated me that those calculations worked at all when I knew my calculations were already correct.
Does this help clarify this discussion at all?
Bookmarks