~Ferrets Law~

Alright, I came up with this suggestion a while ago, but I want to bring it up again, so it will have a home, in the correct place. This is my idea....

To a basic strategy player, the preservation fo cards prior to the shuffle is not important, because on average, each card has the same EV to the player weather it be before the shuffle, or off the top of a fresh shoe.

This is not true to a card counter, where at times, the remainging cards to be dealt represnt positive ev to a player who could potentially take advantage of it. For this reason i am proposing that based upon the count, every card left undealt has and ~average EV~ whatever it may be, in addition, this average EV would be dependant on the count.

The EV for each card would simply be the instantanious ev to the player, divided by the average number of cards consumed each round at the current count. For anybody who actually attempts to tackle this puzzle i am proposing, take note that the average number of cards consumed each roudn shoudl be different at different counts.

To my knowledge, the formulation of both basic strategy and index plays are based on the dollar return of all the permutation of a given hand. so if a play that consumed 4 cards on average was more profitable than a play that consumed only 1 or even 0, the basic strategy action, **EVEN IF BY A MINESCULE DIFFERENCE** or the index for that play woudl be set to point out when the most profitabel play is regardless of how many cards it consumes.

I feel that this is a lack of efficiency in how indexes are formulated because to the card counter, at counts where index take place, cards will have an average ev to the player when consumed. For every card consumed you reduce the ~average~ number of hands you are dealt prior to the shuffle. It shoudl be no argument that maximising the number of hands prior to the shuffle is worth doing so long as the means to do so are justifiable.

I beleive that indexes shoudl be tailored to accomadate for the value of the cards consumed. and the number of players sitting at the table, since the number of players sitting at the table determines the average number of cards consumed each round, and thus the average ev of each card.

It shoudle be fairly straigth forward to do, just find when the charts of ev for basic strategy actions fall short of the index play action by exactly the value of the differnce of the average number of cards consumed for each of the two actions rather than simply markign the index exactly where the charts cross.

I dont have these charts, so im just tossing my idea into the open. Im also mandating that since in the past, the number of tables at the table was thought to be irrelevant, the fact that it does matter, and have an effect on "potential ev" to be known as "ferrets law"

"Ferrets law" states that the number of players at the table has an effect on the *potential* player advantage, but must be taken note of and indexes modified accordingly to benefit from.

Quite frankly this sounds a bit like being "potentially pregnant".

This reminds me of the Snyder Profit Index in a weird way. Takes into account the total players sittting at the table you are playing at. Says that the more players there are, the less of an advantage you have because (obviously) you would be playing less hands per hour which would result in a lower net gain per hour.

It sounds like you are suggesting to incorporate not only the results on this particular hand, but the subsequent effect of card usage. For instance, in a high count, standing on 16 v T may be the best play right now, and it also uses one fewer card than hitting, and hence may allow us to get one extra round before the shuffle card. Likewise, doubling picks up an extra boost compared to hitting on a hand such as A2 v 4.

I have done some sims for some applications that take this into account, by simming with a shuffle card in the shoe, and playing out hands in realistic (but computationally expensive) fashion. I suspect that most commercial simulators are not designed to do this, as this minor effect would not be worth the computational inefficiency. The place to find a difference would be in single-deck games for *particular* penetrations relative to the number of players at the table. I'm sure Norm/QFIT has thought about this issue, and might know of some instances where it matters.

Two separate scenarios.

Single-deck: One problem here is that there are too many possible situations -- combinations of penetration and players. You may also find that results are not what you would like as the times where you manage to squeeze in another round may produce poor rounds due to the cut card effect.

Shoes: Here you could generalize and ignore number of players. You would simply look at the times that there you might produce one more round. You could get an idea of the impact using a CVData multi-playing strategy. But, as valuable as an extra round is, I have difficulty seeing a significant difference as you would only alter a play just before the cut card. Trying to add an extra round in the middle of a shoe does not necessarily increase penetration. And penetration is what matters, not number of rounds.

Incidentally, the CVData index generator when it finds a minuscule difference does not go for the best decision, but the least risk decision, even if risk-aversion is turned off. It does this when the difference in decisions falls below a threshold that I think makes the decision a coin toss ignoring risk.

Why is one less card in the middle of shoe different than one less card at the end of the shoe?

If your playing a shoe and the count jumps to TC +5, the TC should stay there for the rest of the shoe therefore your goal is to get as many rounds out of the shoe as possible. And if you take one less card on 5 borderline decisions throughout the shoe that could be the equivalent of one more round.

If you are in the middle of a shoe, an extra card used in the round may or may not add to penetration. It is as likely to add a round as subtract a round. And adding a round at that point isn't even good as it means a bad round as per the cut card effect. It is happenstance. There is no way to predict the effect.

If you are just before the cut card, and you know it, and the count is high, you have a chance of adding to penetration. Unfortunately, decisions probably would not make any difference. The most common coin-toss decision is 16vT. At a high count it might make sense to avoid a hit to get an extra round. One problem, that's the normal play in a high count.

I agree it has the potential to do either, but it will add a round much more often than it subtracts a round.

Why do you think this?

I having trouble of thinking a good way to mathematically explain this, but I'm going to try.

Let's say you take 20 less cards, during the shoe playing heads up. Of course this will add a few extra rounds to the shoe. The number of rounds relates linearly to the number of cards added (doubling the number of decks doubles the number of rounds assuming equal % penetration), therefore adding 1 card will add 1/20th as many rounds as adding 20 cards.

Doubling the decks slightly less than doubling number of cards.

Sorry, I meant to talk about altering penetration. Taking one fewer card in the middle of the shoe does not move the cut card. It may increase the number of rounds, but I see no reason that it would increase penetration. As I said earlier, it is penetration that you want to increase, not number of rounds. Violating strategy touse one fewer card in the middle of the shoe will reduce EV and is as likely to decrease as increase penetration.

This is the value that i am attemting to measure, and factor into the ev of individual playing decisions, the avearge EV as a result of one card not being dealt. based on the count, and how it relates to the number of players.

Obviously the effect would be the most important if there were less players at the table.

We cannot know the number of cards consumed each round, for the next rounds, but in all the possible series of hands we coudl be dealt some consuming 4, some consuming 8, adding any number of cards should effect the AVERAGE number of hands dealt before the cut card emerges.

Another curious idea is that at higher counts you would expect the number of cards consumed each round to be more predictable, and have a lower average increasing the potency of the strategy modifications

Well the fluctuation in adding or subtracting a round is unimportant except in calculating risk averse indices. For the pure index calculation you just need the average rounds it will add.

The dealer uses 2.9 cards on average each hand while the player uses 2.7. Therefore when playing heads up 5.6 cards will be used each round. Therefore each card saved is worth
(1/5.6)*(Adv of TC)
Let's say the the TC is 5 and your making $100 bets. Not taking one card would save you about $0.45. It really is a small amount but it could affect borderline decisions.

Any squabbles with this methodology?

That is interesting. It would increase the value of saving a card.

Again, adding a round is not helpful if it does not increase penetration. Not hitting in the middle of a shoe does not increase penetration. All of the things mentioned in this thread are easy to sim.

Adding a round is helpful if and only if the count is high. It is in the player's best interest to place as many +EV bets as possible.

That true count theorem is what tells us that if the count is high in the middle of the shoe, every bet made for the rest of the shoe has a positive expectation.

Yes, it states that the remaining hands will more likely than not have a positive true count, although certainly not a guarantee. Of course if the count is already high (and therefore probably your bet), purposely playing the current round incorrectly in the hope that you will get an extra round sounds a bit risky. The move most likely to create a new round would be to avoid a split. Most people don't bother with split indexes for shoes these days. A sim could be run trying to increase the index for 99vA and 99v7, or 44v4 in DAS to see if there is a difference. It would need to be compared to a player using these indexes. Unfortunately, these indexes very rarely come into play. And a person not using split indexes wouldn't split these hands anyway.

I agree. Though 15v10 and 16v9 might also be affected.

The problem there is the unlikelihood of changing the number of rounds, and making the non-risk-averse play by removing the possibility of a push.

Now what you gotta do is find the index plays where that $0.45 dollar gain is enough to ofset the index value for a deviation, and whabam, new deviation numbers, that increase profits by creating more hands.

Surey there are deviations where at one point count TC less or more, the difference between the EV of the BS action and the new action is less than $0.45 for a 100 dollar bet.

Also consider plays where more than one card is preserved such as not splitting.

Im so excited you actually see what i am looking at stophon