MangoJ
MangoJ
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December 4th, 2012 at 4:33:36 AM permalink
Could someone around here explain the infamous "cut card effect" to some (possibly ignorant) member around here ?

From what I read about the effect it states that the player experiences a different EV when playing blackjack (by strict basic strategy) when dealt from a shoe versus CSM.

What exactly is meant by "different EV"? EV per hand ? EV per shoe ?

If it is EV per shoe, then I don't know how to measure a "shoe" in a CSM game.
If it is EV per hand, then I will come in conflict that the cards are homogeneous (to a non-counting player) throughout the entire shoe, as it is for the CSM game. So the very last hand before the cut card should be no different than the first hand, which should be no different from any CSM-dealt hand.


What I do believe is, i.e. when the average hand number per shoe is 12 - then the 15th hand played into the shoe will be of less EV to the player compared to the 1st hand. However this I understand as simply counting "hands", which is strongly correlated to counting cards (higher card values results in less cards per hand, which results in more hands before the cut card). So when you reach an over-average hand number before the cut card, this is a consequence of observing more higher-valued cards - which is equivalent to a negative count scenario with less EV. Of course counting hands is much less efficient than counting cards, but qualitatively has the same results.
But I don't think this effect can be summarized by "CSM games are better EV". If you want to play 100 hands you should get the exact same EV from a CSM or a shoe game. Right ? Wrong ?
Wizard
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Wizard
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December 4th, 2012 at 6:11:25 AM permalink
To start, did you read my blackjack appendix 10.

To answer your question the EV per hand is greater on a CSM.

To address your last question, the player lose less on average playing 100 hands on a CSM than a cut-card game.
It's not whether you win or lose; it's whether or not you had a good bet.
MangoJ
MangoJ
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December 4th, 2012 at 12:32:26 PM permalink
Thanks Mike, I've already read your analysis years ago, and so I just did it again.

Honestly I'm still somehow confused, and cannot yet grasp the origin of this effect. A CSM game is equivalent to a shoe game where the cut card is placed right near the front (shuffling after each hand). So if the cut card has any effect, it should be strongest on a CSM game.

Looking at table #3 (card distribution of a CSM game) you show an imbalance against the "expected" card frequency 1/13 or 4/13 each.
I think this expected frequency is guessed too naively. 1/13 and 4/13 is certainly true for the initial two cards (dealer and player hand), but not for all cards shown during a round. As there are less cards shown if the initial cards are of high value, high valued cards will be overrepresentated (confirmed by your simulation in table #3 in the CSM game). But this is simply a biased (i.e. wrong) measurement of card distribution, I honestly cannot see how it would affect EV of the game.
AxiomOfChoice
AxiomOfChoice
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December 4th, 2012 at 1:16:58 PM permalink
Mango:

The cut card effect is due to the fact that in hands which produce positive counts (little cards come out), more cards are dealt than hands which produce negative counts (big cards come out). As a result, if the cut card is at a fixed depth, you play more negative-count hands than positive-count hands, in the long term.

If the deck is shuffled after every hand (or if the cut card is placed so that it is always reached on the first hand of the shoe) then there is no such effect, since every hand is played with a starting count of 0.

To see the effect, suppose the cut card was placed just a little bit down. Just deep enough that you have room for one or two hands, depending on how many cards came out during the first hand.

If lots of cards came out during the first hand, that means that most of the cards were little, and the count is probably positive. But, then you hit the cut card and shuffle right away, so you don't get to play the positive count.

On the other hand, if only a few cards came out during that first hand, then most of them were big, and the count is probably negative. Since only a few cards came out, you DO play that 2nd hand. So, you have to play the negative count.

In this experiment, you play some negative counts, but never positive counts. Obviously, this increases the house edge.

In real life, the cut card would be deeper than this, but the effect is still there. In fact, once you've dealt down to what could be the 2nd last or last hand (depending on how many cards come out) you are in pretty much the same spot (the house is basically telling you, we are going to deal this hand, and then, if the count gets better we are going to shuffle, but if it gets worse we will deal another hand). It's basically a very weak form of a preferential shuffle.
MangoJ
MangoJ
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December 4th, 2012 at 4:06:36 PM permalink
Wow thanks Axiom, the analogy to the preferential shuffle made the trick.

So I think I got my head around it: if the Dealer would normally deal N rounds, but would supposely deal N+1 rounds if the count becomes negative at the end, then the player is clearly at a disadvantage, as the dealer squeezed in a negative count hand. Now the dealer does not count himself, the game mechanic does it (with short hands producing negative count while prolonging the game).

My mistake was probably: The N+1 hand is fair unconditional (it's still a shuffled deck). But if you conditionally play it during negative counts, it becomes an unfair hand.
AxiomOfChoice
AxiomOfChoice
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December 4th, 2012 at 4:33:34 PM permalink
Yeah, this is a subtle concept for sure. For the longest time I was completely confused about it (and, actually, had it backwards -- I thought that the cut card helped the player!!) My logic was wrong, of course, but my logical error was subtle and it took me a long time to figure it out.

Next up: the floating advantage :)

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