For those that don’t know what the cut-card effect is, it’s the reason that BJ from a CSM has a lower house edge than BJ from a shoe (all else being equal). The rationale is described as a shoe plays (sort of) to a fixed number of cards (until the cut card is reached and the current round is then finished). When playing to a fixed number of cards, you’ll play more hands if the hands are 10 and A rich because you’ll take fewer hits. In that circumstance the remaining hands are low card rich and that’s bad.
See explanations in these links:
If there are many high cards (e.g. tens) dealt, we will end up with two- and three-card hands. If there are small cards dealt, we will end up with hands with many cards. So, if we are dealing to a fixed point, and we are dealt a lot of large cards, then we will use fewer cards per round and get an extra round or two. The problem is that these extra rounds will be dealt from a deck with fewer high cards because they have been used up. And we know that a deck with few high cards left is bad for the player.
And Wizard here: https://wizardofodds.com/games/blackjack/appendix/10/
Now here are my inutive issues with this. (Don’t get me wrong, I’m not disputing the existence of the cut card effect given the simulations that Wizard shows in the above link, but I just don’t buy the explanation.)
Assume 6 deck shoe with cut card leaving 1.5 decks I played. Those 1.5 unplayed decks will either have a positive TC, negative TC or 0 TC. If the unplayed 1.5 has a negative TC that means the played part of the shoe had a positive TC. That means it should have been a good shoe for the player (A and T rich) and the shoe would have played more hands (because you take less hits in a A and T rich shoe. See quote above.)
Conversely, if the 1.5 decks have a positive TC then the played part of the shoe had a negative TC. That means it was a bad shoe for the player (on an EV basis). But the player would have played less hands (because more hits in a low card rich shoe).
So, overall, players get more hands on good shoes and less hands on bad shoes. If that logic holds it intuitively seems as if the cut card effect should decrease the HE. But that’s incorrect so something in my above intuitive reasoning must be wrong. I just can’t figure out what.
Here’s another long of reasoning: when I’ve played CSM blackjack, the dealer tends to let the discard pile build up to 10 or 15 cards before putting it in the shuffler. Isn’t that identical to a cut card effect with the cut card being a few cards shy of 10 to 15 (so dealer finishes current round just like in a real cut card shoe)? So doesn’t CSM effectively have a cut card effect when the dealer does this? How does the cut card effect vary based on the penetration of the cut card?
A final point: the Wiz says
However, if the dealer deals out much more than the average number of hands in a cut card game, then the last hands tend to be very bad for the player. This is because in the early hands the players and dealer didn't hit much, which in turn is because lots of large cards came out, leaving more small cards for later in the shoe.
Given that, is there a rule that BS players should follow by quitting any shoe after X many hands have been dealt (with X depending on penetration of cut card)? Since once X hands happened and the shoe hasn’t ended it should mean that the remaining count is negative?
Still not clicking for me. I understand that if you happen to play a cut card shoe that has an above average number of hands played, then the last few hands are player bad. (Because you only got to play the extra hands due to having a ten rich early part of the shoe.)
But, I think each of the explanations in the links fails to account for the lower HE the player experienced in those instances. In other words, look at this pic (https://www.qfit.com/cutc0.jpg). It purports to show the HE of two games, one dealt for a fixed number of 8 rounds and one dealt to a fixed penetration (cut card) that tends to give 6-9 rounds. The latter has an off the chart HE in rounds 8 and 9.
But what (I think) that chart fails to account for is that you only get to round 8 and 9 in certain shoes. And those certain shoes have something in common, they were player friendly in early rounds! The chart doesn’t show that, however, because the early round HE is a mix of shoes that will get to round 8 and 9 and shoes that won’t.
Those better at math and with more familiarity with this issue, would love to hear you weigh in.
In CSM, the TC is virtually always 0 so BS is the correct play that minimizes HE. In a shoe game, the TC fluctuates up and down around zero, during those fluctuations, BS is not necessarily the correct strategy as it ignores index plays. So in theory, the BS player is not minimizing the HE.
Or to put it another way, what is the HE using BS if the TC is always zero, compared to the HE using BS if the TC is on average 0 but with a standard deviation associated with it.
This explanation for the HE discrepancy makes perfect sense to me.
Also, this thread is starting to feel like unJon’s Corner. Sigh.
Say you're playing one spot head's-up on a single-deck game where the dealer places the CC precisely six cards from the front of the deck. She burns card #1, then deals card #2 to you, #3 to herself, #4 to you, and #5 to herself.
Now, if you and the dealer both have pat hands, or if at least one of you has a BJ, then she'll deal a second round. If you or the dealer (or both of you) draw any cards, then the CC will appear and she won't deal a second round.
Naturally, the True Count at the start of round 1 is precisely zero. When the dealer actually deals a second round, what will the HiLo T.C. be?
The most it will be is zero: for example, you get a BJ and the dealer has two small cards (or, sadly, vice versa), or both you and the dealer are dealt pat 17's consisting of an 8 and a 9. In every other case, the TC will be negative when round 2 is dealt, since every other pat hand uses at least one big card and no small cards.
So, what is the average T.C. for your game? Clearly, it will be negative for this penetration.
Contrast this with a single-deck game that's shuffled every round, like a true CSM BJ game. In this case, the average T.C. is once again precisely zero.
If you compare these two hypothetical games, you can see that, counter (ha ha)-intuitively, the CSM game will be the better play, because the 6-card game will have a lower average T.C. due to the CCE.
Hope this helps!
Thank you for taking the time to respond. This was a very clear and easy to follow example.
I get the effect.
My follow up question would be that the simulations Wizard ran comparing CSM to various penetration deck games may conflate this particular effect with the effect noted above of BS play not always being optimal as the TC fluctuates. It would be interesting to disaggregate those two effects.
And it sounds like there could be a new “beyond BS” rule of thumb (like the rule of 45 or Dr. Prepper rule): If you are at a X deck shoe that’s a full table, and cut card cuts off about Y decks, stop playing after Z hands because you only get past Z hands when the remaining count is bad for you.
Can you explain this? I would have thought based on the explanation for the cut card effect that you don’t cut off the ends of shows with favorable counts because those shoes tend to actually end on or before Z rounds. The ones that go past Z rounds by their nature are left with unfavorable counts.Quote: BleedingChipsSlowly
The TC for a shoe is more likely to be large, positive or negative, towards the end of a shoe. If you don’t count, you don’t know. Your “beyond BS” rule would avoid playing shoes when the potential of highly unfavorable counts is greater. It would also stop you from playing highly favorable ones. And you would not play the ends of shoes that are neutral. Per the CCE, this might be an overall advantage, but it would not be a style most people would be comfortable playing, imho.