Questions about house edge at different TCs

Hello everybody,

I am currently reading BJA3 and the charts in the "World's Greatest Blackjack Simulation" made me wonder a couple of things.

Lets take the 4.5/6 S17 DAS LS game

a)  I know the house edge for that game is about 0.26% (Wizard of odds), but the edge at TC 0 is -0.12, so about half that. Why isnt it the average house edge?

b) If I were to backcount until I reach a true 1 and then play without counting any further, would the average TC remain at +1 until the shuffle or would it revert back to 0 over time? just speaking on average of course. and if it remains an average +1 (which has an edge for the player), would that mean entering at that point and just playing basic strategy would be +EV?

c) If I add up all the values it seems that the overall expectation remains positive even if we only eliminate all hands at TC -4 and below. So in theory we could play 97% of hands at this game while flatbetting and still be +EV? (even though at the slightest of margins)

Thanks for your time

First time heard of the “World's Greatest Blackjack Simulation.” Ask one question a time. Stay focused.

As far as I know, the world's greatest Blackjack simulator is Phil, pjsatz. He is around the forum. 

Let me try to answer your first question. House edge (HE) is a function of TC and penetration (PEN), that is,

HE = f (TC, PEN).

When PEN = 1/6, HE =  f (TC, 1/6);

When PEN = 3/6, HE =  f (TC, 3/6);

When PEN = 4.5/6, HE =  f (TC, 4.5/6);

When PEN = 5/6, HE =  f (TC, 5/6).

At a fixed TC=0, the HE value usually decreases with increasing PEN. 

ATC, thanks for writing. As you're new here, please ignore everything aceside writes, as 98% of what he says is incorrect. Not sure if he does this on purpose, just for the sport of it, or because he's truly ignorant about all these things (more likely), but in any event, let me answer your questions correctly.

A) The edge at TC = 0 permits you to use the I18 indices, which include standing on 16 vs. 10 at TC>= 0. So that permits you to gain extra advantage. Also, do NOT confuse the BS edge with TC =0. They're not the same thing! BS is derived from off-the-top of the deck calculations. TC = 0 is derived from whenever the TC = 0 anywhere in the shoe. From the Floating Advantage (did you read that chapter?), we know that the edge for TC = 0 increases as number of decks remaining decreases. Look at the four charts on pages 240-241. Do you see how the TC = 0 edge goes from -0.13, to -0.12, to -0.11, to -0.09?

B) Not sure why you'd want to backcount, jumping in at +1 but then stop counting altogether, but if you did, yes, the average TC would remain +1. Unlike the RC, which has to revert to zero at the end of the shoe (but not necessarily when you reach the cut card!), the TC shows no such tendency on average; that is, it tends to stay the same. See bottom of page 383, top of page 384 for a discussion of this. So yes, just playing BS at that point would give you a slight edge, but if you don't use the indices, you'd lose that extra advantage, which would be somewhat costly.

C) You didn't get that -4 from the charts, nor from CVCX, so did you use another simulator (CVData?) for that observation? Or did you look at the positive TC values and assume that the negative frequencies and edges (absolute value) are symmetrical? If so, they aren't. 😊 In any event, I suppose it might be true, but, again, it would be an awfully foolish way to play, if we're talking about a live casino.

Don

Thanks a lot for the answers Don

a) I have finished the floating advantage chapter and I took from it that the shift is not very significant. I kinda look at it like the difference in a 6deck and 2deck game with same rules, where a 2deck is better for the player. So I assume that a 6deck game played down to 2 decks left with a count of 0 now is like a 2deck at the start. Might be a bit of an oversimplification but again, the shift in edge didnt seem to relevant for practical purposes.

b) I just wanted to make sure my assumption about the TC staying the same over time (on average) was correct. Havent reached Chapter 13 yet, but will read it within the next days. (It really is a great book)

c) What I did to get that -4 value was multiply the TC frequency with the EV W/L % and add those values together. I wanted to see where the total turns negative, to see which TCs could still be played while being profitable. Just looking for the breakeven point for different games. I will just give my sample calculation for the game mentioned in the OP. Its possible I made mistakes, so I would be grateful for critique

Table 10.51  (starting with the TC values from bottom to top)

>9 -- 0.14 * 6.57 = 0.9198

  9 -- 0.10 * 5.51 = 0.551

  8 -- 0.26 * 4.83 = 1.2558

and so forth

since values under 0 are not given I assumed that the frequencies would be the same for 1 and -1, 2 and -2 etc. I also estimated the EV to drop by 0.6% per TC, since that was roughly the change between positive TCs

with that method the overall result stayed positive down to -3, and only when adding the -4 value it tipped into negative. So thats where my assumption came from

I dont own any CV software but will most likely buy it in the near future

Thanks again

Edit:

I just took another look at the tables and I think I realized my mistake in assuming the TC frequencies are the same for positve and negative counts. since flooring is used this seems to be false. I redid the math increasing the numbers by about 66% for negative counts because the total for negative is 45% and for the postive about 27%. so a 66% increase should be somewhat close to the truth. Now the tipping point is obviously earlier and playing down to TC of -2 is still +EV.

”So I assume that a 6deck game played down to 2 decks left with a count of 0 now is like a 2deck at the start. Might be a bit of an oversimplification”

Good observation! This part has been discussed a lot of times. I think it’s not an oversimplification, it’s strict math. I’d like to hear what Don might say about this part. 

A) For the most part, as long as you're counting, yes, this is the idea of floating advantage.

B) Again, yes. Glad you're enjoying the book.

C) So, right, neither the frequencies nor the edges are symmetrical. You need to simulate to see the exact values. Get Norm's software; you won't be sorry.

Don

I've already said it many times and, especially, in the FA chapter. See the entire introduction and also Wong's conclusion at the top of page 71.

Don

It seems overkill spending so .much discussion, hence not getting the hours in for your EV.,,,,, W/accuracy, just go do it. 

Revere, "without a true count, you have no

Akracy"

Without math derivation posted at BJ21, you have no EV.  Stop chasing your own tail quoting others. Time changes, so do blackjack games. Currently, there are only about three regular posters here at BJ21. I'm one of them. 
 

Show your math, right here.