Early Sur; Simulations don't match your predictions.

A continuation from "best game in the world" thread 2 weeks back. Wow, thank you very much for all of your careful thought on this subject.

My simulations do not match your figures. I do have the Wong book with me and also his blackjack analyzer program. It does have a feature that allows you to program early surrender. And simulations that I am running are as follows:
For a 78 card cut; Win $/100 rounds $25 Win Rate 1.9 % Standard deviation $194
for a 104 card cut; Win $/100 rounds 20$ Win Rate 1.7% Standard deviation $176
For a 130 card cut; Win $/100 rounds $16 Win Rate 1.5 % Standard deviation $ 166

These are the cuts that I normally have to deal with. I also ran a simulation of;
156 card cut; Win $/100 rounds $12.50 Win Rate 1.3 % Standard deviation $142
All of the simulations were run to 40 million hands. The only variable changed was the cut card. These seem pretty linear. But of course we will see a curve if we plot more points. Maybe I will run some additional simulations soon. These simulations above, reflect the exact rules, counting system, and bet & matrix number variations that I actually play with. I normally deal with a 2 dk cut. But with a dollar or two, I can buy my way to 78 cards with about 50% of the dealers. There is no heat.

Remember that Wong, used this simulator to arrive at the figures in his book which you are using in your e-mail postings. Also remember that true count conversions, take into account the number of decks remaining. We do not see the extreme drop-off in profitability that you mention in your postings. But as you remember, my actual experience in the 140 hours I played this year do not reflected in this Win rate. I am actually a full two standard deviations below the 1.7% Win rate we see here.

This is a European-style no-hole card game. And all bets are lost to a dealer blackjack. Therefore there is no splitting or doubling against an ace or 10 (except splitting ace ace versus a dealer 10). I have taken this into account in the simulations above. I also play a very rapidly. I am almost always playing alone and playing with two hands. I go to four hands of one dollar when the count goes below -1. This is to move my way through the negative shoes quickly. I do not use any cover at all. All of these factors are taken into account in the simulations above.

Again that I request your knowledgeable and insightful comments. All of you guys really showed an astute knowledge of the game and I am deeply impressed. Thank you again for your comments in advance.

Gratefully
BigRed

In that previous thread, I wrote: "The loss of $3 per hour in EV is not a constant rate..."

If you plot the data provided by your simulations using penetration from the front of the deck as your x-axis and the hourly winnings in dollars as your y-axis, the four points do describe a slope.

The four data-points should be (156, $12.50), (182, $16.00), (208, $20.00), and (234, $25.00).

My estimate of $9-$11 is lower than your simulation shows because I visualized the slope as having already begun a steep rise by the time we get to the middle of a six-deck shoe. Clearly, that portion of the shoe is still "early" in the slope.

[I deleted a prior version of this post because I apparently lack the skill to add 26 (cards) to any given value. My apologies. :)]

and you'll see how the win rate dramatically skyrockets much faster than a linear rate. Across large segments of penetration (especially mediocre pen) the changes in win rate may appear to be much more linear, but it's still a slight slope that gets steeper as the penetration gets deeper.

I agree with your post, above. I also agree that simulation results would show a curve in relation to penetration. Over the next few days I will run if you more simulations and acquire more points and plot them. Then we can see the shape of the curve.

But my original question was why am I so for under my expectation. I continue to play this game for about three hours six days a week. At my rate of speed I still think I have an expectation of around $40 per hour. Do you agree with this?
do you consider it just an unusually long swing to be two standard deviations (about $4000) under this?

I agree with your post, above. I also agree that simulation results would show a curve in relation to penetration. Over the next few days I will run if you more simulations and acquire more points and plot them. Then we can see the shape of the curve.

But my original question was why am I so for under my expectation. I continue to play this game for about three hours six days a week. At my rate of speed I still think I have an expectation of around $40 per hour. Do you agree with this?
do you consider it just an unusually long swing to be two standard deviations (about $4000) under this?

First, the slope of a line is pretty simple to compute. (y2-y1)/(x2-x1) gives you that. Using your data points:

(156, $12.50), (182, $16.00), (208, $20.00), and (234, $25.00).

The slope of the straight line connecting the first two points is .13, connecting the second and third points, the slope is .15, and taking the last two points, I get .19. So the slope is going up. The slope for the first/last points only is .15. So clearly the slope is increasing as the penetration increases.

However, it is obvious (to me anyway) that the slope can not continue to increase without bound, because if _all_ cards are dealt, the win rate can not possibly run off to +infinity. So it has to start backing down near the actual end of the cards to prevent this. I have not gotten CVCX to allow me to run simes out to 100% pen so that I could provide the data points for the end of the above curve. Would be interesting to see what happens.

Logically, it would max out at the highest win-rate available, based on the monetary amount of your wager, the casino rules and how often (per hour) you'd play the final cards of a shoe. The measurement we're using is a dollar-amount per hour; since you aren't wagering an infinite amount per hour, there's no reason to realistically think the profit-per-hour would approach infinity, anyway. The data-points would be theoretically "capped" at a point where the player wins every hand. That is NOT an infinite advantage.

I imagine that figures for 100% penetration aren't available because all hands consume cards, but some possible outcomes consume more cards than others. As soon as you reach a point in the shoe where all possible outcomes can't be realized, then any calculations based on penetration to that point will be jaded. For example, suppose in a 6-deck game there's one possible outcome that will consume 16 cards (yours and the dealer's combined). Any calculation based on a penetration of more than 296 cards (((6 * 52) - 16) will be inaccurate, since a re-shuffle of the shoe would be necessary before we could complete all possible hands. It would be something of a programmings nightmare to accommodate a re-shuffle. No sane programmer is going to endure the headache just to compute the player-advantage in a scenario that is unlikely to ever happen again in real-world play, at least not with any regularity or predictability. (Okay, maybe one programmer would! ;))

Hello Big Red:

Sorry about the above misunderstanding about your advantage.

From your original post:

"Wong�s blackjack analyzer says that this gives me a 0.4% edge with basic strategy and 1.8% edge when I count."

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Even at a 0.4% advantage, it seems that it would be worthwhile to simply use basic strategy. If you can play two hands at $100. per hand and get in at least 120 hands per hour, you would be making 100 x 120 x 0.4% = $48. per hour.

I play at a game in Eastern Europe that has a .4% player edge with only basic strategy. In response to my post entitled, "best game in the world," a player responded that if I did two hands of $100 I would average $48 an hour and profit.
I thought I had been way ahead of him. I had previously run simulations on Wongs blackjack analyzer that showed, for much lower levels of play, I would only average about $10 an hour. The maximum for this game is $60. When I read the post about $40 per hour. I plugged three hands of $60 and ran some simulations. If the actual result showed a $66 per 100 rounds. That works out to well over $100 per hour. Now that is a real money!! The problem is that my standard deviation is $1622 for less than one hour of play. It is not uncommon to run two standard deviations out and three standard deviations from time to time. I ran a fluctuation of $5,000 for 40 hours of play, the simulation reveals that I will bottom out (nadier) 62% of the time. If I up the fluctuation to $10,000 I still run the risk of losing in the entire $10,000, 39% of the time. The risk is simply too high for my bankroll limits. I will play with it and see if I can find something I can live with. But for right now I enjoy counting. It would be interesting to come in with $20,000 and just get drunk on Russian vodka, sit and play basic for eight hours a day. But right now my main occupation is chasing Russian girls ;-).

... at top left especially "Do not post the same message multiple times, either on the same message board or on different boards."

I was replying to the repeat of your post further up the page. The problem was probably caused by someone deleting a post with replies.