Did I ask that?
Let me ask this question, after you see a TC reaching 6, how often do you see the count goes higher vs goes lower?
According to the True Count Theorem, the TC should stay about the same. Only the RC should be expected to decrease slightly.
http://www.bjmath.com/bjmath/counting/tcproof.htm (Archive copy)
Even though you know the tens and aces are coming, you have no idea when or where they will show up. They will land on first base and third base with equal probability. Everyone at the table has the same chances of getting those cards. And, as Rhino pointed out, you only get 1 card first. Your second card comes after everyone else has taken a card, so by your logic wouldn’t there be more of a chance that everybody gets one high card then a low card?
-Sonny-
However, how do you explain the differences that I observed in my sims?
According to the True Count Theorem, the TC should stay about the same. Only the RC should be expected to decrease slightly.
The True count MUST always demonstrate the tendency of 'regressing toward the mean', which, in a balanced count, is ZERO.
Au contrair, mon frer. I beleive the above description to be incorrect. What you are saying is true of the RUNNING count, but not the TRUE count. zgWith all due respect, and without reading the cited text, I beg to differ.
The True count MUST always demonstrate the tendency of 'regressing toward the mean', which, in a balanced count, is ZERO. This tendency is present, but weak, at modest True Counts like +1, +2, -1, -2; but become progressively more powerful at BIG counts like +6, +10, -5, -12, etc. indeed, the tendency is directly proportional to the inbalance that creates the True Counts. To put this more succinctly, it is factual that the tendency for a true count to move toward zero is ever-present and is exaggerated at LARGE plus or minus counts.
Flat bet will take away the advantage that I suspect the 1st base player has. Imagine near the end of a shoe with high count and max bet, I think the chance for the first seat to get a natual 20 is greater than 3rd base. Let me ask this question, after you see a TC reaching 6, how often do you see the count goes higher vs goes lower? Chances are the count will go down near the end of the shoe. So the first base player will get cards more like what the player predicated when he lays down the bet, no matter the first card or the second card.
Since my last post, I did another sim. The result was just like the second sim. So unless I did something wrong, I think there is a differenece between these two seats. I wish some experts will test this out as well. Of course life is not always ideal and the differences between all seats are small. I will not hesitate to sit anywhere when the penetration is good.
Sorry for the long message.
Sorry, for the confusion, the flat bet idea by me was silly, my bad (to late yesterday)! I was a little skeptical about your results, because they weren't what I expected. And the deviations between both sims seem a little to big for me. What I anticpated was that the player at 3rd base has a higher SCORE than 1st base, because he has more information when he plays his hand than the first player.
To check this I also ran a sim today with the following settings: 4 players, 1 hand each player, 6D S17 DAS LS RPL4, 3 Billion rounds.
Player 1 and 4 were using a slightly modified version of the UBZ-OS with a 1-15 spread, player 2 and 3 were playing basic strategy (flat bet). These are my results:
Player 1: winrate/hour: $17.04 TBA: 1.014% SCORE: 36.77 N0: 27193 SE:0.01
Player 2: winrate/hour: $1.80 TBA: -0.317% SCORE: -9.99 SE: 0.002
Player 3: winrate/hour: $1.81 TBA: -0.319% SCORE: -10.10 SE: 0.002
Player 4: winrate/hour: $17.09 TBA: 1.015% SCORE: 36.91 N0: 27094 SE: 0.010
These results reflect better what I expected, the difference is negligible but existent. Maybe we are both wrong?![]()
There is no way that your true count will stay the same. The true count theorem only states that the expected true count will be the same. Here’s an example let’s say you’re using hi-lo with a +1 running count with 26 cards remaining, true count = +2. Now remove 25 cards, what is the true count? The true count theorem states that the expected true count is +2, however we know realistically that the real true count is +52, 0, or -52. The true count is now a discrete random variable, that’s mean is +2.
It seems to me that a person who receives his cards immediately would have an advantage over someone with a lag. The person who receives his cards immediately will be making the bet with a known true count, while the person with the lag will have an unknown true count with associated probability density function. If a person’s optimal bet is related to the true count, which we know in card counting it is via the Kelly criterion, then the person who receives the cards immediately will make the optimum bet with 100% accuracy. Likewise the person with a lag will be off due to the distribution of the true count and suffer a loss function. To tell the truth I do not know what this loss function will be or if it is significant without computing the probability density function of the true count, which seems difficult because it is discrete. Anyhow, the fact that there is a loss function compared to zero loss would give an advantage to the player who immediately gets his card.
Translated to the original question of 1st or 3rd base, No doubt 1st base would be more accurate in predicting it’s true count over 3rd base even though they have the same expected true counts because there are less cards removed for 1st than 3rd. This should increase 1st’s betting efficiency, whether it is significant I do not know.
No doubt 1st base would be more accurate in predicting it’s true count over 3rd base even though they have the same expected true counts because there are less cards removed for 1st than 3rd.
It would be interesting to perform these same sims on SD. My gut tells me that the Delta SCORE would be significantly higher, while the N0 way lower, naturally. You'd have to drop the DAS and RSA.
I vote wrong, on both counts. zgTranslated to the original question of 1st or 3rd base, No doubt 1st base would be more accurate in predicting it’s true count over 3rd base even though they have the same expected true counts because there are less cards removed for 1st than 3rd. This should increase 1st’s betting efficiency...