True count problem !

[PlayHunter]

We know that getting a 10 value card is about just under 31%. My question is how much is this percent affected depending on what the True Count is in certain situations for a 2 deck shoe ?

So, my question would be like this: - How likely (in terms of percents) is to get a 10 value card for a 2 deck shoe when the true count is +2, +4, +6, +8, +10 ?

- Why do I care about this aspect ? Because I was in the following situation:

Last hand with me first to act.

Rules:

- minumum/maximum bet 100/1000

- doubling in soft 21 (natural blackjack) allowed

- natural blackjack pays 3 to 2

- dealer peeks for blackjack

BR1 (me) 2802 (betting 800) and been dealt BJ

BR2 2400 (betting 1000) and been dealt BJ

Dealer upcard: 10

I think I did the correct play by doubling down and getting a ~51% to win the game rather than to let my oponent to double down on his turn and to get that 51% instead of me. (please someone to correct me if I am wrong)

But additional to the described situation, there was ~ 1,5 decks left and the True Count was showing -3. (into this account I have included current dealt cards) This is where I get concerned. What was the % of getting a ten value card in that respective situation ? I still had a double ?

 

[Billy C]

Easy decision

If the cards were dealt up, you had no choice but to double down for an amount that would cover the $98 that you know he's got you beat by.

BillyC1

 

[PlayHunter]

If the cards were dealt up, you had no choice but to double down for an amount that would cover the $98 that you know he's got you beat by.

BillyC1

No Billy, actually I was up with 98 chips and I would had won if no one would double.

And the count before any cards were dealt was zero but counting them after the cards were dealt was -5 and I have rounded the remaining decks to 1,5 so the true count should be calculated as -5/1.5=-3.33

 

[Billy C]

No Billy, actually I was up with 98 chips and I would had won if no one would double.

And the count before any cards were dealt was zero but counting them after the cards were dealt was -5 and I have rounded the remaining decks to 1,5 so the true count should be calculated as -5/1.5=-3.33

My bad---------yes, you were actually $102 up at that point $4002 vs. $3900. (I blame it on being Monday morning)

Billy C

 

[PlayHunter]

My bad---------yes, you were actually $102 up at that point $4002 vs. $3900. (I blame it on being Monday morning)

Billy C

Yes, now you are right too. I were up with 102 and not 98 as I mistakenly stated earlier. However, the true problem it really is about how much the true count affect those ten value cards (and the correct play) in certain situations ?

 

[Billy C]

Stand

Most of the really good tourney playing members here will tell you to forget about counting in tournaments. They feel it's of VERY little value and that there are more important things to focus on (like opponents bankrolls, last hand bet position, etc.) and I can't argue with that.
Having said that, if counting is a habit, why not use the very small edge it provides at times?
The count you show in your example is probably not significant enough to play into the decision you have to make.
I think I would stand on the BJ because it limits your opponent to only one option. He HAS to double.

Billy C

 

[PlayHunter]

I think I would stand on the BJ because it limits your opponent to only one option. He HAS to double.

Billy C

Yes, that is perfectly right. But allowing him to double means that I will allow him to do the right play and to get that 51% winning chances of beating the dealer and winning the game. Why I would allow him to get that 51% when I can be the one who will get that 51% ?

 

[London Colin]

I think I would stand on the BJ because it limits your opponent to only one option. He HAS to double.

Billy C

I believe Playhunter's point here is that the correct play without counting is to double, but only very marginally, so that if you did happen to know the count you might find that standing is better.

Forcing your opponent to double when that has a 51% chance of success is worse than doubling yourself.

I wouldn't be counting, so the situation would never arise for me. (And it occurs to me that if HiLo is being used it may not correlate all that well with the decision, since drawing a 9 would also be a pretty good result, but we aren't counting those.)

That being said, given that it's a coin-flip and there must be some small chance that your opponent won't realise that he can (and must) double, maybe standing is indeed the right option unless you know your opponent well enough to discount that possibility.

 

[PlayHunter]

I believe Playhunter's point here is that the correct play without counting is to double, but only very marginally, so that if you did happen to know the count you might find that standing is better.

Yes, this was my point. And this is why I really want to find the right answer for my first question in this tread:

- How likely (in terms of percents) is to get a 10 value card for a 2 deck shoe when the true count is +2, +4, +6, +8, +10 ?

Forcing your opponent to double when that has a 51% chance of success is worse than doubling yourself.

Almost the same coin flip would be if dealer upcard would be 9 instead of 10. It would be a 52% winning chance for the player which do doubling down.

That being said, given that it's a coin-flip and there must be some small chance that your opponent won't realise that he can (and must) double, maybe standing is indeed the right option unless you know your opponent well enough to discount that possibility.

Yes, this is another very important point ! Some people might not realise that they still have to double to get a chance ! And taking this into account might very vell make it to be a stand. However, it is basically the same thing if our opponent have a hard 11 instead of BJ. - And here the correct play for him is obviously: our opponent will double. But at that point if we know how much the true count does matter for such a close decision, we will know what to do...

 

[hopinglarry]

There are a variety of counting systems out there. Most people would probably be using a simple plus/minus count where 2-6 are -1 and 10-A are +1. Assuming you are using a 1/2 deck to calculate a true count, then with one deck remaining a true count of +2 would mean you have 4 extra cards that are 10-A. It might be four 10 counts or could be four Aces.

Assuming that it is four 10 counts, then you have 20 ten counts in the remaining 52 cards or 5/13 (about 38.5%). If they were 4 extra Aces, then your ratio of 10s to non 10s would be the original 30.8%. If you have a +4 true count, then you might have as many as 8 ten counts extra, which would be 6/13 (about 46.2%).

So look at your count system and decide what you want to use as your average % for the various true counts. Also the burn card has more effect the smaller the number of cards remaining.

 

[gronbog]

So, my question would be like this: - How likely (in terms of percents) is to get a 10 value card for a 2 deck shoe when the true count is +2, +4, +6, +8, +10 ?

I can run a sim for this and get you an answer, however this is only partially relevant to your tournament situation since you can still win your double without getting a 10.

I think I did the correct play by doubling down and getting a ~51% to win the game rather than to let my oponent to double down on his turn and to get that 51% instead of me. (please someone to correct me if I am wrong)

This is the real question at hand. Even as the first hand dealt after shuffling, we already know that the deck is depleted by 3 10's and 2 Aces (true count = -2.5 for 2 decks), which is close to your actual scenario. I can easily run a sim for this to get the actual percentages, taking the depletion into account.

But additional to the described situation, there was ~ 1,5 decks left and the True Count was showing -3. (into this account I have included current dealt cards) This is where I get concerned. What was the % of getting a ten value card in that respective situation ? I still had a double ?

With some modification to my software, I can run a sim for this as well, but the situation is confusing. A true count of -3 for 1.5 decks remaining translates to a running count of -4.5, which is not possible. Did you mean a running count of -3? If not, then the running count must have been -4 (TC=-2.67) or -5 (TC=-3.33). Can you clarify the situation please?

 

[PlayHunter]

With some modification to my software, I can run a sim for this as well, but the situation is confusing. A true count of -3 for 1.5 decks remaining translates to a running count of -4.5, which is not possible. Did you mean a running count of -3? If not, then the running count must have been -4 (TC=-2.67) or -5 (TC=-3.33). Can you clarify the situation please?

That would be just great..

The count before any cards were dealt was zero. I have added the running count wich is -5, then I have rounded the remaining decks to 1,5 (because all remaining cards were around 80) so the true count should be calculated as -5/1.5=-3.33 (of course, this is not exact.. so I have rounded to -3 in my example)

 

[gronbog]

Last hand with me first to act.

[ ... ]
BR1 (me) 2802 (betting 800) and been dealt BJ
BR2 2400 (betting 1000) and been dealt BJ
Dealer upcard: 10

I think I did the correct play by doubling down and getting a ~51% to win the game rather than to let my oponent to double down on his turn and to get that 51% instead of me. (please someone to correct me if I am wrong)

While waiting for clarification of the true count at 1.5 decks remaining, I started a 2 deck sim starting from immediately after the shuffle, since the situation was close (RC=-5 -> TC=-2.5) to what was described. In the sim, I used optimal strategy for BR2 which is to double if BR1 stands and to stand if BR1 doubles.

The result surprised me at first, since the discussion so far seemed to assume that doubling would result in victory more than 50% of the time.

2 decks: Stand: 50.40%, Double: 49.60%, TC=-2.63

It would appear that the depletion of 3 10s and 2 aces from 2 decks is enough to make doubling the wrong play overall. I went ahead and ran sims for 1, 4, 6, 8 and infinite decks and got the expected trend:

1 deck: Stand: 51.94%, Double: 48.06%, TC=-5.53
4 decks: Double: 50.34%, Stand: 49.66%, TC=-1.28
6 decks: Double: 50.59%, Stand: 49.41%, TC=-0.85
8 decks: Double: 50.71%, Stand: 49.29%, TC=-0.63
inf decks: Double: 50.88%, Stand: 49.12%, TC= 0.00

Looks like we have a case where counting has some value after all. It might even be useful to develop some indices for when doubling various totals vs various up cards crosses the 50% success rate line .

I hope to have some time on the weekend to make the modifications to my software necessary to sim the 1.5 decks remaining situation, however, I expect the results to be similar to the 2 deck sim above.

 

[PlayHunter]

Thanks a lot !

Well, is not really necessary to calculate it for 1,5 decks. Now after I saw your results I am sure that it will be under 50% win rate when double doubling down.

And I dont think that counting in half deck increments vs full deck increments would be of such a great value, but it is only how I am used to do the count..

But it would be of great help if you can do the same simulation (as you did with TC -2,63) for when TC is +2, +4, +6, +8, +10 (especially for 1, 2, and 4 decks)

- I deem that some of these percentages are of great value in some certain player vs player scenarios.

 

[gronbog]

So, my question would be like this: - How likely (in terms of percents) is to get a 10 value card for a 2 deck shoe when the true count is +2, +4, +6, +8, +10 ?

Here are the percentages for the first card dealt in each of 2 billion rounds of black jack, 2 decks, 2 players playing basic strategy, at various true counts. You asked for true counts up to +10, but it was easy to extract the data for the negative counts as well. The expected trends are revealed.

PlayHunter, I hope you find these results useful.

True
Count    A       2       3       4       5       6       7       8       9      T
------------------------------------------------------------------------------------------------------------------------------
-10     5.77%   9.63%   9.66%   9.47%   9.59%   9.54%   7.77%   7.69%   7.72%  23.16%
 -9     5.87%   9.33%   9.46%   9.41%   9.36%   9.30%   7.80%   7.71%   7.79%  23.96%
 -8     6.21%   9.28%   9.27%   9.23%   9.16%   9.17%   7.69%   7.70%   7.73%  24.57%
 -7     6.43%   9.15%   9.10%   9.05%   8.96%   8.92%   7.72%   7.70%   7.67%  25.30%
 -6     6.16%   8.79%   8.80%   8.84%   8.86%   8.83%   7.79%   7.75%   7.79%  26.38%
 -5     6.76%   8.62%   8.64%   8.66%   8.65%   8.66%   7.72%   7.73%   7.74%  26.83%
 -4     6.98%   8.48%   8.48%   8.44%   8.42%   8.43%   7.73%   7.71%   7.69%  27.63%
 -3     6.71%   8.11%   8.18%   8.23%   8.30%   8.37%   7.75%   7.79%   7.88%  28.68%
 -2     7.05%   7.94%   8.01%   8.07%   8.12%   8.17%   7.72%   7.76%   7.80%  29.36%
 -1     7.57%   7.95%   7.93%   7.90%   7.89%   7.89%   7.67%   7.68%   7.66%  29.86%
  0     7.71%   7.71%   7.71%   7.69%   7.69%   7.69%   7.68%   7.68%   7.67%  30.76%
  1     7.95%   7.69%   7.61%   7.50%   7.39%   7.35%   7.71%   7.65%   7.59%  31.57%
  2     8.09%   7.24%   7.28%   7.30%   7.33%   7.38%   7.66%   7.70%   7.72%  32.30%
  3     8.35%   7.10%   7.10%   7.10%   7.10%   7.14%   7.69%   7.71%   7.71%  33.00%
  4     8.48%   6.99%   6.96%   6.90%   6.88%   6.89%   7.72%   7.71%   7.70%  33.78%
  5     8.73%   6.80%   6.75%   6.72%   6.71%   6.71%   7.72%   7.70%   7.67%  34.48%
  6     9.06%   6.71%   6.64%   6.54%   6.46%   6.45%   7.72%   7.67%   7.62%  35.12%
  7     9.09%   6.28%   6.33%   6.31%   6.37%   6.38%   7.74%   7.73%   7.75%  36.01%
  8     9.18%   6.08%   6.17%   6.18%   6.22%   6.22%   7.72%   7.76%   7.77%  36.70%
  9     9.59%   6.23%   6.04%   5.97%   5.80%   5.84%   7.70%   7.65%   7.72%  37.47%
 10     9.69%   5.80%   5.77%   5.72%   5.75%   5.77%   7.70%   7.80%   7.78%  38.21%

 

[PlayHunter]

A BIG Thank You for this chart Gronbog, it is just BRILLIANT !!!

 

[gronbog]

More Sims

I managed to find time to make the necessary modifications to my software in order to run the remaining sims. I added the ability to randomly stack the deck to a given running count at a given point with given cards already dealt (or not).

Thanks a lot !
Well, is not really necessary to calculate it for 1,5 decks. Now after I saw your results I am sure that it will be under 50% win rate when double doubling down.

While not really necessary, it did make a good test for my modifications, since the result is expected to lie along the already-established trend line. I ran the situation of BJ, BJ vs 10 with 78 cards(1.5 decks) remaining out of 2 decks, after the hands were dealt and a running count of -5. This was PlayHunter's actual original situation as I understand it. The result was

Stand: 50.83%, Double: 49.17%

The percentage for standing does indeed fall between the result for 1 deck (51.94%) and 2 decks (50.40%)

But it would be of great help if you can do the same simulation (as you did with TC -2,63) for when TC is +2, +4, +6, +8, +10 (especially for 1, 2, and 4 decks)

- I deem that some of these percentages are of great value in some certain player vs player scenarios.

I then went ahead and ran these sims (15 in all). Since it's not possible to have a positive count after dealing BJ, BJ vs 10 at the top of any shoe, I needed to simulate these as the number of decks remaining out of a larger number of decks. I arbitrarily chose 8 decks. So, for example, the first sim was set up as BJ, BJ vs T, 1 deck remaining (out of 8) with a running count of +2 (TC=+2).

Here are the results:

1 deck, TC=2, Double: 52.88%, Stand: 47.12%
2 decks, TC=2, Double: 52.83%, Stand: 47.17%
4 decks, TC=2, Double: 52.82%, Stand: 47.18%

1 deck, TC=4, Double: 54.41%, Stand: 45.59%
2 decks, TC=4, Double: 54.36%, Stand: 45.64%
4 decks, TC=4, Double: 54.34%, Stand: 45.66%

1 deck, TC=6, Double: 55.92%, Stand: 44.08%
2 decks, TC=6, Double: 55.87%, Stand: 44.13%
4 decks, TC=6, Double: 55.83%, Stand: 44.17%

1 deck, TC=8, Double: 57.41%, Stand: 42.59%
2 decks, TC=8, Double: 57.36%, Stand: 42.64%
4 decks, TC=8, Double: 57.31%, Stand: 42.69%

1 deck, TC=10, Double: 58.88%, Stand: 41.12%
2 decks, TC=10, Double: 58.83%, Stand: 41.17%
4 decks, TC=10, Double: 58.77%, Stand: 41.23%

I grouped the results by true count in order to highlight that the number of decks remaining really did not matter. The trend in the true count, however, is as expected.

 

[PlayHunter]

I grouped the results by true count in order to highlight that the number of decks remaining really did not matter. The trend in the true count, however, is as expected.

I am a bit surprised to see that the number of remaining decks does not matter. Anyway, yet another wonderful analyse and a great job, Thank You once again !

 

[gronbog]

I am a bit surprised to see that the number of remaining decks does not matter.

While the results are close for each true count (which is not completely unexpected for me) perhaps I did speak too soon. There is a small but consistent trend for a lower probability of success within each true count as the number of decks increases.