Anomaly?

I disagree

with S. Yama, obviously - not because his logic is bad - but because I think he is overlooking that stiffs occur with considerable frequency and have a very negative ev - so that any change in their frequency should have a significant impact on the player's ev - where as other possible skewings involve less frequency of hands - and less impact on ev -

we need a simulation program which will test sequences/tables - only way to really resolve this type of question

 

Meaning of Life

What was the bit about hats?



Cheers

Reachy

 

simple simulation

I have run a very simple simulation using the win, lose and push probabilities from Wong and my PC's RNG. I ran 1,000,000 iterations each of 8 hands and recorded how many times a player would win more than lose, lose more than win, and "push". The results are:-

Win more than lose -> 37.3%
Lose more than win -> 45.6%
Wins = Loses -> 17.1%

An interesting coincidence is that if you assume that "lose more than win" is -EV and all other outcomes are not -EV, then those outcomes that aren't -EV = 54.4%, which is very close to RKuczek's 55% figure for +EV in 8 hand sets. OK I know it's a stretch and almost certainly irrelevant but I thought I'd point it out anyway!!

Have fun!

Cheers

Reachy

 

Interesting that the result you obtained were so similar to what one would expect!

My main concern about this thread was the assumption that agressive betting in the first 8 hands only was to the players advantage.

I don't doubt the skewing effect, I don't doubt the winning 44%, etc....

I just felt, and still feel, that inferring that overly agressive betting - in the first eight hands - is not advantageous!

 

very very simple

Like I said MonkeyS, it is a extremely simple simulation so I wouldn't read too much into it at this stage. I will try and refine it to get more precise data. I'll keep you all posted...

Cheers

Reachy

 

Reachy

good try -

resuts are not surprising given how the win/loss/push probs skew - but you still didn't test my assertion - that the skewing of stiffs would affect outcome - that can't be tested by win/loss/push probs - has to be a stimulation where the hands are actually dealt out - your simulation wouldn't reflect stiff skewing (why does that sound vaguely dirty?)

I would think in a game where the outcomes are as you found - just on win/loss/push skewing - more aggression would be indicated - even if you lose more than win on sequences that don't break even - as you can adjust your bets to reflect the outcomes - and play a risk adverse strategy for hand play -

 

Randomness

I'm also working on incorporating simulation into the stuff I've been putting together. Recently I tried it out and got clearly wrong results. This turned out to be because of a fairly trivial bug, but in tracking it down I started to doubt the randomness of my shuffles.

It turns out there are all kinds of issues you have to be aware of, relating both to how you generate and use pseudo-random numbers and also to the shuffling algorithm itself.

I found useful information on this Wikipedia entry and on some of the pages it links to.

 

Data

My programming exploits have reached the stage where I am able to give this a go.

I've set things up to use the same 6-deck, H17, DAS, late surrender rules as UBT, but dealing 16 rounds between shuffles (which should make no difference except to speed things up, compared to shuffling every round). The playing strategy is currently set to composition-dependent BS.

I'm not sure how large a sample is needed to get the necessary accuracy. I'd appreciate any advice on this point. For the time being, I've recorded two sets of results -

1. 20M individual hands ('sequence' length set to 1)
2. 20M sequences of 7 hands (i.e. 140M hands in all)

I'm not quite sure what to make of the results. At first glance it looks like there actually is a measurable increase in the proportion of winning sequences, but it still falls well short of 50%.

Code:

Known EV: -0.5274%
Hands Played: 20000000   Units Won: -108925
Calculated EV = -0.5446%

Sequence size: 1
Units   No.     Prob. (%)
-8      2       0.0000
-7      46      0.0002
-6      375     0.0019
-5      1833    0.0092
-4      9675    0.0484
-3      40429   0.2021
-2      872881  4.3644
-1      7981221 39.9061
-0.5    975017  4.8751
0       1665120 8.3256
1       6267139 31.3357
1.5     905237  4.5262
2       1214251 6.0713
3       48226   0.2411
4       14702   0.0735
5       2914    0.0146
6       785     0.0039
7       132     0.0007
8       15      0.0001

Win  Seqs: 8453401      (42.27%)        +10277306.50 units.     Value: +121.58%
Lose Seqs: 9881479      (49.41%)        -10386231.50 units.     Value: -105.11%
Push Seqs: 1665120      (8.33%)

Code:

Known EV: -0.5274%
Hands Played: 140000000   Units Won: -743096
Calculated EV = -0.5308%

Sequence size: 7
Units   No.     Prob. (%)
-15     3       0.0000
-14.5   1       0.0000
-14     13      0.0001
-13.5   9       0.0000
-13     61      0.0003
-12.5   25      0.0001
-12     207     0.0010
-11.5   106     0.0005
-11     921     0.0046
-10.5   438     0.0022
-10     3596    0.0180
-9.5    1957    0.0098
-9      14454   0.0723
-8.5    8386    0.0419
-8      48442   0.2422
-7.5    30434   0.1522
-7      124299  0.6215
-6.5    80451   0.4023
-6      261121  1.3056
-5.5    166264  0.8313
-5      493210  2.4661
-4.5    330557  1.6528
-4      754628  3.7731
-3.5    478426  2.3921
-3      1106971 5.5349
-2.5    743594  3.7180
-2      1345037 6.7252
-1.5    840569  4.2028
-1      1557103 7.7855
-0.5    1029757 5.1488
0       1564739 7.8237
0.5     962843  4.8142
1       1456457 7.2823
1.5     932202  4.6610
2       1223975 6.1199
2.5     735159  3.6758
3       920324  4.6016
3.5     559422  2.7971
4       639497  3.1975
4.5     369427  1.8471
5       391187  1.9559
5.5     221559  1.1078
6       218142  1.0907
6.5     118787  0.5939
7       106090  0.5304
7.5     55587   0.2779
8       45442   0.2272
8.5     22386   0.1119
9       17101   0.0855
9.5     7922    0.0396
10      5399    0.0270
10.5    2325    0.0116
11      1633    0.0082
11.5    603     0.0030
12      374     0.0019
12.5    179     0.0009
13      104     0.0005
13.5    49      0.0002
14      27      0.0001
14.5    11      0.0001
15      3       0.0000
15.5    1       0.0000
16      3       0.0000
16.5    1       0.0000

Win  Seqs: 9014221      (45.07%)        +23872083.50 units.     Value: +37.83%
Lose Seqs: 9421040      (47.11%)        -24615180.00 units.     Value: -37.33%
Push Seqs: 1564739      (7.82%)

 

london:

wow, and i strive to count to 21. i am impressed. thanks for giving this infomation. what a great learning site we have at our fingertips!!!!!

i pale at times, at the feet of my fellow man

 

nice stuff London

the results for seven hand sequences do seem to show some tilt towards more than expected positive ev sequences - even if the cummulative ev was more negative than the expectation -

what I had suggested was that the lower frequency of stiffs in seven hand sequences would skew the seven hand sequences towards more positive results - while eight hand sequences would show the majority of sequences with positive ev - that might have gotten mixed up - as I was discussing both -

can you try doing some more runs - more seven hand sequences and some eight hand sequences runs - hopefully with cummulative results coming out both more and less positive than expected?

can you track the number of stiffs in a sequence - and see if that correlates with results?

this is very good stuff - you are doing here

my argument was based on the contention that the skewing of stiffs was sufficient to skew the sequences evs - as S. Yama said - other factors may skew the other way - so more testing would be great, if you can and want to do it -

 

A work in progress

I'd really like to gain some confidence that there are no errors being produced before getting too carried away, and also find some ways to speed things up - run times are currently measured in hours, not minutes. Do the figures for a single hand look right? (E.g., 42% chance of a win, not 44%; a combined effect of using BS - rather than 'no DD,no split,no surr.' - and the H17 rule?)

Currently, every run generates a fresh set of hands. With a few changes, I could notionally chop up a single run into sequences of various lengths, so 100M hands could be looked upon as 50M x 2, 33.3M x 3, etc.

But, in the mean time, I ran 20M x 8 overnight, as requested - :sleep:

Code:

Known EV: -0.5274%
Hands Played: 160000000   Units Won: -840753
Calculated EV = -0.5255%

Sequence size: 8
Units   No.     Prob. (%)
-15.5   1       0.0000
-15     8       0.0000
-14.5   3       0.0000
-14     22      0.0001
-13.5   24      0.0001
-13     150     0.0008
-12.5   74      0.0004
-12     584     0.0029
-11.5   394     0.0020
-11     2409    0.0120
-10.5   1546    0.0077
-10     9039    0.0452
-9.5    5986    0.0299
-9      28349   0.1417
-8.5    19881   0.0994
-8      72800   0.3640
-7.5    51941   0.2597
-7      158922  0.7946
-6.5    114067  0.5703
-6      305719  1.5286
-5.5    224596  1.1230
-5      502123  2.5106
-4.5    359561  1.7978
-4      768217  3.8411
-3.5    567907  2.8395
-3      1016609 5.0830
-2.5    716939  3.5847
-2      1261665 6.3083
-1.5    915035  4.5752
-1      1395455 6.9773
-0.5    959473  4.7974
0       1423474 7.1174
0.5     1003474 5.0174
1       1333351 6.6668
1.5     895363  4.4768
2       1132149 5.6607
2.5     767450  3.8373
3       894769  4.4738
3.5     583456  2.9173
4       636983  3.1849
4.5     408425  2.0421
5       420221  2.1011
5.5     261199  1.3060
6       249297  1.2465
6.5     149925  0.7496
7       134141  0.6707
7.5     78268   0.3913
8       65476   0.3274
8.5     36086   0.1804
9       28210   0.1411
9.5     14946   0.0747
10      10920   0.0546
10.5    5356    0.0268
11      3703    0.0185
11.5    1699    0.0085
12      1074    0.0054
12.5    485     0.0024
13      318     0.0016
13.5    141     0.0007
14      75      0.0004
14.5    32      0.0002
15      23      0.0001
15.5    5       0.0000
16      2       0.0000
16.5    3       0.0000
17      1       0.0000
17.5    1       0.0000

Win  Seqs: 9117027      (45.59%)        +25486460.00 units.     Value: +34.94%
Lose Seqs: 9459499      (47.30%)        -26327213.00 units.     Value: -34.79%
Push Seqs: 1423474      (7.12%)

I'm not sure about the feasibility of tracking stiffs, but I'll look into it.

 

Just keeps coming back to the house edge of 0.5%, doesn't it? Enough said.

 

What I am finding interesting

is that with 7 and 8 hand sequences, the odds of ending the sequence with a positive result is GREATER than the odds of winning a single hand - even though you are more likely to lose hands than win them - I think this proves my point that you can play the probabilities for sequences - just as you can play the probabilities for single hands - and that short sequences skew towards positive results - and lend themselves towards more agressive play

 

First of all, I think the results of London Colin's simulation are flawed. I find some changes in the "probability" column to be too radical in some cases. It doesn't flow in a logical manner. But I'm not here to discuss London Colin's work. Programming a simulation is tough with all of the possibilities involved, so something may have "fallen through the cracks". But it's a noble effort and I applaud him if he wants to continue his refinements..

Now, for the moment, let's assume London Colin's probabilities are correct. In the statement I quoted above, RKuczak said "the odds of ending the sequence with a positive result is GREATER than the odds of winning a single hand - even though you are more likely to lose hands than win them". Well this tells me that you are still more likely to get a "sequence" of net losing hands than a "sequence" of net winning hands. Therefore, once again, betting more just because it is the first 7 or 8 hands will result in more net loses than net wins.

The problem remains: How can you forecast which hands, within a "sequence", will have a probability of a net win? I haven't seen anything that can do that.

 

you don't

have to 'forecast' which hands within a sequence are winning hands - toolman - stop thinking "HANDS" - you can size your bets or use progressions - to take advantage of the fact that the probability of a sequence is greater that the ev will be neutral or positive than negative - the point is to play the sequences - not play the individual hands - since the sequence is more likely to be positive - or at least neutral - than any single hand -

 

I used hands but we can use "sequences" if you like. Comes out the same. The "sequence" is more likely to be negative. Show me with numbers taken from London Colin's simulation how you figured that the sequence is more likely to be positive because I just don't see it. Yes the numbers show that the "sequences" are not as negative as expected but the "sequences" are still negative. Except for the case of 0.5 units (or one or two others that I may have missed), his summary shows a net negative expectation for every unit value. For example: The probability of a "sequence" ending up with -1 unit is greater than ending up with a +1 unit. The probability of a "sequence" ending up with -1.5 units is greater than ending up with a +1.5 units. And so on. The only exception to this is when you come to 0.5 units. But as I posted earlier, I believe the simulation is flawed.

Now as far as progressions, everyone knows they are losers. Even in a tournament were the spread between the minimum and maximum bet is 50 units, you cannot double up after 6 losses (assuming you start with a minimum bet) - you simply bump up against the max bet. If you stop a progression before a win then you just lost a bundle. If you do win while in a progression, you win a net of 1 unit (or 1 minimum bet). So maybe the progression will yield 3 or 4 units in eight hands most of the time. That 3 or 4 units are minimum bets and are not that valuable but you always run the chance of being eliminated before the first 8 hands are played. If you start the progression with a unit equal to an amount greater than the minimum, then you bump up against the max bet that much sooner with the higher probability of busting out.

 

These calculations

dont they represent the dealer vs the player? As we well know this game is players vs players with the dealer as a tool. The simple reason you need to be more aggressive in EBJ is the game is always in the "final stretch" It is grind time. When you have 7 players there is bound to be 1 heck even 2 3 or 4 players getting as good cards as dealer. Their EV is better than yours if you are drawing crap. To do a proper simulation you would need to do it for 7 players vs the dealer. Like outcome is real but not 100%. With 7 players someone is going to grab good cards. In ebj, oh my God I think Im already breaking my no UBT pledge!, you will end up low BR if you catch all crap. Low BR equals trouble and especially if you have bad position. :juggle:

 

What we have here ...

is a failure to communicate.

This thread started out talking about the perception of some people that online UBT play was somehow weighted towards the dealer winning. RKuczek invoked his previously mentioned theories about short sequences as the reason behind this. I'm afraid I have to say I find this slightly absurd, for a couple of reasons -

1. The perception of bias in the online games is just that - a 'perception'. The human mind is notoriously unreliable in such matters. Once we believe we have noticed a pattern we can't help but find lots of evidence to support it and subconsciously ignore all evidence to the contrary. (And, for what it's worth, I've never noticed any such bias when playing.)
2. I'm currently fretting over how large a sample size is required to confirm an apparent change of a couple of percent in the probability of winning a sequence - How many 100s of millions? How many billions? And yet, how many UBT games does the combined online career of all BJTers add up to? A few thousand? For an effect to be noticable over that short span it would surely have to be a lot cruder than anything we are currently considering. (i.e. the fix really would have to be in, or the RNG would have to be totally screwed up.)

I'd appreciate any feedback that helps me track down any issues. Could you elaborate on what looks wrong to you? (I was initially confused by the values for the 'X.5 unit' rows. To see a smooth progression, I think you have to move in steps of one, not a half. Half a unit implies at least one BJ or surrender in the sequence, and an odd number if it's > 1, which I think accounts for the reduction in the odds for all the X.5 rows.)

I was already working, rather aimlessly, on a simulator. Ken's challenge seemed like a good way to breathe some life into the project. It's always better to be working towards a goal. I'm as doubtful as anybody about how any of this could be usefully applied to tournament play, but for now I'm concerning myself with the more abstract questions -

1. Is there a measurable effect?
2. How big is it?

What I believe RKuczek is saying is that (if my results can be trusted) you enter into any 8-hand sequence of flat bets with 45.6% chance of finishing ahead and 52.7% chance of not finishing behind. Whereas, going into a single hand, your chances are 42.3% and 50.6%. (I think the influence of the surrender option is probably quite large here. It might be more meaningful to exclude it, at least for the single-hand simulation.)

Indeed. As I mentioned above, I'm really just investigating what effect, if any, exists. Pure science, so to speak. It seems to me that, even if we sat down to play a tournament using a single deck and the most favourable rules, so that each hand has a positive EV, the fundamentals of tournament strategy would be largely unaffected (if you exclude card counting from the equation).

If you tweak the rules to the extent that a single hand is more likely to be won than lost then some things certainly must change - In a two-player show-down you ought to always take the high if you can. But even under these conditions, I would think that the fundamental principles of tournament money management would remain the same - there aren't enough rounds to benefit from the long-term favourability of the game by routinely betting big. (Or so I imagine )