Anomaly?

[RKuczek]

very interesting

fantastic work London

I think the critical factor is not the win and loss percentages as such - but the gap between wins and losses -

we know the approximate odds for win/push/loss is 44%/8%/48% - so if the sequence gives a gap of lower than 4% - the sequence gives the player better odds of a positive result than playing a single hand does -

in the four hand sequence - there is only a 0.37 gap between wins and losses - this is much less than 4%!

likewise - the eight hand sequence shows a gap of less than 2% -

common wisdom is bet conservatively (or even min bet) - then make very big moves to take the lead - using as few hands as possible for your move -

this data says that you have better odds if you play short sequnces of hands more aggressively - to target positive results - and establish a lead - than if you put all your jhopes on a single hand or two-step move from behind -

 

[RKuczek]

one additional comment

London - your results for two hand sequences show you are more likely to have a positive ev for the sequence than negative - this seems anomolous to me - you are very definitely more likely to lose two hands in a row than win two - and it is hard to imagine doubles, splits and bjs having this large an affect -

 

[Reachy]

Progressions

I'd be interested to know how progressions come out with this simulator. Can you re-task the simulator to look at the probabilty of winning various lengths of progressions? I'd be suprised if it came up with anything different to what's already been calculated but you never know...

Cheers

reachy

 

[toolman1]

Where do you get 44.83% from? The figure for 1000-hand sequences is 43.87%.

Don't know. Either I had a typo or was looking at something different. Anyway, you understood what I was saying and that's the important thing.

PS: TOOLMAN TOWERS - I like that. Now all I need is a few billion to make it happen.

 

[London Colin]

fantastic work London

Thank you.

this data says that you have better odds if you play short sequnces of hands more aggressively - to target positive results - and establish a lead - than if you put all your jhopes on a single hand or two-step move from behind -

I'm not convinced. I think maybe the factor you are overlooking is that as soon as you fall behind by losing any single bet, your opponents are able to size their bets in relation to yours, so as to stay ahead of you. Your level of aggression would have to escalate with each lost hand, and you essentially wind up in a 'forced' progression.

Conversely, if you allow others to be the early aggressors, then this advantage is yours.

London - your results for two hand sequences show you are more likely to have a positive ev for the sequence than negative - this seems anomolous to me - you are very definitely more likely to lose two hands in a row than win two - and it is hard to imagine doubles, splits and bjs having this large an affect -

I'm just here to report the results, rather than interpret them. Actually, my immediate thought is this -
Splits and doubles should make little difference, since they will be roughly balanced in the win/lose stakes. However, any 2-hand sequence that contains a BJ (about 9%?) will be a winner unless you lose a split/double on the other (non-BJ) hand. I think that might account for this result.

I'd be suprised if it came up with anything different to what's already been calculated but you never know...

I'd be astounded! It wouldn't be that easy to do at the moment, so I'll put that idea to one side if you don't mind. (Unless of course you wish to fund my research. )

Actually, there is one reason why the precise figures for a progression might be sligfhtly better than you would conventionally calculate. When not shuffling every hand, the probabilty of winning the next hand actually goes up slightly when you lose the current hand. (On average, that is. If you were counting cards then you might know different in specific cases.) However, it apparently goes down more following a push than it does following a win, which might work against you in a progression.

 

[London Colin]

Yes and No

Anyway, you understood what I was saying and that's the important thing.

What I don't know is whether you feel 43.87% is still too high. Certainly, the trend is in the right direction, once you get over the curious 'hump' at 60 hands.

 

[toolman1]

What I don't know is whether you feel 43.87% is still too high. Certainly, the trend is in the right direction, once you get over the curious 'hump' at 60 hands.

Post deleted. See next post.

 

[toolman1]

What I don't know is whether you feel 43.87% is still too high.

My feeling was that the 43.87% was too high but since have changed my mind. My simulator allows me to set up a simulation that would, with some manipulation, act to verify the "1,000 hand sequence" in your simulation. My limitation is that I can only verify a sequence at a time whereas you can do all the sequences at one time. The results were interesting.

Of course the percentages will not come out exact but they were close enough that it looks like your percentages are correct. From the analysis my simulator provides, as expected, the more hands in a sequence the greater the overall dollar loss per sequence.

An interesting thing about your numbers is that, generally, as the percent of "push" sequences decline, the percent of "loss" sequences increase as the percent of "win" sequences declines. Don't know what that means but it's interesting. And yes, I need a life.

PS: Good job my friend, good job.

 

[Hollywood]

Actually, there is one reason why the precise figures for a progression might be sligfhtly better than you would conventionally calculate. When not shuffling every hand, the probabilty of winning the next hand actually goes up slightly when you lose the current hand. (On average, that is. If you were counting cards then you might know different in specific cases.) However, it apparently goes down more following a push than it does following a win, which might work against you in a progression.

and the bigger reason is...

adding in the probability of getting a blackjack or optimal DD situation with more money out...since the reason to use progressions has less to do with winning hands and MORE to do with the accumulation of bankroll (wherein winning hands simply becomes the inciting incident to this result), when looking at pure win/loss probability you must somehow accomodate the additional BR, over and above standard win/loss. done right, progressions give you more BR upswing than the pure RoR calculations themselves illuminate. still not a break even proposition, by far, by it certainly mitigates the absolute win/loss angle & provides bonus EV not usually considered ---

-hd.

 

[London Colin]

and the bigger reason is...

That's a whole other issue (and one I look forward to reading all about some day soon ).

I was really just making a passing comment that, contrary to what I had just said, the precise RoR figures arrived at by a simulation could be ever-so-slightly different to what you might calculate, because the successive hands of the progression are not independent trials.

 

[London Colin]

Reachy

This is really interesting data Colin. These results are essentially binary as far as I can see since they give no information on the size of win or loss sequences (which may answer some of Toolmans queries, maybe not). The only thing we have exact data on are the push sequences since they = zero. Interestingly the loss sequences go over 50% somewhere between 40-50 hands. Currently I'm not sure what to do with this information since I have "man flu" and am spaced out on co-codamol and must go to bed right now!

Sorry. I missed this post when it first appeared. I hope you are feeling better today.

I do actually have the detailed information - that's what the graph was derived from. My first attempt to post everything exceeded the size limit for a post, so I gave the executive summary instead.

Here's the breakdown of percentages for sequences 1 -10 :

        10      9       8       7       6       5       4       3       2      1

-19     0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-18     0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-17.5   0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-17     0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-16.5   0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-16     0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-15.5   0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-15     0.0003  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-14.5   0.0003  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-14     0.0013  0.0005  0.0002  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-13.5   0.0010  0.0003  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-13     0.0050  0.0021  0.0007  0.0002  0.0001  0.0000  0.0000  0.0000  0.0000 0.0000
-12.5   0.0040  0.0014  0.0004  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
-12     0.0169  0.0079  0.0030  0.0010  0.0003  0.0001  0.0000  0.0000  0.0000 0.0000
-11.5   0.0139  0.0056  0.0018  0.0005  0.0001  0.0000  0.0000  0.0000  0.0000 0.0000
-11     0.0503  0.0276  0.0121  0.0044  0.0014  0.0003  0.0001  0.0000  0.0000 0.0000
-10.5   0.0428  0.0208  0.0074  0.0021  0.0006  0.0001  0.0000  0.0000  0.0000 0.0000
-10     0.1289  0.0836  0.0450  0.0182  0.0060  0.0018  0.0004  0.0001  0.0000 0.0000
-9.5    0.1112  0.0654  0.0299  0.0098  0.0025  0.0006  0.0001  0.0000  0.0000 0.0000
-9      0.2934  0.2156  0.1419  0.0724  0.0265  0.0081  0.0022  0.0005  0.0001 0.0000
-8.5    0.2541  0.1708  0.0998  0.0413  0.0116  0.0026  0.0005  0.0001  0.0000 0.0000
-8      0.5933  0.4818  0.3647  0.2427  0.1159  0.0374  0.0102  0.0025  0.0004 0.0000
-7.5    0.5138  0.3834  0.2614  0.1517  0.0552  0.0124  0.0024  0.0004  0.0000 0.0000
-7      1.0696  0.9510  0.7912  0.6231  0.4202  0.1802  0.0487  0.0120  0.0025 0.0003
-6.5    0.9145  0.7628  0.5714  0.4001  0.2269  0.0676  0.0118  0.0019  0.0002 0.0000
-6      1.7662  1.6484  1.5311  1.3039  1.0875  0.7377  0.2644  0.0574  0.0123 0.0019
-5.5    1.5149  1.2993  1.1275  0.8339  0.6182  0.3296  0.0708  0.0091  0.0009 0.0000
-5      2.6413  2.6209  2.5153  2.4727  2.1375  1.9673  1.2966  0.3476  0.0590 0.0092
-4.5    2.2123  2.0942  1.7975  1.6505  1.1772  0.9665  0.4489  0.0557  0.0050 0.0000
-4      3.6507  3.7157  3.8449  3.7681  4.0099  3.4447  3.7393  2.2322  0.3633 0.0487
-3.5    3.0677  2.8764  2.8299  2.3904  2.3939  1.5678  1.5460  0.5303  0.0208 0.0000
-3      4.6300  4.8822  5.0849  5.5361  5.4980  6.5476  5.3573  7.6077  3.5499 0.2033
-2.5    3.7851  3.8290  3.5803  3.7193  3.0118  3.4201  1.8857  2.5054  0.4333 0.0000
-2      5.4536  5.8172  6.3081  6.7108  7.7712  7.6711  10.7119 7.7474  16.7770 4.3692
-1.5    4.4627  4.3992  4.5762  4.2011  4.6872  3.4786  4.7333  1.8763  3.9053 0.0000
-1      5.9656  6.4172  6.9715  7.7878  8.3823  10.4806 9.9527  17.2989 9.6512 39.8946
-0.5    4.7451  4.9044  4.8001  5.1575  4.5434  5.5481  3.5056  6.1149  1.2100 4.8663
0       6.0438  6.5399  7.1249  7.8311  9.0023  9.6468  13.1902 11.4252 26.2246 8.3300
0.5     4.7844  4.8175  5.0206  4.8177  5.3408  4.3505  5.9195  2.7878  6.6675 0.0000
1       5.7406  6.1248  6.6570  7.2753  8.0088  9.3790  9.7625  14.4122 10.5219 31.3363
1.5     4.4152  4.5140  4.4722  4.6614  4.2834  4.8527  3.4542  5.1871  1.3463 4.5324
2       5.0352  5.3541  5.6643  6.1202  6.5855  7.1223  8.1537  7.9433  11.0232 6.0737
2.5     3.8300  3.8165  3.8328  3.6798  3.7420  3.1894  3.5251  1.9784  2.8717 0.0000
3       4.1480  4.2811  4.4759  4.6009  4.8331  4.9080  5.0209  4.8117  4.1096 0.2404
3.5     3.0803  3.0190  2.9099  2.7953  2.5317  2.3757  1.7718  1.5860  0.5615 0.0000
4       3.1707  3.2013  3.1856  3.1953  3.0698  2.9989  2.5341  2.2123  0.5422 0.0741
4.5     2.3001  2.1906  2.0411  1.8540  1.6193  1.3131  0.9550  0.5559  0.0238 0.0000
5       2.2573  2.1849  2.1036  1.9509  1.7896  1.4651  1.1693  0.4983  0.0813 0.0150
5.5     1.6003  1.4621  1.3048  1.1060  0.8963  0.6220  0.3974  0.0776  0.0072 0.0000
6       1.4904  1.3822  1.2485  1.0885  0.8781  0.6465  0.3502  0.0835  0.0201 0.0039
6.5     1.0278  0.8985  0.7506  0.5945  0.4151  0.2621  0.0904  0.0120  0.0015 0.0000
7       0.9113  0.8025  0.6733  0.5318  0.3776  0.2236  0.0741  0.0187  0.0048 0.0006
7.5     0.6119  0.5025  0.3906  0.2751  0.1710  0.0767  0.0162  0.0029  0.0004 0.0000
8       0.5184  0.4238  0.3276  0.2286  0.1386  0.0573  0.0162  0.0046  0.0010 0.0001
8.5     0.3357  0.2573  0.1811  0.1127  0.0567  0.0170  0.0037  0.0007  0.0001 0.0000
9       0.2697  0.2049  0.1418  0.0867  0.0410  0.0133  0.0040  0.0011  0.0002 0.0000
9.5     0.1690  0.1189  0.0744  0.0400  0.0148  0.0038  0.0009  0.0001  0.0000 0.0000
10      0.1293  0.0890  0.0549  0.0281  0.0107  0.0033  0.0010  0.0002  0.0000 0.0000
10.5    0.0778  0.0494  0.0275  0.0116  0.0036  0.0009  0.0002  0.0000  0.0000 0.0000
11      0.0566  0.0350  0.0187  0.0078  0.0026  0.0008  0.0002  0.0000  0.0000 0.0000
11.5    0.0327  0.0187  0.0086  0.0031  0.0009  0.0002  0.0000  0.0000  0.0000 0.0000
12      0.0226  0.0123  0.0055  0.0021  0.0007  0.0002  0.0000  0.0000  0.0000 0.0000
12.5    0.0126  0.0062  0.0026  0.0008  0.0002  0.0001  0.0000  0.0000  0.0000 0.0000
13      0.0081  0.0040  0.0016  0.0005  0.0002  0.0000  0.0000  0.0000  0.0000 0.0000
13.5    0.0044  0.0019  0.0006  0.0002  0.0001  0.0000  0.0000  0.0000  0.0000 0.0000
14      0.0026  0.0012  0.0004  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
14.5    0.0014  0.0005  0.0002  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
15      0.0008  0.0003  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
15.5    0.0004  0.0002  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
16      0.0002  0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
16.5    0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
17      0.0001  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
17.5    0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
18      0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
18.5    0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
19      0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
19.5    0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
20      0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
20.5    0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000
21.5    0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000  0.0000 0.0000

I screwed up slightly by losing the source data (i.e. nos. of sequences, rather than percentages) and rounding the percentages to 4 decimal places. So the results at the extreme ends contain rows full of '0.000', when at least some of those are not truly zero.

P.S. RKuczek,
If you look at the figures for 2-hand sequences, I think they bear out my earlier analysis of why there are more winners than losers. (Compare the +0.5 and -0.5 figures)

 

[RKuczek]

some thoughts

reviewing the posts on this thread - and the work London has posted (really excellent stuff London) - I have some thoughts about what we are finding here -

1. we are all familiar with the probabilities of winning/pushing/losing individual hands - and take those probablities into account in our play - also are aware that the only way to have a positive ev outcome on a hand is to win it - talking about results, not odds

it seems pretty obvious that we can talk about odds and expected evs on sequences of hands - as well as individual hands - and should be able to take those probabilities into account in our play as well

2. it is also obvious that the probabilities of a positive outcome for short sequences are better for the player than the probability of a positive outcome for a single hand - a smaller differential between the probs for positive and negative outcomes - and a higher probability of a positive outcome -

3. besides the better chances of a positive ev result for a sequence - if you push a sequence - this much more often than not means you won as many hands as you lost - so if played right - with progressive bets - even the push sequences can benefit the player -

4. Hollywood's post about using progressions is very sensible, taking into account the above - calculating progression odds on an independent trials basis - may not be reflective of the real odds - given short sequence skewing - also - using a risk adverse strategy may enhance the results of sequence or progression play - as can taking advantage of double/split possibilities during a sequence/progression - also - progressions other than a martingale may be usable because of the skewing

5. my contention that a short sequence shifts odds in favor of the player may be too strong - as S. Yama pointed out - other things will skew besides just the proportion of stiffs - but - there is an obvious shift in favor of the player - even if less strong than I anticipated

6. I would say that we have established that playing the sequence probabilities and/or progressions, is a very valid strategy for tbj/ebj - the question we need to deal with - is what is the best way of doing that?