New deck at cut

[Cacarulo]

Hi everyone,

After dusting off my streaks simulator and adapting it to the problems raised in this thread, my conclusion is that Don's results are correct.
Here are the results:

Prob   = 0.48
Trials = 7000
Iterations = 100000000

+---------+---------------------+-----------------+-----------------+-----------------+
| Lengths |        Total        |      Exact      |     At Least    |     At Most     |
+---------+---------------------+-----------------+-----------------+-----------------+
|    7    |                3144 |      0.0031440% |    100.0000000% |      0.0031440% |
|    8    |              703956 |      0.7039560% |     99.9968560% |      0.7071000% |
|    9    |             8651149 |      8.6511490% |     99.2929000% |      9.3582490% |
|   10    |            22772998 |     22.7729980% |     90.6417510% |     32.1312470% |
|   11    |            25891452 |     25.8914520% |     67.8687530% |     58.0226990% |
|   12    |            18997148 |     18.9971480% |     41.9773010% |     77.0198470% |
|   13    |            11204096 |     11.2040960% |     22.9801530% |     88.2239430% |
|   14    |             5939298 |      5.9392980% |     11.7760570% |     94.1632410% |
|   15    |             2989988 |      2.9899880% |      5.8367590% |     97.1532290% |
|   16    |             1469950 |      1.4699500% |      2.8467710% |     98.6231790% |
|   17    |              713757 |      0.7137570% |      1.3768210% |     99.3369360% |
|   18    |              343954 |      0.3439540% |      0.6630640% |     99.6808900% |
|   19    |              165652 |      0.1656520% |      0.3191100% |     99.8465420% |
|   20    |               79695 |      0.0796950% |      0.1534580% |     99.9262370% |
|   21    |               38258 |      0.0382580% |      0.0737630% |     99.9644950% |
|   22    |               18418 |      0.0184180% |      0.0355050% |     99.9829130% |
|   23    |                8742 |      0.0087420% |      0.0170870% |     99.9916550% |
|   24    |                4251 |      0.0042510% |      0.0083450% |     99.9959060% |
|   25    |                2105 |      0.0021050% |      0.0040940% |     99.9980110% |
|   26    |                1011 |      0.0010110% |      0.0019890% |     99.9990220% |
|   27    |                 505 |      0.0005050% |      0.0009780% |     99.9995270% |
|   28    |                 228 |      0.0002280% |      0.0004730% |     99.9997550% |
|   29    |                 123 |      0.0001230% |      0.0002450% |     99.9998780% |
|   30    |                  64 |      0.0000640% |      0.0001220% |     99.9999420% |
|   31    |                  30 |      0.0000300% |      0.0000580% |     99.9999720% |
|   32    |                  18 |      0.0000180% |      0.0000280% |     99.9999900% |
|   33    |                   6 |      0.0000060% |      0.0000100% |     99.9999960% |
|   34    |                   4 |      0.0000040% |      0.0000040% |    100.0000000% |
+---------+---------------------+-----------------+-----------------+-----------------+

Prob   = 0.50
Trials = 1000
Iterations = 100000000

+---------+---------------------+-----------------+-----------------+-----------------+
| Lengths |        Total        |      Exact      |     At Least    |     At Most     |
+---------+---------------------+-----------------+-----------------+-----------------+
|    4    |                   5 |      0.0000050% |    100.0000000% |      0.0000050% |
|    5    |               27069 |      0.0270690% |     99.9999950% |      0.0270740% |
|    6    |             1794056 |      1.7940560% |     99.9729260% |      1.8211300% |
|    7    |            12073304 |     12.0733040% |     98.1788700% |     13.8944340% |
|    8    |            23683845 |     23.6838450% |     86.1055660% |     37.5782790% |
|    9    |            23875425 |     23.8754250% |     62.4217210% |     61.4537040% |
|   10    |            17006410 |     17.0064100% |     38.5462960% |     78.4601140% |
|   11    |            10141066 |     10.1410660% |     21.5398860% |     88.6011800% |
|   12    |             5539192 |      5.5391920% |     11.3988200% |     94.1403720% |
|   13    |             2890323 |      2.8903230% |      5.8596280% |     97.0306950% |
|   14    |             1476050 |      1.4760500% |      2.9693050% |     98.5067450% |
|   15    |              745373 |      0.7453730% |      1.4932550% |     99.2521180% |
|   16    |              374087 |      0.3740870% |      0.7478820% |     99.6262050% |
|   17    |              187213 |      0.1872130% |      0.3737950% |     99.8134180% |
|   18    |               93321 |      0.0933210% |      0.1865820% |     99.9067390% |
|   19    |               46487 |      0.0464870% |      0.0932610% |     99.9532260% |
|   20    |               23359 |      0.0233590% |      0.0467740% |     99.9765850% |
|   21    |               11630 |      0.0116300% |      0.0234150% |     99.9882150% |
|   22    |                5937 |      0.0059370% |      0.0117850% |     99.9941520% |
|   23    |                2896 |      0.0028960% |      0.0058480% |     99.9970480% |
|   24    |                1495 |      0.0014950% |      0.0029520% |     99.9985430% |
|   25    |                 693 |      0.0006930% |      0.0014570% |     99.9992360% |
|   26    |                 369 |      0.0003690% |      0.0007640% |     99.9996050% |
|   27    |                 188 |      0.0001880% |      0.0003950% |     99.9997930% |
|   28    |                 105 |      0.0001050% |      0.0002070% |     99.9998980% |
|   29    |                  55 |      0.0000550% |      0.0001020% |     99.9999530% |
|   30    |                  23 |      0.0000230% |      0.0000470% |     99.9999760% |
|   31    |                  12 |      0.0000120% |      0.0000240% |     99.9999880% |
|   32    |                   8 |      0.0000080% |      0.0000120% |     99.9999960% |
|   33    |                   2 |      0.0000020% |      0.0000040% |     99.9999980% |
|   34    |                   1 |      0.0000010% |      0.0000020% |     99.9999990% |
|   35    |                   1 |      0.0000010% |      0.0000010% |    100.0000000% |
+---------+---------------------+-----------------+-----------------+-----------------+

Enjoy.

Sincerely,
Cac

[DSchles]

Thanks, Cac. Appreciate the double-check, but, of course, these things have been known (except to toolyp) since forever. I suppose I've been answering streak questions for about 40-45 years or so. Hard to figure out if toolyp is just an annoying troll, an arrogant newcomer, or a well-intentioned, but uniformed, player. No matter. This thread should have closed a long time ago, but I'll ask Norm to do as much now.

Don

[G Man]

Hard to figure out if toolyp is just an annoying troll, an arrogant newcomer
Don

My understanding of this thread would be: both of the above !
He treated you with total disrespect.

[toolyp]

My understanding of this thread would be: both of the above !
He treated you with total disrespect.

“toolyp is just an annoying troll, an arrogant newcomer”
QED. That’s what you call respect!

No offence, just my honest opinion.

[toolyp]

Thanks, Cac. Appreciate the double-check, but, of course, these things have been known (except to toolyp) since forever. I suppose I've been answering streak questions for about 40-45 years or so. Hard to figure out if toolyp is just an annoying troll, an arrogant newcomer, or a well-intentioned, but uniformed, player. No matter. This thread should have closed a long time ago, but I'll ask Norm to do as much now.

Don

“This thread should have closed a long time ago, but I'll ask Norm to do as much now.”
QED. That’s how you argue.

“I suppose I've been answering streak questions for about 40-45 years or so.”
Warren Weaver did it before you. Difference: He did it right. You Don still dont know what a streak is. You should ask Freightman (not me; he knows French too).

No offence, just my honest opinion.