What is the likelihood of this?

[jas2587]

Did I see soft 18 not doubled against a dealer's 3 upcard, just glanced at all though including posts

Maybe Eliot will come set the record straight on 16 or I could for most games,decks,rules.

OK!! General B.S. (Most Vegas Games)
If possible, surrender 7,9 and 6,10 against dealer's 9,10,A otherwise hit
Always split 8's (unless dealer hits soft 17, then surrender 8,8 against dealer's A--usually in 6 to 8 deck game)
7,9 and 6,10 against dealer's 2 thru 6, stay
7,9 and 6,10 against dealer's 7 or 8, hit
Soft 16 always hit but double against dealer's 4,5, or 6

A three or more card 16 against dealer's 10 that includes a 4 or 5 you can stay where you normally hit but the difference in expectation is very minimal.


LOL Cindy, Laughing Out Loud

smarty pants sigh

Cindy

[TOC]

Hey, when someone pointed out that I should have hit on a soft 18 vs. a 10, I didn't get defensive, I can man up and admit when I'm wrong...

Because when you're wrong, you're wrong... and staying on a 16 versus a 10 or A is the wrong thing to do. Doesn't matter if you hit 3 times on 16 and bust each time - hitting in that situation is statistically the right thing to do every time.

You are correct, my bad. I don't know what I was thinking, for some reason I was looking at 16 and not thinking that all you could see was the 7. I stand corrected, sorry about that. A 6 would have been a different story..

[aka23]

yw, btw,to clarify, that 1/30,000 number is the chance of winning exactly 5 hands out of 26. The more important number is probably the probility of winning 5 hands or less, which is about 1/24,000.

Treating it as a binomial chance (either win or don't win), the chance of 5 of fewer wins out of 26 hands is about 1 in 90... not 1 in 24 thousand. It is not beyond normal variance, especially considering that optimal strategy was not used for all hands. The "Are My Results Fair?" Calc/Sim in my signature may or may not be relevant, depending on how close your bet size was to fixed.

[aka23]

You are correct, my bad. I don't know what I was thinking, for some reason I was looking at 16 and not thinking that all you could see was the 7. I stand corrected, sorry about that. A 6 would have been a different story..

16 vs 10 is close enough that optimal strategy depends on the specific card composition of your hand. With 2-card 16, hit has higher EV. And with 3+ card 16, stand has higher EV. If you be even more precise, use the rules listed below for 3-card 16 vs 10s with multi-deck BJ instead of always standing/hitting. The lower number rules override the following rules.
1. Any hand with a 5 -- Stand
2. Any hand with a 6 or 10 -- Hit
3. All other hands -- Stand

[DaveG39]

Treating it as a binomial chance (either win or don't win), the chance of 5 of fewer wins out of 26 hands is about 1 in 90... not 1 in 24 thousand. It is not beyond normal variance, especially considering that optimal strategy was not used for all hands. The "Are My Results Fair?" Calc/Sim in my signature may or may not be relevant, depending on how close your bet size was to fixed.

I think you'll see I corrected my 1/24k in a later post, but only down to about 1/2500. I'd be interested to see the math behind the 1/90.

[aka23]

I think you'll see I corrected my 1/24k in a later post, but only down to about 1/2500. I'd be interested to see the math behind the 1/90.

One simple way to get numerical results is to use a binomial calc or Excel, entering the # wins, # hands played , with # chance of event. A good binomial calc is at http://faculty.vassar.edu/lowry/binomialX.html . This page also summarizes the math behind the results. The 1 in 90 chance I listed is based on chance of 5 wins in 26 hands. However, reading the full thread, I see that the 26 hands is with ties removed. If you change it to 5 of fewer wins in 30 hands, then I get 1 in ~400... still within reasonable variance.

[DaveG39]

One simple way to get numerical results is to use a binomial calc or Excel, entering the # wins, # hands played , with # chance of event. A good binomial calc is at http://faculty.vassar.edu/lowry/binomialX.html . This page also summarizes the math behind the results. The 1 in 90 chance I listed is based on chance of 5 wins in 26 hands. However, reading the full thread, I see that the 26 hands is with ties removed. If you change it to 5 of fewer wins in 30 hands, then I get 1 in ~400... still within reasonable variance.

I was leaving out ties in my calculations because no money changes hands, and, therefore, would seem irrelevant (sp.). However, if you treat ties as technical losses ("non-wins"), then yes 1/400 is correct. Reasonable though? Isn't .05 (1/20) and above considered reasonable, stats-wise? Then again, with a sample this small, the margin of error would be huge.

[aka23]

Reasonable though? Isn't .05 (1/20) and above considered reasonable, stats-wise? Then again, with a sample this small, the margin of error would be huge.

In stats, p-value varies depending on what you are trying to show. 0.05 might be appropriate for estimating whether certain experimental variables are correlated, but it is not rare enough to show unfair software, as questioned in the first post of this thread. Many people in this thread have played more than 20 sessions of BJ with Playtech software, so many are expected to have seen a result with odds rarer than 0.05 in a random distribution. Instead, you'd need a far rarer result (or combination of results) that should hardly ever occur in a random distribution. This is what I mean by "within reasonable variance".