Question on simple "winning the hand" percentages...

[Fun_at_21]

Hi everyone,

I'm new here. I've always loved the game of blackjack, mostly just for its fun yet isolated and systematic nature (just you versus a dealer). I'm likely not as "hardcore" as most here. I suppose I'm more of just a blackjack "romantic" rather than a blackjack "expert". I always attempt to play basic strategy as well as possible but I'm not a "counter". In Vegas I always play 6 deck. I know it's slightly less favorable than one or two but I simply prefer it better superficially, in terms of having the cards dealt face-up, more tables available etc. I enjoy casually playing for fun at Mandalay Bay, Rio, Paris and Palms (yes I love the bunny!) when I get the chance

At any rate, consider me very "dumb" at Math but does anyone know where I can find (or calculate for myself) simple percentages of winning any given 2 card hand vs every dealer upcard? Now I know that, for instance, Edward Thorp's Beat the Delaer book has the 2 card for each upcard tables in the back of the book but, unless I'm REALLY bad at Math (which I could be), I don't see how you can figure simple percentages of winning a given 2 card hand vs that upcard. They seem to just give expected value percentages which really doesn't tell you how many times, on average, out of a 100 you will win with that 2 card hand versus that upcard...

For instance with say a 2,2 versus a dealer 2, such charts/tables really just tell you what is the best thing to do. But what I want to know is just simply how many times out of a hundred (on average) will I win a 2,2 hand versus a dealer 2. As simple, to me, as this sounds, I never have found any chart/table that lists these (for each and every possible 2 card hand versus each dealer upcard). Can't these be easily calculated (relative to expected value percentages) for each possible 2 card hand vs every upcard? Where can one find (or calculate) these?

I realize the common EV charts for any possible hand are probably more important and useful to "true" blackjack "players" as they're based more on what your expected value is when say hitting vs standing or doubling vs hitting etc. Yet, just for casual curiosity sake I'm one who just likes to know (in 5th grade terms) what my average percentage is (out of a 100%) that I will win the hand when having 2,2 versus a 2, when having 2,3 versus a 2, when having 2,4 versus a 2, etc etc etc for every 2 hand versus every dealer upcard.

In summary, I'm glad to have EV charts to tell me the benefit or loss of making hand decisions BUT sometimes I just want to simply know how many times I can expect to simply win the hand (out of a 100), when I DO make these correct hand decisions, or even if I don't I guess...

Thanks for any help. I greatly appreciate it!

 

[bj bob]

Here's the math

There are several good resources which cover this very topic, one of which is Revere's Playing Blackjack as a Business. The combination of 12 v 2, when hit will yield 4 more winning wagers / 100 than standing; 12 v. 3 will yield 1. The entire chart can be found on p.55. I believe that Blackjack Attack also covers this, as well as several of the more notable classics.

 

[callipygian]

where I can find (or calculate for myself) simple percentages of winning any given 2 card hand vs every dealer upcard?

You can pretty easily make one for yourself on Excel if you're willing to live with an infinite deck approximation.

Player's hand across, dealer's upcard down.

Hard hands:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0.96	0.59	0.47	0.35	0.23	0.2	0.22	0.23	0.25	0.27	0.51	0.43	0.36	0.32	0.29	0.29	0.3
9	0.94	0.82	0.47	0.35	0.23	0.22	0.23	0.25	0.27	0.29	0.53	0.5	0.39	0.34	0.31	0.31	0.32
8	0.93	0.86	0.73	0.37	0.24	0.24	0.26	0.28	0.3	0.33	0.56	0.55	0.49	0.38	0.34	0.35	0.36
7	0.93	0.85	0.77	0.63	0.26	0.26	0.28	0.31	0.33	0.36	0.6	0.58	0.53	0.48	0.38	0.38	0.4
6	0.89	0.78	0.67	0.55	0.44	0.44	0.44	0.44	0.44	0.44	0.63	0.61	0.56	0.52	0.49	0.49	0.49
5	0.89	0.78	0.66	0.54	0.42	0.42	0.42	0.42	0.42	0.42	0.62	0.59	0.54	0.5	0.47	0.47	0.47
4	0.89	0.77	0.65	0.52	0.4	0.4	0.4	0.4	0.4	0.4	0.61	0.58	0.53	0.48	0.45	0.45	0.46
3	0.88	0.76	0.63	0.5	0.38	0.38	0.38	0.38	0.38	0.36	0.59	0.56	0.51	0.46	0.43	0.43	0.43
2	0.88	0.75	0.62	0.49	0.36	0.36	0.36	0.36	0.36	0.35	0.58	0.55	0.5	0.45	0.41	0.41	0.42
1	0.9	0.7	0.49	0.28	0.2	0.2	0.21	0.23	0.25	0.27	0.5	0.45	0.37	0.3	0.28	0.28	0.3

Soft hands:

	21	20	19	18	17	16	15	14	13
10	0.96	0.55	0.06	0.37	0.34	0.35	0.36	0.38	0.39
9	0.94	0.76	0.29	0.39	0.37	0.38	0.39	0.41	0.43
8	0.93	0.79	0.59	0.11	0.41	0.42	0.44	0.45	0.47
7	0.93	0.77	0.62	0.4	0.44	0.46	0.48	0.5	0.52
6	0.89	0.68	0.45	0.22	0.53	0.53	0.54	0.55	0.56
5	0.89	0.67	0.44	0.19	0.51	0.52	0.52	0.53	0.54
4	0.89	0.66	0.42	0.17	0.49	0.5	0.51	0.52	0.52
3	0.88	0.65	0.4	0.14	0.47	0.48	0.49	0.5	0.51
2	0.88	0.64	0.38	0.11	0.46	0.47	0.47	0.48	0.49
1	0.9	0.6	0.19	0.35	0.34	0.35	0.36	0.38	0.39

Paired hands:

	11	10	9	8	7	6	5	4	3	2
10	0.57	0.59	0.35	0.64	0.23	0.27	0.43	0.32	0.29	0.31
9	0.58	0.82	0.42	0.36	0.25	0.29	0.5	0.34	0.31	0.33
8	0.62	0.86	0.53	0.41	0.28	0.33	0.55	0.38	0.35	0.37
7	0.65	0.85	0.63	0.52	0.39	0.36	0.58	0.48	0.46	0.47
6	0.7	0.78	0.59	0.55	0.5	0.53	0.61	0.52	0.54	0.55
5	0.68	0.78	0.58	0.53	0.47	0.51	0.59	0.5	0.52	0.53
4	0.67	0.77	0.56	0.51	0.45	0.49	0.58	0.48	0.5	0.51
3	0.65	0.76	0.54	0.49	0.43	0.47	0.56	0.46	0.43	0.44
2	0.64	0.75	0.52	0.47	0.41	0.35	0.55	0.45	0.41	0.42
1	0.54	0.7	0.28	0.61	0.23	0.27	0.45	0.3	0.28	0.31

Keep in mind that P(loss) + P(win) < 1 because P(tie) > 0.

 

[Fun_at_21]

There are several good resources which cover this very topic, one of which is Revere's Playing Blackjack as a Business. The combination of 12 v 2, when hit will yield 4 more winning wagers / 100 than standing; 12 v. 3 will yield 1. The entire chart can be found on p.55. I believe that Blackjack Attack also covers this, as well as several of the more notable classics.

Thanks for the reply. I'll try and check out those books and see if they have specifically what I'm looking for. The irony is I actually have checked out quite a few "classic" blackjack books and have still really never seen just simply stated winning percentages for winning the hand with any 2 card vs any dealer upcard. Like I said, most books/sites just have expected values for every hand. Again, maybe I just dont know how to "calculate" these into what I'm specifically looking for.

For example, you mentioned that the Playing Blackjack as a Business book has listings that will tell me that a total of 12 versus a 2, when hit, will yield 4 more winning wagers out of 100 hands rather than standing. This is good and even essential to know as far as deciding rather to stand, hit, double etc but what I just want to know is simply how many times can I expect that 12 (or more particularly a 2,T and 3,9 and 4,8 etc versus a 2) to simply win the hand against that 2 (out of 100 hands), regardless whether I win it playing "right" or even by playing it wrong and getting "lucky" or having the dealer bust. Just overall, on average as a simple winning percentage per 100. In other words, when this book says hitting a total of 12 vs a 2 will yield 4 more winning wagers per hundred hands, what are these 4 extra winning hands relative to? 4 more than the 50 you'd normally win if you didn't hit? 4 more than 35? How many hands am I supposed to win per hundred with a T,2 (as just one example of the 12) versus a 2 to begin with? This is the the simple overall percentage that never seems to be given anywhere (unless I dont know where I'm looking or how to do math, both of which might be true...). It seems most these charts just list percentages in terms of bets or a gain/loss of your bet amount. I realize this is most "important" since we play with money but I'm still just wanting to know how many times do I win any given hand versus any upcard (on average) whether I double, split, stand, hit or the dealer just busting...

 

[KenSmith]

For doubling (and only doubling unfortunately), this site has a table that shows the Win / Push / Lose percentages.
http://www.blackjackinfo.com/bjtourn-doublechart.php

 

[Fun_at_21]

You can pretty easily make one for yourself on Excel if you're willing to live with an infinite deck approximation.

Player's hand across, dealer's upcard down.

Hard hands:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0.96	0.59	0.47	0.35	0.23	0.2	0.22	0.23	0.25	0.27	0.51	0.43	0.36	0.32	0.29	0.29	0.3
9	0.94	0.82	0.47	0.35	0.23	0.22	0.23	0.25	0.27	0.29	0.53	0.5	0.39	0.34	0.31	0.31	0.32
8	0.93	0.86	0.73	0.37	0.24	0.24	0.26	0.28	0.3	0.33	0.56	0.55	0.49	0.38	0.34	0.35	0.36
7	0.93	0.85	0.77	0.63	0.26	0.26	0.28	0.31	0.33	0.36	0.6	0.58	0.53	0.48	0.38	0.38	0.4
6	0.89	0.78	0.67	0.55	0.44	0.44	0.44	0.44	0.44	0.44	0.63	0.61	0.56	0.52	0.49	0.49	0.49
5	0.89	0.78	0.66	0.54	0.42	0.42	0.42	0.42	0.42	0.42	0.62	0.59	0.54	0.5	0.47	0.47	0.47
4	0.89	0.77	0.65	0.52	0.4	0.4	0.4	0.4	0.4	0.4	0.61	0.58	0.53	0.48	0.45	0.45	0.46
3	0.88	0.76	0.63	0.5	0.38	0.38	0.38	0.38	0.38	0.36	0.59	0.56	0.51	0.46	0.43	0.43	0.43
2	0.88	0.75	0.62	0.49	0.36	0.36	0.36	0.36	0.36	0.35	0.58	0.55	0.5	0.45	0.41	0.41	0.42
1	0.9	0.7	0.49	0.28	0.2	0.2	0.21	0.23	0.25	0.27	0.5	0.45	0.37	0.3	0.28	0.28	0.3

Soft hands:

	21	20	19	18	17	16	15	14	13
10	0.96	0.55	0.06	0.37	0.34	0.35	0.36	0.38	0.39
9	0.94	0.76	0.29	0.39	0.37	0.38	0.39	0.41	0.43
8	0.93	0.79	0.59	0.11	0.41	0.42	0.44	0.45	0.47
7	0.93	0.77	0.62	0.4	0.44	0.46	0.48	0.5	0.52
6	0.89	0.68	0.45	0.22	0.53	0.53	0.54	0.55	0.56
5	0.89	0.67	0.44	0.19	0.51	0.52	0.52	0.53	0.54
4	0.89	0.66	0.42	0.17	0.49	0.5	0.51	0.52	0.52
3	0.88	0.65	0.4	0.14	0.47	0.48	0.49	0.5	0.51
2	0.88	0.64	0.38	0.11	0.46	0.47	0.47	0.48	0.49
1	0.9	0.6	0.19	0.35	0.34	0.35	0.36	0.38	0.39

Paired hands:

	11	10	9	8	7	6	5	4	3	2
10	0.57	0.59	0.35	0.64	0.23	0.27	0.43	0.32	0.29	0.31
9	0.58	0.82	0.42	0.36	0.25	0.29	0.5	0.34	0.31	0.33
8	0.62	0.86	0.53	0.41	0.28	0.33	0.55	0.38	0.35	0.37
7	0.65	0.85	0.63	0.52	0.39	0.36	0.58	0.48	0.46	0.47
6	0.7	0.78	0.59	0.55	0.5	0.53	0.61	0.52	0.54	0.55
5	0.68	0.78	0.58	0.53	0.47	0.51	0.59	0.5	0.52	0.53
4	0.67	0.77	0.56	0.51	0.45	0.49	0.58	0.48	0.5	0.51
3	0.65	0.76	0.54	0.49	0.43	0.47	0.56	0.46	0.43	0.44
2	0.64	0.75	0.52	0.47	0.41	0.35	0.55	0.45	0.41	0.42
1	0.54	0.7	0.28	0.61	0.23	0.27	0.45	0.3	0.28	0.31

Keep in mind that P(loss) + P(win) < 1 because P(tie) > 0.

Thanks! I appreciate the charts. This at least looks more on target to what I'm looking for. I'm still thinking that something would list the specific hands versus each upcard rather than totals (in the event that not all totals win the same amount of hands when the cards comprising the totals are different). For example, if I'm reading these tables right, a 2,2 versus a 2 can be expected to win on average 42 out of 100 hands. But is this assuming I'm splitting the 2's on every one of these 100 hands (as I should be doing in such a hand)? How many times out of 100 can I expect to win with this hand if I just hit it? Or if (just for insanity's sake) doubled? Or (again, for insanity's sake) stood? Then, I assume, one could make a "true" average of how many times one can expect to win with a 2,2 versus a 2 if one didn't particularly follow the right play but simply played the hand all 4 ways equally (out of a 100) and just hoped for the best. I realize this wouldn't be of much logical use. After all the percentage that wins the most out of a 100 is the only one we should ever need to be concerned with. But just for curiosity sake (and to see the relative differences of how many more times (per 100) you win/lose doing each of the 4 major decisions), I'm surprised these simple average percentages arent broken down somewhere. Or if they are where? Or if not, how could one do them? Is doing such a thing on a software simulation the easiest route to go? Nonetheless, these charts are still helpful though, thanks!

When you say this can easily be done on excel how do you go about this? Apparently I dont have an easy-working brain... Does excel itself calculate these tables somehow? Is their actually a math formula for determing odds of winning any given hand out of a 100 (obviously provided that you know the two cards dealt and the upcard)?

Thanks again...

 

[bj bob]

This ought to help you out (I hope).http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

 

[Fun_at_21]

For doubling (and only doubling unfortunately), this site has a table that shows the Win / Push / Lose percentages.
http://www.blackjackinfo.com/bjtourn-doublechart.php

Hi Ken,

Thanks! That's exactly what I'm looking for! Like you said, too bad it isn't for ANY hand in ANY decision situation but for doubling it will definitely work!

 

[Fun_at_21]

This ought to help you out (I hope).http://www.bjmath.com/bjmath/ev/ev.htm (Archive copy)

Thanks but unfortunately those are still dealing with expected values. For example on the first one given for a 1 deck game (3,2 vs A), all these tell me is that my best decision is to hit (at least it loses the least money of all decisions available). This is certainly most important to know but doesn't tell me how many times (out of 100 hands) I will win with this 3,2 vs A when I hit it? Or even, for curiosities sake, how many times will I win (out of 100 hands) if I doubled on it? Or stood? I know none of these decisions could result in too many wins out of a 100, they are all disadvantage situations (versus an A) but, still, how many could I expect to win? I know that hitting provides only a -32% disadvantage (based on the expected value chart) but I assume this doesn't necessarily mean that, on average, I'll win only 32 out of 100 hands if I hit with this hand? Or am I wrong? (Actually, in this example I would guess that only winning 32 hands out of a 100 with this hand DOES sound about right. But again, I'm still just guessing by logical intuition now...).

 

[Kasi]

I know that hitting provides only a -32% disadvantage (based on the expected value chart) but I assume this doesn't necessarily mean that, on average, I'll win only 32 out of 100 hands if I hit with this hand? Or am I wrong? (Actually, in this example I would guess that only winning 32 hands out of a 100 with this hand DOES sound about right. But again, I'm still just guessing by logical intuition now...).

Well, to get exactly what you want, you'd have to do what Ken did for doubling in a 6D game (was it S17, can't remeber) except do it for 1,2,4,6 $ 8D and then do it again for all that for whether you hit, stand double or split, and then do it again for all that for each subset of rules like LS or ES or NDAS or DAS etc.

In your example, no it doesn't necessarily mean you will win 32 of 100 hands. It might though lol.

I'd use Callipygian's charts for a ball park - I don't know how he did it either lol. I assume his charts are for the winning % of the correct BS play.

So, in your example, say one will win 30% of the time (in C's charts) with a 5 vs Ace and the EV is -0.32. That would mean one loses 62% of the time and push 8% of the time to get the -0.32 EV.

EV is a function of the %age of hands won, lost & tied. You just don't know if a -2% EV means 51% hands lost and 49% of hands won and 0% hands tied or whether it means 3% hands lost, 1% hands won and 96% hands tied.

Using Callipygian's tables can at least put you in the ball park - at least they seemed to make sense to me.

Not sure why you care anyway since EV is really what matters. Although I've always really liked what Ken did in those doubling tables.

You can use his tables and compare them to EV for alot of 2-card hands using something like Don's EV tables for a 6D game to understand how it all relates.

I've never seen something comparable to what Ken did anywhere. Although, for some weird reason I don't fully understand, I'd really like to too lol.

 

[QFIT]

Depends on rules and strategy. This is for six decks, S17, DAS, 75% penetration, Basic Strategy:

http://www.qfit.com/handswlp.HTM

 

[Fun_at_21]

Well, to get exactly what you want, you'd have to do what Ken did for doubling in a 6D game (was it S17, can't remeber) except do it for 1,2,4,6 $ 8D and then do it again for all that for whether you hit, stand double or split, and then do it again for all that for each subset of rules like LS or ES or NDAS or DAS etc.

In your example, no it doesn't necessarily mean you will win 32 of 100 hands. It might though lol.

I'd use Callipygian's charts for a ball park - I don't know how he did it either lol. I assume his charts are for the winning % of the correct BS play.

So, in your example, say one will win 30% of the time (in C's charts) with a 5 vs Ace and the EV is -0.32. That would mean one loses 62% of the time and push 8% of the time to get the -0.32 EV.

EV is a function of the %age of hands won, lost & tied. You just don't know if a -2% EV means 51% hands lost and 49% of hands won and 0% hands tied or whether it means 3% hands lost, 1% hands won and 96% hands tied.

Yeah, it must be the pushes that help to make EV charts confusing to me somehow. I know I'm supposed to use EV charts to just simply see what the best decision is to make, but something in my simplistic head always wants to just look for straight-forward percentages of winning the hand and I can never seem to calculate that from EV tables. I always want to move the decimal over 2 places to the right then take that percentage and assume that means I'll win that hand that percentage of the time if I hit/stand/double etc, but I know that's not usually accurate (or what the tables are even for)...

Not sure why you care anyway since EV is really what matters. Although I've always really liked what Ken did in those doubling tables.

Well, like I said, I understand that EV tables are actually more "useful". Just making the right play decision is what's most "important" and should be all we're interested in. But I just simply relate better, I guess, to seeing straight-forward winning the hand percentages. It registers in my memory in more black and white terms if I just know I can expect to win such and such a hand this many times out of a 100, rather than trying to envision how much "better" off I am to hit versus stand versus double etc. Maybe we can blame it on our natural gravitation to interpret things on a 100% scale, like when back in school . Now I know that way of thinking can, in some cases, lead to trouble. For doubling, for instance, l know that its sometimes to possible to have an expected winning percentage of such and such and yet still make more money than having a higher winning percentage out of a 100 (if you were to just hit the same hand). In these cases, I understand that black and white winning the hand percentages actually "lie" and dont tell you the "right" story. Still, in general terms, they make more relatable "sense" to me than trying to discern between EV decisions on a table (I mean, being a basic strategy player I have the best play decisions largely memorized anyways). Plus, I'm the type who just mostly enjoys blackjack as a "gambling" game (not expecting I'm supposed to win, consistently anyway). I was always initially drawn just to some of the simple percentages of it, how often do you get such and such a hand, what are your simple overall odds to beat a dealer with such and such a hand versus this upcard etc. I try to play as correct as I can so the game is even (more or less) but most importantly, I feel, I play for fun, not necessarily for expected money (advantage). After all life is short. I know, call me crazy

I've never seen something comparable to what Ken did anywhere. Although, for some weird reason I don't fully understand, I'd really like to too lol.

Yeah, neither have I! That's been the whole problem! Those doubling tables are exactly what I've been after but it is puzzling, just for handy average reference purposes, that they arent listed for ALL hands/decisions anywhere. Again, I know they aren't as important as EV decision tables but they would be more "casually useful/interesting/simpler" to us non-blackjack experts who just enjoy the general probability of the game for what it is and who just like knowing the simple odds of winning any hand/situation out of 100.

Perhaps that can be a good project for someone who is good at Math, has a fast simulator or is making a new blackjack book/or site/ program??? Have a list of every possible 2 card hand dealt vs every possible up card (not just hand TOTALS) and just simply list average odds of winning the hand (out of 100). Nothing more, nothing less. In addition, just for pure curiosities sake, do this with each 2 card hand if you hit it, stand, split, double down. Heck, if you have a ton of time on your hands one could then even list the simple odds of winning with that initial 2 card hand PLUS if they ended up drawing just one card to it, then 2, then 3 etc. In other words, someone could list what the odds are of winning with a 2, 2 versus a 2 (out of 100) if the 2,2 hand ended up with 5 cards in the hand, or just 3 etc. Or just for all-purpose sake, how many hands does the player win on average out of a 100 when his hand quantity (regardless of what the cards are) is 5 cards (he hit 3 cards to his initial 2 card hand). I can guess that your probability of busting increases with higher quantity hands, on average. But, still, these kind of general, average, simple percentages would be interesting to know! Maybe not useful, but still interesting! They also may not be of any practical use in terms of betting with money and making hand decisions but for just us pure blackjack lovers Id be most curious to know such trivial things (in simple terms and on average of a 100 hands). Hey, at least you'd have one buyer of this new book...

 

[Fun_at_21]

Depends on rules and strategy. This is for six decks, S17, DAS, 75% penetration, Basic Strategy:

http://www.qfit.com/handswlp.HTM

Thanks for the chart! It looks like this may work as well, at least for general hand total odds purposes. I appreciate it.

 

[bj bob]

Thanks for the chart! It looks like this may work as well, at least for general hand total odds purposes. I appreciate it.

Just a caveat here. Be careful not to get overly analytical with the math minutia. For example, take the hand 7,7 v. 10 (SD,H17 DOA,LS). Now first you have to know what correct BS dictates, which is the best way to play this hand, then you refer to your "best way" chart. But what is the best way's advantage over "other" ways? According to BS, the best way to play this hand is to surrender, however there are several other "worse" ways it can be played, e.g. stand, split, hit and even double down (if you're a complete idiot). Now you have to do all the other mental math and, consequently check yourself in to the nearest psych ward, comprende?

 

[Fun_at_21]

Just a caveat here. Be careful not to get overly analytical with the math minutia. For example, take the hand 7,7 v. 10 (SD,H17 DOA,LS). Now first you have to know what correct BS dictates, which is the best way to play this hand, then you refer to your "best way" chart. But what is the best way's advantage over "other" ways? According to BS, the best way to play this hand is to surrender, however there are several other "worse" ways it can be played, e.g. stand, split, hit and even double down (if you're a complete idiot). Now you have to do all the other mental math and, consequently check yourself in to the nearest psych ward, comprende?

True. That's why, in a perfect world, it would be handy if simple "odds of winning the hand out of a 100" charts could be compiled that specifically list how many times you're likely to win any given 2 card hand for ANY way that you might play it. Then to the right, one could just simply average the sum of all these likely percentages and you could get just a "general" odds of winning any 2,2 versus a 2 hand (as one example), whether you always stood, split, hit, doubled, etc or did the "right" play sometimes and the wrong way other times. In effect the sums divided by four would just tell you what your odds are with any given hand if you dont particularly know what you're doing or which of the four decisions is the correct way. Again, just for pure trivial purposes this would be interesting- obviously in actual play you would only need to look up the one percentage that is the best play...

And one could still use such "winning the hand out of a 100" charts to determine how to make the best play by simply seeing which winning the hand percentage is highest for any decision option. The exceptions as I mentioned in the above post would be doubling vs hitting - in some cases the hit percentage odds would be highest but you should really double the hand (if the idea is to make more money on the hand). Or the surrender option, as you mentioned, might fall through the cracks of these charts as well (although one could just highlight such 2 card hands in yellow or something indicating to just surrender this hand no matter what the odds of winning the hand say).

At any rate, I can envision exactly how these charts could be (and even how simple and straightforward they could be) but the problem is I dont have a simulator to get the "long run results" of any possible hand. I am in the process of doing hand-dealt results to myself and doing every possible two card hand vs every upcard say 100 or 500 times each. Like they say, no better way than to just see and validate the probabilities yourself in front of your own eyes! The problem with this is 1) this is fun but obviously time-consuming and probably a bit ridiculous and 2) no matter if I do 100, 500 or even 100,000 hands, it likely isnt enough to reliably use for accurate reference. Still, I'll likely keep doing them, bit by bit, hand by hand just to have my own little database and just to see how close to long term probabilities I do in fact get with each hand versus each upcard. I'm guessing some will fall right into true long term odds, some will likely give exaggerated odds out of a 100, either to my benefit or the dealers. Still, I figure it cant be a completely pointless short term experiment. I've learned it can be enlightening to repeatedly play a particular hand in front of your own eyes, even if just for curiosity sake. Even out of just 100 hands, you do start to see that, yes, I do actually win a fair share of hands when I stand on that 13 versus a dealer 6 etc. In the casinos you often dont believe the basic strategy sometimes - you swear the dealer's winning everything. It can be fun to prove it to yourself by doing the hands repeatedly in front of your own eyes, at least as far as "short term" results can "prove" it...

Still, between the awesome doubling chart Ken showed me and the couple others provided here, I mostly have what I'm generally looking for, I think...

 

[callipygian]

if I'm reading these tables right, a 2,2 versus a 2 can be expected to win on average 42 out of 100 hands. But is this assuming I'm splitting the 2's on every one of these 100 hands (as I should be doing in such a hand)?

The tables I posted are simply win percentages for the best decision - in the case of 2,2 vs. 2, yes, that means split, but in the case of 2,2 vs. A, that means hitting.

How many times out of 100 can I expect to win with this hand if I just hit it? Or if (just for insanity's sake) doubled? Or (again, for insanity's sake) stood? ... I'm surprised these simple average percentages arent broken down somewhere.

They're calculated in every simulator, but often only P(win)-P(lose) is presented because that's what's most relevant. I happen to have them calculated separately from a spreadsheet I used to calculate strategy for match play coupons (in which case 2*P(win)-P(lose) is the most relevant figure).

My next post will contain all the data I believe you're looking for, with the caveat that it's all for infinite deck.

 

[callipygian]

Win Percentages

Stand:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0.96	0.59	0.47	0.35	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23
9	0.94	0.82	0.47	0.35	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23
8	0.93	0.86	0.73	0.37	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24
7	0.93	0.85	0.77	0.63	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26
6	0.89	0.78	0.67	0.55	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44
5	0.89	0.78	0.66	0.54	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42
4	0.89	0.77	0.65	0.52	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4
3	0.88	0.76	0.63	0.5	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38
2	0.88	0.75	0.62	0.49	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36
1	0.9	0.7	0.49	0.28	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2

Hard Double:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0	0.07	0.12	0.16	0.18	0.2	0.22	0.24	0.25	0.27	0.51	0.43	0.34	0.29	0.24	0.23	0.23
9	0	0.07	0.14	0.17	0.2	0.22	0.23	0.25	0.27	0.29	0.52	0.49	0.36	0.28	0.24	0.23	0.23
8	0	0.07	0.14	0.19	0.22	0.24	0.26	0.28	0.3	0.32	0.55	0.53	0.45	0.32	0.25	0.24	0.24
7	0	0.07	0.14	0.2	0.24	0.26	0.28	0.3	0.32	0.34	0.58	0.56	0.49	0.41	0.29	0.26	0.26
6	0	0.07	0.13	0.18	0.22	0.26	0.29	0.32	0.36	0.39	0.63	0.61	0.55	0.49	0.45	0.44	0.44
5	0	0.07	0.13	0.18	0.22	0.25	0.28	0.32	0.35	0.38	0.62	0.59	0.53	0.47	0.43	0.42	0.42
4	0	0.07	0.13	0.18	0.22	0.25	0.28	0.31	0.34	0.37	0.61	0.58	0.51	0.45	0.41	0.4	0.4
3	0	0.07	0.13	0.18	0.21	0.24	0.27	0.3	0.33	0.36	0.59	0.56	0.5	0.44	0.39	0.38	0.38
2	0	0.07	0.13	0.17	0.21	0.24	0.27	0.29	0.32	0.35	0.58	0.55	0.48	0.42	0.37	0.36	0.36
1	0	0.07	0.12	0.16	0.18	0.2	0.21	0.23	0.24	0.26	0.48	0.44	0.33	0.25	0.21	0.2	0.2

Hard Hit:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0	0.07	0.12	0.16	0.18	0.2	0.22	0.23	0.25	0.27	0.51	0.43	0.36	0.32	0.29	0.29	0.3
9	0	0.07	0.14	0.17	0.2	0.22	0.23	0.25	0.27	0.29	0.53	0.5	0.39	0.34	0.31	0.31	0.32
8	0	0.07	0.14	0.19	0.22	0.24	0.26	0.28	0.3	0.33	0.56	0.55	0.49	0.38	0.34	0.35	0.36
7	0	0.07	0.14	0.2	0.24	0.26	0.28	0.31	0.33	0.36	0.6	0.58	0.53	0.48	0.38	0.38	0.4
6	0	0.07	0.13	0.18	0.22	0.26	0.29	0.32	0.36	0.39	0.63	0.61	0.56	0.52	0.49	0.49	0.49
5	0	0.07	0.13	0.18	0.22	0.25	0.28	0.32	0.35	0.38	0.62	0.59	0.54	0.5	0.47	0.47	0.47
4	0	0.07	0.13	0.18	0.22	0.25	0.28	0.31	0.34	0.37	0.61	0.58	0.53	0.48	0.45	0.45	0.46
3	0	0.07	0.13	0.18	0.21	0.24	0.27	0.3	0.33	0.36	0.59	0.56	0.51	0.46	0.43	0.43	0.43
2	0	0.07	0.13	0.17	0.21	0.24	0.27	0.29	0.32	0.35	0.58	0.55	0.5	0.45	0.41	0.41	0.42
1	0	0.07	0.12	0.16	0.18	0.2	0.21	0.23	0.25	0.27	0.5	0.45	0.37	0.3	0.28	0.28	0.3

Soft Double:

	21	20	19	18	17	16	15	14	13
10	0.51	0.43	0.4	0.37	0.34	0.34	0.34	0.34	0.34
9	0.52	0.49	0.41	0.38	0.36	0.36	0.36	0.36	0.36
8	0.55	0.53	0.5	0.42	0.39	0.39	0.39	0.39	0.39
7	0.58	0.56	0.54	0.51	0.43	0.43	0.43	0.43	0.43
6	0.63	0.61	0.58	0.55	0.53	0.53	0.53	0.53	0.53
5	0.62	0.59	0.57	0.54	0.51	0.51	0.51	0.51	0.51
4	0.61	0.58	0.55	0.52	0.49	0.49	0.49	0.49	0.49
3	0.59	0.56	0.53	0.5	0.47	0.47	0.47	0.47	0.47
2	0.58	0.55	0.52	0.49	0.46	0.46	0.46	0.46	0.46
1	0.48	0.44	0.39	0.34	0.32	0.32	0.32	0.32	0.32

Soft Hit:

	21	20	19	18	17	16	15	14	13
10	0.51	0.43	0.4	0.37	0.34	0.35	0.36	0.38	0.39
9	0.53	0.5	0.42	0.39	0.37	0.38	0.39	0.41	0.43
8	0.56	0.55	0.52	0.44	0.41	0.42	0.44	0.45	0.47
7	0.6	0.58	0.56	0.53	0.44	0.46	0.48	0.5	0.52
6	0.63	0.61	0.58	0.55	0.53	0.53	0.54	0.55	0.56
5	0.62	0.59	0.57	0.54	0.51	0.52	0.52	0.53	0.54
4	0.61	0.58	0.55	0.52	0.49	0.5	0.51	0.52	0.52
3	0.59	0.56	0.53	0.5	0.47	0.48	0.49	0.5	0.51
2	0.58	0.55	0.52	0.49	0.46	0.47	0.47	0.48	0.49
1	0.5	0.45	0.4	0.35	0.34	0.35	0.36	0.38	0.39

 

[callipygian]

Loss Percentages

Stand:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0	0.04	0.41	0.53	0.65	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77
9	0	0.06	0.18	0.53	0.65	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77	0.77
8	0	0.07	0.14	0.27	0.63	0.76	0.76	0.76	0.76	0.76	0.76	0.76	0.76	0.76	0.76	0.76	0.76
7	0	0.07	0.15	0.23	0.37	0.74	0.74	0.74	0.74	0.74	0.74	0.74	0.74	0.74	0.74	0.74	0.74
6	0	0.11	0.22	0.33	0.45	0.56	0.56	0.56	0.56	0.56	0.56	0.56	0.56	0.56	0.56	0.56	0.56
5	0	0.11	0.22	0.34	0.46	0.58	0.58	0.58	0.58	0.58	0.58	0.58	0.58	0.58	0.58	0.58	0.58
4	0	0.11	0.23	0.35	0.48	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6	0.6
3	0	0.12	0.24	0.37	0.5	0.62	0.62	0.62	0.62	0.62	0.62	0.62	0.62	0.62	0.62	0.62	0.62
2	0	0.12	0.25	0.38	0.51	0.64	0.64	0.64	0.64	0.64	0.64	0.64	0.64	0.64	0.64	0.64	0.64
1	0	0.1	0.3	0.51	0.72	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8	0.8

Hard Double:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	1	0.92	0.85	0.8	0.77	0.74	0.72	0.7	0.69	0.67	0.42	0.43	0.57	0.66	0.71	0.76	0.77
9	1	0.92	0.85	0.79	0.75	0.72	0.71	0.69	0.67	0.65	0.41	0.42	0.51	0.64	0.72	0.76	0.77
8	1	0.92	0.85	0.79	0.73	0.7	0.68	0.66	0.64	0.62	0.38	0.39	0.47	0.55	0.68	0.75	0.76
7	1	0.92	0.85	0.79	0.73	0.68	0.66	0.64	0.62	0.6	0.35	0.36	0.44	0.51	0.59	0.71	0.74
6	1	0.92	0.85	0.79	0.74	0.7	0.67	0.63	0.6	0.56	0.3	0.32	0.39	0.45	0.51	0.55	0.56
5	1	0.92	0.85	0.79	0.74	0.7	0.67	0.64	0.61	0.57	0.31	0.34	0.41	0.47	0.53	0.57	0.58
4	1	0.92	0.85	0.8	0.75	0.71	0.68	0.64	0.61	0.58	0.32	0.35	0.42	0.49	0.55	0.59	0.6
3	1	0.92	0.86	0.8	0.75	0.71	0.68	0.65	0.62	0.59	0.33	0.36	0.44	0.5	0.56	0.61	0.62
2	1	0.92	0.86	0.8	0.75	0.71	0.68	0.66	0.63	0.6	0.34	0.37	0.45	0.52	0.58	0.63	0.64
1	1	0.92	0.85	0.8	0.76	0.74	0.72	0.71	0.69	0.68	0.43	0.45	0.56	0.67	0.75	0.79	0.8

Hard Hit:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	1	0.92	0.85	0.8	0.77	0.74	0.72	0.7	0.68	0.65	0.39	0.4	0.52	0.57	0.61	0.63	0.61
9	1	0.92	0.85	0.79	0.75	0.72	0.7	0.68	0.66	0.63	0.37	0.38	0.44	0.55	0.59	0.6	0.59
8	1	0.92	0.85	0.79	0.73	0.7	0.68	0.65	0.63	0.6	0.33	0.35	0.39	0.44	0.55	0.57	0.55
7	1	0.92	0.85	0.79	0.73	0.68	0.65	0.63	0.6	0.57	0.3	0.32	0.36	0.4	0.45	0.53	0.52
6	1	0.92	0.85	0.79	0.74	0.7	0.67	0.63	0.6	0.56	0.3	0.32	0.37	0.42	0.45	0.48	0.48
5	1	0.92	0.85	0.79	0.74	0.7	0.67	0.64	0.61	0.57	0.31	0.34	0.39	0.43	0.47	0.5	0.5
4	1	0.92	0.85	0.8	0.75	0.71	0.68	0.64	0.61	0.58	0.32	0.35	0.4	0.45	0.49	0.52	0.51
3	1	0.92	0.86	0.8	0.75	0.71	0.68	0.65	0.62	0.59	0.33	0.36	0.41	0.46	0.5	0.54	0.53
2	1	0.92	0.86	0.8	0.75	0.71	0.68	0.66	0.63	0.6	0.34	0.37	0.42	0.47	0.52	0.55	0.54
1	1	0.92	0.85	0.8	0.76	0.74	0.72	0.7	0.68	0.65	0.39	0.42	0.49	0.57	0.63	0.63	0.61

Soft Double:

	21	20	19	18	17	16	15	14	13
10	0.42	0.43	0.52	0.54	0.57	0.6	0.6	0.6	0.6
9	0.41	0.42	0.45	0.53	0.56	0.58	0.58	0.58	0.58
8	0.38	0.39	0.41	0.44	0.52	0.55	0.55	0.55	0.55
7	0.35	0.36	0.38	0.4	0.43	0.52	0.52	0.52	0.52
6	0.3	0.32	0.35	0.38	0.4	0.43	0.43	0.43	0.43
5	0.31	0.34	0.36	0.39	0.42	0.45	0.45	0.45	0.45
4	0.32	0.35	0.38	0.4	0.43	0.46	0.46	0.46	0.46
3	0.33	0.36	0.39	0.42	0.45	0.48	0.48	0.48	0.48
2	0.34	0.37	0.4	0.43	0.46	0.49	0.49	0.49	0.49
1	0.43	0.45	0.5	0.55	0.6	0.62	0.62	0.62	0.62

Soft Hit:

	21	20	19	18	17	16	15	14	13
10	0.39	0.4	0.49	0.52	0.54	0.55	0.54	0.52	0.5
9	0.37	0.38	0.41	0.49	0.52	0.52	0.5	0.48	0.46
8	0.33	0.35	0.37	0.4	0.48	0.49	0.46	0.44	0.42
7	0.3	0.32	0.34	0.36	0.39	0.46	0.44	0.42	0.39
6	0.3	0.32	0.35	0.38	0.4	0.43	0.42	0.4	0.39
5	0.31	0.34	0.36	0.39	0.42	0.44	0.43	0.42	0.41
4	0.32	0.35	0.38	0.4	0.43	0.46	0.45	0.43	0.42
3	0.33	0.36	0.39	0.42	0.45	0.47	0.46	0.45	0.43
2	0.34	0.37	0.4	0.43	0.46	0.49	0.47	0.46	0.45
1	0.39	0.42	0.46	0.51	0.56	0.55	0.53	0.51	0.49

 

[Fun_at_21]

Stand:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0.96	0.59	0.47	0.35	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23
9	0.94	0.82	0.47	0.35	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23	0.23
8	0.93	0.86	0.73	0.37	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24	0.24
7	0.93	0.85	0.77	0.63	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26	0.26
6	0.89	0.78	0.67	0.55	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44	0.44
5	0.89	0.78	0.66	0.54	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42	0.42
4	0.89	0.77	0.65	0.52	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4	0.4
3	0.88	0.76	0.63	0.5	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38	0.38
2	0.88	0.75	0.62	0.49	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36	0.36
1	0.9	0.7	0.49	0.28	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2

Hard Double:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0	0.07	0.12	0.16	0.18	0.2	0.22	0.24	0.25	0.27	0.51	0.43	0.34	0.29	0.24	0.23	0.23
9	0	0.07	0.14	0.17	0.2	0.22	0.23	0.25	0.27	0.29	0.52	0.49	0.36	0.28	0.24	0.23	0.23
8	0	0.07	0.14	0.19	0.22	0.24	0.26	0.28	0.3	0.32	0.55	0.53	0.45	0.32	0.25	0.24	0.24
7	0	0.07	0.14	0.2	0.24	0.26	0.28	0.3	0.32	0.34	0.58	0.56	0.49	0.41	0.29	0.26	0.26
6	0	0.07	0.13	0.18	0.22	0.26	0.29	0.32	0.36	0.39	0.63	0.61	0.55	0.49	0.45	0.44	0.44
5	0	0.07	0.13	0.18	0.22	0.25	0.28	0.32	0.35	0.38	0.62	0.59	0.53	0.47	0.43	0.42	0.42
4	0	0.07	0.13	0.18	0.22	0.25	0.28	0.31	0.34	0.37	0.61	0.58	0.51	0.45	0.41	0.4	0.4
3	0	0.07	0.13	0.18	0.21	0.24	0.27	0.3	0.33	0.36	0.59	0.56	0.5	0.44	0.39	0.38	0.38
2	0	0.07	0.13	0.17	0.21	0.24	0.27	0.29	0.32	0.35	0.58	0.55	0.48	0.42	0.37	0.36	0.36
1	0	0.07	0.12	0.16	0.18	0.2	0.21	0.23	0.24	0.26	0.48	0.44	0.33	0.25	0.21	0.2	0.2

Hard Hit:

	21	20	19	18	17	16	15	14	13	12	11	10	9	8	7	6	5
10	0	0.07	0.12	0.16	0.18	0.2	0.22	0.23	0.25	0.27	0.51	0.43	0.36	0.32	0.29	0.29	0.3
9	0	0.07	0.14	0.17	0.2	0.22	0.23	0.25	0.27	0.29	0.53	0.5	0.39	0.34	0.31	0.31	0.32
8	0	0.07	0.14	0.19	0.22	0.24	0.26	0.28	0.3	0.33	0.56	0.55	0.49	0.38	0.34	0.35	0.36
7	0	0.07	0.14	0.2	0.24	0.26	0.28	0.31	0.33	0.36	0.6	0.58	0.53	0.48	0.38	0.38	0.4
6	0	0.07	0.13	0.18	0.22	0.26	0.29	0.32	0.36	0.39	0.63	0.61	0.56	0.52	0.49	0.49	0.49
5	0	0.07	0.13	0.18	0.22	0.25	0.28	0.32	0.35	0.38	0.62	0.59	0.54	0.5	0.47	0.47	0.47
4	0	0.07	0.13	0.18	0.22	0.25	0.28	0.31	0.34	0.37	0.61	0.58	0.53	0.48	0.45	0.45	0.46
3	0	0.07	0.13	0.18	0.21	0.24	0.27	0.3	0.33	0.36	0.59	0.56	0.51	0.46	0.43	0.43	0.43
2	0	0.07	0.13	0.17	0.21	0.24	0.27	0.29	0.32	0.35	0.58	0.55	0.5	0.45	0.41	0.41	0.42
1	0	0.07	0.12	0.16	0.18	0.2	0.21	0.23	0.25	0.27	0.5	0.45	0.37	0.3	0.28	0.28	0.3

Soft Double:

	21	20	19	18	17	16	15	14	13
10	0.51	0.43	0.4	0.37	0.34	0.34	0.34	0.34	0.34
9	0.52	0.49	0.41	0.38	0.36	0.36	0.36	0.36	0.36
8	0.55	0.53	0.5	0.42	0.39	0.39	0.39	0.39	0.39
7	0.58	0.56	0.54	0.51	0.43	0.43	0.43	0.43	0.43
6	0.63	0.61	0.58	0.55	0.53	0.53	0.53	0.53	0.53
5	0.62	0.59	0.57	0.54	0.51	0.51	0.51	0.51	0.51
4	0.61	0.58	0.55	0.52	0.49	0.49	0.49	0.49	0.49
3	0.59	0.56	0.53	0.5	0.47	0.47	0.47	0.47	0.47
2	0.58	0.55	0.52	0.49	0.46	0.46	0.46	0.46	0.46
1	0.48	0.44	0.39	0.34	0.32	0.32	0.32	0.32	0.32

Soft Hit:

	21	20	19	18	17	16	15	14	13
10	0.51	0.43	0.4	0.37	0.34	0.35	0.36	0.38	0.39
9	0.53	0.5	0.42	0.39	0.37	0.38	0.39	0.41	0.43
8	0.56	0.55	0.52	0.44	0.41	0.42	0.44	0.45	0.47
7	0.6	0.58	0.56	0.53	0.44	0.46	0.48	0.5	0.52
6	0.63	0.61	0.58	0.55	0.53	0.53	0.54	0.55	0.56
5	0.62	0.59	0.57	0.54	0.51	0.52	0.52	0.53	0.54
4	0.61	0.58	0.55	0.52	0.49	0.5	0.51	0.52	0.52
3	0.59	0.56	0.53	0.5	0.47	0.48	0.49	0.5	0.51
2	0.58	0.55	0.52	0.49	0.46	0.47	0.47	0.48	0.49
1	0.5	0.45	0.4	0.35	0.34	0.35	0.36	0.38	0.39

Split:

	11	10	9	8	7	6	5	4	3	2
10	0.51	0.39	0.37	0.3	0.3	0.25	0.27	0.35	0.36	0.37
9	0.52	0.48	0.41	0.38	0.37	0.32	0.4	0.41	0.42	0.43
8	0.55	0.55	0.53	0.45	0.4	0.43	0.44	0.45	0.47	0.48
7	0.58	0.58	0.57	0.56	0.45	0.47	0.48	0.5	0.51	0.52
6	0.63	0.61	0.6	0.65	0.66	0.67	0.67	0.67	0.68	0.68
5	0.62	0.59	0.58	0.58	0.64	0.64	0.65	0.65	0.65	0.62
4	0.61	0.58	0.57	0.56	0.62	0.62	0.62	0.63	0.59	0.6
3	0.59	0.56	0.55	0.54	0.59	0.59	0.56	0.57	0.57	0.57
2	0.58	0.55	0.53	0.52	0.53	0.5	0.5	0.51	0.52	0.52
1	0.48	0.4	0.35	0.27	0.22	0.24	0.27	0.34	0.35	0.36

Thanks for all the charts. I appreciate it. It is more of what I'm looking for but, again, I always seem to get confused with these things as far as them being consistent with each other. For example...

1) In your original tables you sent in your first post, the pair charts were assumed that you win this many hands out of a 100 if you used the correct basic strategy decision with that pair. To use the 2,2 versus 2 example that I always use as my default example, that first chart says I should win, on average, 42 out of a 100 hands if I SPLIT the 2,2 versus the 2 (as this is what the 42% odds are resting on - that I'll play the 2,2 the correct way). However, in the recent chart you gave for "winning percentages", the "split" table has 2,2 vs a 2 as winning, on average, 0.52 (52%) out of a 100 hands? This is a 10% difference of what I thought, if I'm reading the two tables correctly, was the same action against the 2?

2) Also, in the recent tables you provided, the winning percentage one has the 0.52 (52%) listed for splitting 2,2 versus a 2 while the losing percentages chart shows that splitting a 2,2 versus a 2 will lose 0.56 (56%) of the time. These don't match up evenly to 100%. Does this have something to do with pushes that are throwing me off again? Were pushes considered half wins for BOTH player and dealer's perspective, thus giving the odds of winning and losing this hand a bit higher percentage than reality?

3) In the case of the 2,2 vs 2 hand, I still don't see which charts would reveal how many times out of a 100 I'm likely to win by drawing, standing and doubling (which I guess would actually be the same odds as winning the hand by hitting just that you'd lose twice the money). Though starting with totals of 5 (or a 2,3 vs a 2) I see where I can find them...

Hopefully I don't sound like I'm being too particular or difficult. This is still more helpful and closer to what I'm after than anything else I've been able to find for the most part! Thanks!

 

[k_c]

An even money pay EV can be converted to win percent by this formula:
win percent = (1+EV)/2 and this assumes a push = 50% win, 50% loss.

In blackjack there is the possiblilty of blackjack, doubling, and splitting incorporated into the EV, so that needs to be considered.

If dealer has a ten or ace as up card, EV can be computed 2 ways:
conditional EV: assumes dealer has checked for BJ and doesn't have it
unconditional EV: player non-BJ loses to dealer BJ

Most EV listings for ten and ace up use conditional EV. However, in order to calculate a winning percent unconditional EV needs to be used.

To convert conditional EV to unconditional EV:
pDBJ=prob(dealer blackjack); prob(dealer BJ)=0 if up card is not ten or ace
uev = cev - pDBJ(cev+1)
If up card is not ten or ace, uev and cev are the same thing.

Once uev is determined, a win percent can be calculated from the EV that counts pushes as 50% win and 50% loss.

Stand and hit:
win percent = (1+uev)/2

Double
win percent = (2+uev+pDBJ)/4

Split (1 split)
win percent = (2+uev+pDBJ)/4

Split (multi splits)
win percent = (2+uev+pDBJ(expected hands - 1))/4
expected hands can be computed, but this normally won't be known.

The above is for full peek. If ENHC (no peek) is in effect, just eliminate pDBJ from the above because in that cause player's non-BJ always loses to dealer BJ even for splits and doubles.

If this is done, the percentage of pushes still won't be known so if that's important to you this won't be of much help.