14.1 How do targets and stop losses affect us? 14.2 What are dealer hand total and bust frequencies? 14.3 How long are streaks? 14.4 What does a positive progression session look like? 14.5 What does a Martingale session look like? 14.6 How does the third base player affect you? Blackjack Shuffle Tracking Charts. The probability of a blackjack with six decks is (24/312). (96/311). 2 = 0.0474. 100 = 4.74% Converting Probability into Odds Odds are different than probability in that they show us the ratio between the number of desired outcomes occurring and the number of. Suppose that you are playing blackjack against the dealer. In a freshly shuffled deck (standard $52$ cards), what is the probability that neither of you are dealt a blackjack. Blackjack being $2$ c.
- Appendices
- Miscellaneous
- External Links
Introduction
The following tables display expected returns for any play in blackjack based on the following rules: dealer stands on a soft 17, an infinite deck, the player may double after a split, split up to three times except for aces, and draw only one card to split aces. Based on these rules, the player's expected value is -0.511734%.
To use this table, look up the returns for any given play, the one with the greatest return is the best play. For example suppose you have two 8's and the dealer has a 10. The return by standing is -0.5404, by hitting is -0.5398, doubling is -1.0797, and by splitting is -0.4807. So splitting 8's you stand to lose the least, 48.07 cents per original dollar bet, and is thus the best play. Facebook casino slot games.
Stand
Player's Expected Return by StandingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 0-16 | -0.292784 | -0.252250 | -0.211063 | -0.167193 | -0.153699 | -0.475375 | -0.510518 | -0.543150 | -0.540430 | -0.666951 |
| 17 | -0.152975 | -0.117216 | -0.080573 | -0.044941 | 0.011739 | -0.106809 | -0.381951 | -0.423154 | -0.419721 | -0.478033 |
| 18 | 0.121742 | 0.148300 | 0.175854 | 0.199561 | 0.283444 | 0.399554 | 0.105951 | -0.183163 | -0.178301 | -0.100199 |
| 19 | 0.386305 | 0.404363 | 0.423179 | 0.439512 | 0.495977 | 0.615976 | 0.593854 | 0.287597 | 0.063118 | 0.277636 |
| 20 | 0.639987 | 0.650272 | 0.661050 | 0.670360 | 0.703959 | 0.773227 | 0.791815 | 0.758357 | 0.554538 | 0.655470 |
| 21 | 0.882007 | 0.885300 | 0.888767 | 0.891754 | 0.902837 | 0.925926 | 0.930605 | 0.939176 | 0.962624 | 0.922194 |
Hit
Player's Expected Return by HittingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 4 | -0.114913 | -0.082613 | -0.049367 | -0.012380 | 0.011130 | -0.088279 | -0.159334 | -0.240666 | -0.289198 | -0.253077 |
| 5 | -0.128216 | -0.095310 | -0.061479 | -0.023979 | -0.001186 | -0.119447 | -0.188093 | -0.266615 | -0.313412 | -0.278575 |
| 6 | -0.140759 | -0.107291 | -0.072917 | -0.034916 | -0.013006 | -0.151933 | -0.217242 | -0.292641 | -0.337749 | -0.304147 |
| 7 | -0.109183 | -0.076583 | -0.043022 | -0.007271 | 0.029185 | -0.068808 | -0.210605 | -0.285365 | -0.319055 | -0.310072 |
| 8 | -0.021798 | 0.008005 | 0.038784 | 0.070805 | 0.114960 | 0.082207 | -0.059898 | -0.210186 | -0.249375 | -0.197029 |
| 9 | 0.074446 | 0.101265 | 0.128981 | 0.158032 | 0.196019 | 0.171868 | 0.098376 | -0.052178 | -0.152953 | -0.065681 |
| 10 | 0.182500 | 0.206088 | 0.230470 | 0.256259 | 0.287795 | 0.256909 | 0.197954 | 0.116530 | 0.025309 | 0.081450 |
| 11 | 0.238351 | 0.260325 | 0.283020 | 0.307350 | 0.333690 | 0.292147 | 0.229982 | 0.158257 | 0.119482 | 0.143001 |
| 12 | -0.253390 | -0.233691 | -0.213537 | -0.193271 | -0.170526 | -0.212848 | -0.271575 | -0.340013 | -0.381043 | -0.350540 |
| 13 | -0.307791 | -0.291210 | -0.274224 | -0.257333 | -0.235626 | -0.269073 | -0.323605 | -0.387155 | -0.425254 | -0.396930 |
| 14 | -0.362192 | -0.348729 | -0.334911 | -0.321395 | -0.300726 | -0.321282 | -0.371919 | -0.430930 | -0.466307 | -0.440007 |
| 15 | -0.416594 | -0.406249 | -0.395599 | -0.385457 | -0.365826 | -0.369762 | -0.416782 | -0.471578 | -0.504428 | -0.480006 |
| 16 | -0.470995 | -0.463768 | -0.456286 | -0.449520 | -0.430927 | -0.414779 | -0.458440 | -0.509322 | -0.539826 | -0.517149 |
| 17 | -0.536151 | -0.531674 | -0.527011 | -0.522986 | -0.508753 | -0.483486 | -0.505983 | -0.553695 | -0.584463 | -0.557300 |
| 18 | -0.622439 | -0.620005 | -0.617462 | -0.615260 | -0.607479 | -0.591144 | -0.591056 | -0.616528 | -0.647671 | -0.626515 |
| 19 | -0.729077 | -0.728033 | -0.726937 | -0.725991 | -0.722554 | -0.715450 | -0.713660 | -0.715574 | -0.729449 | -0.724795 |
| 20 | -0.855230 | -0.854977 | -0.854710 | -0.854480 | -0.853628 | -0.851852 | -0.851492 | -0.850833 | -0.849029 | -0.852139 |
| Soft 12 | 0.081836 | 0.103507 | 0.126596 | 0.156482 | 0.185954 | 0.165473 | 0.095115 | 0.000066 | -0.070002 | -0.020478 |
| Soft 13 | 0.046636 | 0.074119 | 0.102477 | 0.133363 | 0.161693 | 0.122386 | 0.054057 | -0.037695 | -0.104851 | -0.057308 |
| Soft 14 | 0.022392 | 0.050807 | 0.080081 | 0.111894 | 0.139165 | 0.079507 | 0.013277 | -0.075163 | -0.139467 | -0.093874 |
| Soft 15 | -0.000121 | 0.029160 | 0.059285 | 0.091960 | 0.118246 | 0.037028 | -0.027055 | -0.112189 | -0.173704 | -0.130027 |
| Soft 16 | -0.021025 | 0.009059 | 0.039975 | 0.073449 | 0.098821 | -0.004890 | -0.066795 | -0.148644 | -0.207441 | -0.165637 |
| Soft 17 | -0.000491 | 0.028975 | 0.059326 | 0.091189 | 0.128052 | 0.053823 | -0.072915 | -0.149787 | -0.196867 | -0.179569 |
| Soft 18 | 0.062905 | 0.090248 | 0.118502 | 0.147613 | 0.190753 | 0.170676 | 0.039677 | -0.100744 | -0.143808 | -0.092935 |
| Soft 19 | 0.123958 | 0.149340 | 0.175577 | 0.202986 | 0.239799 | 0.220620 | 0.152270 | 0.007893 | -0.088096 | -0.005743 |
| Soft 20 | 0.182500 | 0.206088 | 0.230470 | 0.256259 | 0.287795 | 0.256909 | 0.197954 | 0.116530 | 0.025309 | 0.081450 |
| Soft 21 | 0.238351 | 0.260325 | 0.283020 | 0.307350 | 0.333690 | 0.292147 | 0.229982 | 0.158257 | 0.119482 | 0.143001 |
Double
Player's Expected Return by DoublingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| Hard 4 | -0.585567 | -0.504500 | -0.422126 | -0.334385 | -0.307398 | -0.950750 | -1.021035 | -1.086299 | -1.080861 | -1.333902 |
| Hard 5 | -0.585567 | -0.504500 | -0.422126 | -0.334385 | -0.307398 | -0.950750 | -1.021035 | -1.086299 | -1.080861 | -1.333902 |
| Hard 6 | -0.564058 | -0.483726 | -0.402051 | -0.315577 | -0.281946 | -0.894048 | -1.001256 | -1.067839 | -1.062290 | -1.304837 |
| Hard 7 | -0.435758 | -0.359779 | -0.282299 | -0.202730 | -0.138337 | -0.589336 | -0.847076 | -0.957074 | -0.950866 | -1.130452 |
| Hard 8 | -0.204491 | -0.136216 | -0.066372 | 0.003456 | 0.087015 | -0.187730 | -0.451987 | -0.718501 | -0.746588 | -0.810746 |
| Hard 9 | 0.061119 | 0.120816 | 0.181949 | 0.243057 | 0.317055 | 0.104250 | -0.026442 | -0.300996 | -0.466707 | -0.432911 |
| Hard 10 | 0.358939 | 0.409321 | 0.460940 | 0.512517 | 0.575590 | 0.392412 | 0.286636 | 0.144328 | -0.008659 | -0.014042 |
| Hard 11 | 0.470641 | 0.517795 | 0.566041 | 0.614699 | 0.667380 | 0.462889 | 0.350693 | 0.227783 | 0.179689 | 0.109061 |
| Hard 12 | -0.506780 | -0.467382 | -0.427073 | -0.386542 | -0.341052 | -0.506712 | -0.615661 | -0.737506 | -0.796841 | -0.829344 |
| Hard 13 | -0.615582 | -0.582420 | -0.548448 | -0.514667 | -0.471253 | -0.587423 | -0.690966 | -0.807790 | -0.867544 | -0.880582 |
| Hard 14 | -0.724385 | -0.697459 | -0.669823 | -0.642791 | -0.601453 | -0.668135 | -0.766271 | -0.878075 | -0.938247 | -0.931821 |
| Hard 15 | -0.833187 | -0.812497 | -0.791198 | -0.770915 | -0.731653 | -0.748846 | -0.841576 | -0.948360 | -1.008950 | -0.983059 |
| Hard 16 | -0.941990 | -0.927536 | -0.912573 | -0.899039 | -0.861853 | -0.829558 | -0.916881 | -1.018644 | -1.079653 | -1.034297 |
| Hard 17 | -1.072302 | -1.063348 | -1.054023 | -1.045971 | -1.017505 | -0.966972 | -1.011965 | -1.107390 | -1.168926 | -1.114600 |
| Hard 18 | -1.244877 | -1.240010 | -1.234924 | -1.230519 | -1.214958 | -1.182288 | -1.182112 | -1.233057 | -1.295342 | -1.253031 |
| Hard 19 | -1.458155 | -1.456066 | -1.453874 | -1.451983 | -1.445108 | -1.430899 | -1.427320 | -1.431149 | -1.458898 | -1.449590 |
| Hard 20 | -1.710461 | -1.709954 | -1.709420 | -1.708961 | -1.707256 | -1.703704 | -1.702984 | -1.701665 | -1.698058 | -1.704278 |
| Soft 12 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 13 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 14 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 15 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 16 | -0.071570 | -0.007228 | 0.058427 | 0.125954 | 0.179748 | -0.183866 | -0.314441 | -0.456367 | -0.514028 | -0.624391 |
| Soft 17 | -0.007043 | 0.055095 | 0.118653 | 0.182378 | 0.256104 | -0.013758 | -0.255102 | -0.400984 | -0.458316 | -0.537198 |
| Soft 18 | 0.119750 | 0.177641 | 0.237004 | 0.295225 | 0.381506 | 0.219948 | -0.029917 | -0.290219 | -0.346892 | -0.362813 |
| Soft 19 | 0.241855 | 0.295824 | 0.351154 | 0.405972 | 0.479599 | 0.319835 | 0.195269 | -0.072946 | -0.235468 | -0.188428 |
| Soft 20 | 0.358939 | 0.409321 | 0.460940 | 0.512517 | 0.575590 | 0.392412 | 0.286636 | 0.144328 | -0.008659 | -0.014042 |
| Soft 21 | 0.470641 | 0.517795 | 0.566041 | 0.614699 | 0.667380 | 0.462889 | 0.350693 | 0.227783 | 0.179689 | 0.109061 |
Split
Player's Expected Return by SplittingExpand
| Player's Hand | Dealer's Up Card | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Ace | |
| 2,2 | -0.084336 | -0.015650 | 0.059088 | 0.151665 | 0.226890 | 0.006743 | -0.176693 | -0.386883 | -0.507175 | -0.433570 |
| 3,3 | -0.137710 | -0.056273 | 0.029932 | 0.126284 | 0.201318 | -0.053043 | -0.231843 | -0.436607 | -0.553507 | -0.482405 |
| 4,4 | -0.192325 | -0.108712 | -0.020395 | 0.081913 | 0.151377 | -0.166452 | -0.326068 | -0.511152 | -0.625044 | -0.560206 |
| 5,5 | -0.290154 | -0.208718 | -0.119335 | -0.019231 | 0.045404 | -0.293928 | -0.454237 | -0.634113 | -0.729969 | -0.668811 |
| 6,6 | -0.212560 | -0.119715 | -0.021320 | 0.080912 | 0.153668 | -0.264427 | -0.425122 | -0.610576 | -0.716103 | -0.653362 |
| 7,7 | -0.131478 | -0.043733 | 0.049255 | 0.146678 | 0.247385 | -0.050148 | -0.391981 | -0.577584 | -0.657268 | -0.651641 |
| 8,8 | 0.073852 | 0.146187 | 0.220849 | 0.297475 | 0.409329 | 0.321042 | -0.022736 | -0.387228 | -0.480686 | -0.372535 |
| 9,9 | 0.195625 | 0.258548 | 0.323474 | 0.391987 | 0.471339 | 0.364837 | 0.234447 | -0.078010 | -0.317336 | -0.136810 |
| 10,10 | 0.134774 | 0.212836 | 0.293403 | 0.380367 | 0.468117 | 0.296633 | 0.064443 | -0.206733 | -0.371278 | -0.249494 |
| A,A | 0.470641 | 0.517795 | 0.566041 | 0.614699 | 0.667380 | 0.462889 | 0.350693 | 0.227783 | 0.179689 | 0.109061 |
Play american original slot machine free online. Here are basic strategy tables for infinite decks. Valhalla slot machine.
Oompa loompa slot machine bonus. The only differences between infinite and four decks is to hit soft 13 vs. 5, and soft 15 vs 4 only when the dealer stands on soft 17.
I have had a lot of requests for my actual spreadsheet through the years. It is available to the public at Google docs. Note that this document allows for infinite re-splitting, while the tables above are based on a maximum of three splits (except aces). https://softwarecorp.mystrikingly.com/blog/motor-city-casino-nightclub.
Written by: Michael Shackleford
Easy-to-Memorize Blackjack Basic Strategy Chart PDF
Choose a Basic Strategy for Simplicity and Accuracy
In a blackjack game, the 'basic strategy' is the set of actions that giveyou the best possible return, based on your total and the dealer's visible 'up card.' For a given set of playing rules, thereis only one best action for each possible situation.
Many of the correct decisions tend to fall into regular patterns, butothersseem to have no rhyme or reason. Fortunately, you can use a 'simplified' strategy that sacrifices some less-important playing decisions to geteasier-to-remember patterns.
Here are Super-Easy, Simple, and Great simplified strategies that areeasier to learn, but almost as good, as the perfect basicstrategy. Thefollowing table can help you decide which strategy to learn. If you'renot sure, start with the Super-Easy strategy first, and afteryou master it, advance down the list.
| Strategy | Effort to learn | Bet size | Average session | Typical session |
| 1 hour | $10 | lose $11 | lose $130 or win $120 | |
| 1 day | $10 | lose $8 | lose $130 or win $120 | |
| 1 week | $10 | lose $7 | lose $125 or win $120 | |
| Perfect basic | 1 month | $10 | lose $6 | lose $125 or win $120 |
| Card counting | 1 year | $10-$100 | win $5 | lose $500 or win $505 |
A 'session' is 100 hands. Please note that you can easily win or losemuch more than the 'typical' amount in one session or multiplesessions. Risk only what you can afford.
The following table compares the simplified strategies with the perfect basic strategy.
| Strategy type | Average session loss 1 | House edge 2 | Chart for viewing (HTML) | Chart for printing (PDF) |
| Super-Easy | $6.40 + $4.40 | 1.08 % | ||
| Simple | $6.40 + $1.40 | 0.78 % | ||
| Great | $6.40 + $0.40 | 0.68 % | ||
| Perfect basic | $6.40 | 0.64 % | Wizard's website | Wizard's website |
Notes
- Average session loss isbased on playing 100 hands, $10 per hand. The amount is shown as a sum of two figures: the built-in loss using the perfect basic strategy plus the additional loss due to incorrect decisions in the simplified strategy. Please note that this is a long-term average, not the likely result of session! With a bet size of $10, it is not uncommon to win or lose $100 or $150 in a session or a few sessions. Risk only what you can afford.
- House edge means the percentage of your bet that you canexpect to lose in the long run while using thestrategy. This is expressed as a percentageof your original bets, not counting additionalmoney wagered on split hands and double-downs. SeeBlackjack House Edge (video).
Many casinos offer games that pay only 6:5 instead of3:2 on blackjack. In other words, for a $10 bet, a blackjack pays only$12 instead of the usual $15. Avoid these games! This lousy rule triples your average loss, from $6 per session to $20 per session (based on 100 hands at$10 per hand). Even the best 6:5 games are worse than the worst 3:2games. If yousee a sign on the table that says 'Blackjack Pays 6:5,' keep walking and find another table. Oddly enough, you can almost always find a 3:2 game nearby. If all customers refuse to play 6:5 games, casinoswill quickly go back to offering only full-payout games. |
Super-Easy Basic Strategy
The Super-Easy basic strategy is for anyone who would like to try playing blackjackfor fun, for a few hours or a weekend at low stakes, without spending alot of time studying and memorizing. It's also a good strategy thatserious players can give to their non-serious companions to use.
The full strategy explained in a 1-minute video
A description and tutorial in an 8-minute video
Using this strategy, the effective house edge is typically about 1%, so if you're playing100 hands per session, you can expect to lose about one hand per session in the long run.Even though the strategy is highly simplified, the house edge is stillbetter than almost all other bets in the casino, including the Player bet at baccarat (1.2%), Pass betat craps (1.4%), roulette (5.2%), and slot machines (2%-25%).
Average blackjack players make a lot more incorrect decisions than theSuper-Easy Casual strategy, so they typically play with an effective house edge of somewhere between 1 and 2 percent. The most common errors arehitting a 'stiff' (bustable) hand vs. a dealer 4, 5, or 6; and failing to hit 15 or 16 vs. a dealer high card. You can avoid these common mistakes by following the Super-Easy strategy.
Simple Basic Strategy
The Simple strategy is recommended for typical blackjack players. Compared with the Super-Easy Casual strategy, the Simple strategy is slightly more difficult tomemorize but reduces the effective house edge by about one-thirdof a bet per session. If you already know the Super-Easy Casual strategy,these are the additional decisions to learn for the Simple strategy:
- Split 2s, 3s, 6s, 7s, and 9s vs. a dealer low card
- Double on 10 vs. a dealer 7, 8, or 9 (in addition to dealer 2 through 6)
A video introduction to this website's Simple strategy is available on YouTube.
- Average session loss isbased on playing 100 hands, $10 per hand. The amount is shown as a sum of two figures: the built-in loss using the perfect basic strategy plus the additional loss due to incorrect decisions in the simplified strategy. Please note that this is a long-term average, not the likely result of session! With a bet size of $10, it is not uncommon to win or lose $100 or $150 in a session or a few sessions. Risk only what you can afford.
- House edge means the percentage of your bet that you canexpect to lose in the long run while using thestrategy. This is expressed as a percentageof your original bets, not counting additionalmoney wagered on split hands and double-downs. SeeBlackjack House Edge (video).
Many casinos offer games that pay only 6:5 instead of3:2 on blackjack. In other words, for a $10 bet, a blackjack pays only$12 instead of the usual $15. Avoid these games! This lousy rule triples your average loss, from $6 per session to $20 per session (based on 100 hands at$10 per hand). Even the best 6:5 games are worse than the worst 3:2games. If yousee a sign on the table that says 'Blackjack Pays 6:5,' keep walking and find another table. Oddly enough, you can almost always find a 3:2 game nearby. If all customers refuse to play 6:5 games, casinoswill quickly go back to offering only full-payout games. |
Super-Easy Basic Strategy
The Super-Easy basic strategy is for anyone who would like to try playing blackjackfor fun, for a few hours or a weekend at low stakes, without spending alot of time studying and memorizing. It's also a good strategy thatserious players can give to their non-serious companions to use.
The full strategy explained in a 1-minute video
A description and tutorial in an 8-minute video
Using this strategy, the effective house edge is typically about 1%, so if you're playing100 hands per session, you can expect to lose about one hand per session in the long run.Even though the strategy is highly simplified, the house edge is stillbetter than almost all other bets in the casino, including the Player bet at baccarat (1.2%), Pass betat craps (1.4%), roulette (5.2%), and slot machines (2%-25%).
Average blackjack players make a lot more incorrect decisions than theSuper-Easy Casual strategy, so they typically play with an effective house edge of somewhere between 1 and 2 percent. The most common errors arehitting a 'stiff' (bustable) hand vs. a dealer 4, 5, or 6; and failing to hit 15 or 16 vs. a dealer high card. You can avoid these common mistakes by following the Super-Easy strategy.
Simple Basic Strategy
The Simple strategy is recommended for typical blackjack players. Compared with the Super-Easy Casual strategy, the Simple strategy is slightly more difficult tomemorize but reduces the effective house edge by about one-thirdof a bet per session. If you already know the Super-Easy Casual strategy,these are the additional decisions to learn for the Simple strategy:
- Split 2s, 3s, 6s, 7s, and 9s vs. a dealer low card
- Double on 10 vs. a dealer 7, 8, or 9 (in addition to dealer 2 through 6)
A video introduction to this website's Simple strategy is available on YouTube.
Great Basic Strategy
The Great basicstrategy is recommended for serious players playing for long hours and high stakes. Compared with the Simple strategy, the Great strategy ismore difficult to memorize but reduces theeffective house edge by another one-tenth of a hand per session. If you already knowthe Simple strategy, these are theadditional decisions to learn for the Great strategy:- Hit hard 12 vs. a dealer 2 or 3
- Hit soft 18 vs. a dealer 9, 10, or A
- Double on A-2 through A-5 vs. a dealer 5 or 6
- Split 2s, 3s, and 7s vs. a dealer 7
- Split 9s vs. a dealer 8 or 9 (but not a dealer 7)
Perfect Basic Strategy
The Perfect basic strategy gives the absolute bestdecision for every possible combination of player total and dealer upcard. Use this strategy if you are playing for very long hours and highstakes, to get the best possible edge.
The exact playing decisions and house edge depend on the playing rules in effect at thetable. To generate a strategy chart, go to the Wizard of Odds Blackjack Strategy Calculator. Use the pull-down menus to specify the playing conditions: number of decks, whether the dealer stands or hitssoft 17 (the latter is more common), whether doubling is allowed aftersplitting a pair, whether surrender is allowed, and whether the dealerpeeks for blackjack (almost universal in the US). The strategy chart is automatically updated as you set the rules.Note: The Wizard uses a different coloring scheme for the strategy decisions. Also, he combines the splitting and doublingdecisionswith the hit and stand decisions in the same block, which is the usual way of showing strategy tables. However, I think it'seasier to memorize the splitting anddoubling decisions separately from the others, so that's how I've built my strategy tables.To find out the house edge for a given set of rules, go to the Wizard of Odds Blackjack House Edge Calculator. Use the buttons to specify the playing rules, and the 'Realisticresults' field is automatically updated to show the house edge.
Card Counting
Should you learn card counting? For the vast majority ofgamblers, the answer is no. From watching movies like 'Rain Man' and'21,' you might think that card counting is an easy road to riches. Thetruth is that card counting changes your slight disadvantage to only atiny slight advantage. To win, you must risk huge amounts for only asmall gain. For example, if you want to win just $10 per session in thelong run, you will need to bet $100 per hand when the deck is favorableand experience both winning and losing streaks in the thousands ofdollars.
For any gambling trip lasting a few days or less, luck is the overridingfactor that determines whether you win or lose, and by how much. Whether you use a good basic strategy (-0.5 percent) or skillful card counting(+0.3 percent) hardly makes any difference. I recommend card counting onlyif you're playing a lot or for large stakes and you can handle, both financially and emotionally, the long and large losing streaks thatare bound to occur from time to time. You will definitely lose money on some gambling trips, card counting or not.
Learning card counting does not require unusual intelligence or ability, but takes many months of dedicated practice to master the skills. Ifyou decide to learn card counting, the very first step is to learn atleastthe Great basicstrategy or preferablythe Perfect basic strategy, forward and backward, so you can recall every decisionautomatically without hesitation or delay. Spend atleast a few gambling trips using only the basic strategy in the casinobefore you even start to learn card counting.
For a good introduction to card counting, see The Wizard's website
To learn card counting, see NormanWattenberger's free online book, Modern Blackjack
To see how the count typically varies as the cards are dealt: Running Count, True Count, and Player Advantage Simulator
It may take some dedication, practice, and time to build your experience up to a level where you feel comfortable enough to take it to the nextstage. Advanced card counting strategies like Omega II and Wong Halvesare abundant online and can be found on sites likeCasino.org.
For more about card counting, see Does Card Counting Really Work? (web page or YouTube video)
Playing Rules and House Edge
The actual house edge depends to a large extent on the specificrules in effect at the table. Aside from 6:5 games, thehouse edge for perfect basic strategy play is usually between 0.4% and 0.7%. If you play forsignificant amounts of money, it makes sense to seek out the games with the lowest house edge.
If you're gambling in Las Vegas, go to the 'Wizard of Vegas' Las Vegas Blackjack Survey.You'll notice thatmost of the games with the smallest house edge (around 0.26%) have aminimum bet size of $50 or $100; these are 'premium' games on the Strip. The minimum bet sizes become lower (as low as $5) when the house edge gets to 0.40% and higher.
If you're gambling elsewhere in the US, go to the StanfordWong's Current Blackjack News website. Download the free sample(older) newsletter, or better yet, purchase a copy of the latestmonthly issue. The newsletter shows the specific table rules,minimum and maximum bet sizes, house edge, and other playing conditions for almost allcasinos in the US that deal blackjack.
To take full advantage of the better games, you need to learn thestrategy decisions for the specific rules. For example, if the surrenderoption is allowed, it reduces the house edge by 0.08%, but only if youtake advantage of the option and actually surrender when it's best todo so, as indicated in the Perfect basic strategy table.
For a good introduction to the game of blackjack, go to the Wizard of Odds Blackjack page.
For a very good (and free) online book on blackjack, see ModernBlackjack, An Illustrated Guide to Blackjack Advantage Play, by NormanWattenberger.
Wizard of Vegas forum discussion on Simplified Basic Strategy
Good luck playing a simplified basic strategy!
Gambling Videos
Super-Easy Casual Blackjack Basic Strategy -- Memorize in 1 Hour
Does Blackjack Card Counting Really Work?
Blackjack House Edge
Kelly Criterion: Huge Bankroll Needed for Blackjack Card Counting
Gambling Simulation Excel Spreadsheet
Gambling Winning and Losing Streaks and the Standard Deviation
Craps Odds Bet Explained: The Only Casino Bet With a Zero House Edge
Craps Pass Bet With Odds Bet Simulation, Setup in Excel Spreadsheet
Blackjack Basic Strategy and House Edge Calculation Spreadsheet
Poker Probability Chart
This video is a supplement to Blackjack Basic Strategy for InfiniteDecks and Blackjack House Edge with Infinite Decks, two videos by the Wizard of Odds, Michael Shackleford. The Wizard calculates the complete blackjack basic strategy and house edge, starting from a blank Excelspreadsheet, without using computer programming. He completes thesetasks in less than one hour, explaining step-by-step how to fill in thespreadsheet.
If you have trouble believing some of the playing decisions of the basic strategy, or if you're a skeptical type who doesn't accept things onfaith, this spreadsheet provides proof that the basic strategy is trulycorrect. You can modify the spreadsheet for different playing rules andexamine the effects on the strategy and house edge.
Watch the Wizard's videos first. He does a fine job of explaining howhe creates the spreadsheet. If you understand him completely, you haveno need for my video. On the other hand, if you reach a point where youcan't follow his explanation, pause it at that point and take a look atmy video here, and see if that helps. After that, you can go back to the Wizard's video and pick up where you left off.
In my video, I cover the following topics:
Overview (starts at 0:00)
Introduction to the spreadsheet (starts at 3:45)
Modify the spreadsheet for no surrender allowed (starts at 5:55)
Modify the spreadsheet for dealer hits soft 17 (starts at 9:50)
Modify the spreadsheet for 6:5 blackjack payoff (starts at 14:20)
Terminology: infinite decks (starts at 17:00)
Terminology: European hole card rule (starts at 18:35)
Magic formula that fills a whole table (starts at 20:30)
The Wizard's spreadsheet file consists of several worksheet tabs.Clicking a tab displays the sheet for that tab. Each sheet covers oneaspect of the blackjack strategy analysis, summarized as follows:
dealer: This sheet shows the probability of each possible final outcome(17 through 21 or bust), given the dealer's current total. The lowerpart shows the probabilities when the dealer doesn't check the hole card (European hole card rule). The upper part is modified to exclude thepossibility of a dealer blackjack, since the dealer checks for blackjack at the beginning of the round in American games.
stand: This sheet shows the expected return of standing on everypossible player total, including hands that you would never actuallystand on (because hitting would be obviously better, for example,standing on hard 9). 'Expected return' means your average win or loss on a $1 bet, given that you stand on that total. For standing, theexpected return is calculated as ($1)*(probability that the dealer willbust or end up with a worse total) + (-$1)*(probability that dealer will end up with a better total) + ($0)*(probability of a tie).
hit: This sheet shows the expected return of hitting each possibleplayer total, including hands that you would never actually hit (because standing would be obviously better, for example, hitting hard 20).'Expected return' means your average win or loss on a $1 bet, giventhat you hit that total and then take the better choice (either standing or hitting again) on the resulting new total.
hs (hit-stand): This sheet determines the better decision, eitherstanding or hitting, for each possible player total, by comparing theaverage return for the two possible decisions. The color-coded charts on the right calculate and display the results graphically, giving thefamiliar hit-stand tables that you see in all good blackjack books.
double: This sheet calculates the expected return of doubling-down foreach possible player total. 'Expected return' means your average win or loss on a $2 bet, given that you hit that total once and stand onthe new total. To analyze a game in which doubling is allowed only ona player total of 10 or 11, set the expected return of doubling to -1.0 for allplayer totals other than 10 or 11. A return of -1.0 makes doubling the worstdecision, so the spreadsheet always chooses the next-best alternativeaction (hit, stand, or split).
hsd (hit-stand-double): This sheet determines the best decision, eitherstanding, hitting, or doubling, for each possible player total, bycomparing the average return for the three possible decisions. Again,the color-coded charts on the right calculate and display the resultsgraphically.
sur (surrender): This sheet tabulates the value of surrender, which issimply -0.5 for all possible two-card hands or -1.0 for all bustedhands. To modify the spreadsheet for a game that doesn't allowsurrender, you can simply change all the -0.5 values to -1.0.
hsdr (hit-stand-double-surrender): This sheet determines the bestdecision, either standing, hitting, doubling, or surrendering, for eachpossible player total, by comparing the expected values for the fourpossible decisions. Again, the color-coded charts on the right calculate and display the results graphically.
split: This sheet determines whether it's better to keep a pair (eitherstanding, hitting, doubling, or surrendering it) or to split the pair.Splitting changes your point total to one-half the original and doublesthe amount at risk from $1 to $2. The color-coded chart at the bottomdisplays the results graphically. This completes the calculation of thefull basic strategy.
prob (probability): This sheet calculates the probability of being dealt each possible combination of player cards and dealer up-card. Thisinformation is needed to calculate the total expected value (houseedge).
er (expected return): This sheet calculates the expected return of eachpossible combination of initial player total and dealer up-card, giventhat the player takes the best action for each possible situation.
ev (expected value): This sheet calculates the expected value of eachpossible combination of initial player total and dealer up-card,calculated by multiplying the probability of being dealt thatcombination and the expected return of that combination. The totalexpected value is the sum of all the individual expected values. Afteraccounting for the probability of a dealer blackjack, the 'grand total'return is reported as -0.485 percent, or about one-half of one percentof your original bet for this set of playing rules.
Probability In Blackjack
To develop the Super-Easy, Simple, and Great simplified strategies, I modified the spreadsheet with simplification decisions and examined the effects on the total return.
For example, an obvious simplification is standing on 12 vs. a dealer 2or 3. To analyze the effect of this change in the strategy, go to the hit sheet and set the cost of hitting to -1 (enter -1 into cells B10 andC10). This tells the spreadsheet that hitting 12 vs. 2 or 3 is a baddecision, so it chooses the next-best decision, which is standing. These two incorrect decisions lower the total return from -0.485 percent to-0.532 percent, or about 47 cents per playing session (100 hands at $10per hand). This accounts for about half of the difference between the Simple strategy (which uses this simplification) and Great strategy (which does not).
For a good introduction to blackjack, go to the Wizard's web site
For a very good online book on blackjack, see ModernBlackjack, An Illustrated Guide to Blackjack Advantage Play, by NormanWattenberger
For a detailed technical look at the game, see Wattenberger's How Blackjack Works
Blackjack Probability Chart
To simulate gambling results yourself, see Gambling Simulation Excel Spreadsheet (video)
Odds Of Getting Blackjack
