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Last Updated: January 20, 2019

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Expected Returns with Infinite Decks

Introduction

This page shows the player's expected return for any initial hand. It also shows the expected value by just the player's hand, and player's first card.

The tables are based on these rules:

  • Dealer does not have a blackjack
  • Dealer stands on a soft 17
  • Double after split allowed
  • Infinite resplitting
  • Split aces get one card each
  • Infinite number of decks.

Based on these rules the house edge is 0.5093975%.

Expected Value for any Initial Hand

Player's Expected Return Using Basic Strategy

Player's
Hand
Dealer's Up Card
2 3 4 5 6 7 8 9 10 Ace
5 -0.1282 -0.0953 -0.0615 -0.024 -0.0012 -0.1194 -0.1881 -0.2666 -0.3134 -0.2786
6 -0.1408 -0.1073 -0.0729 -0.0349 -0.013 -0.1519 -0.2172 -0.2926 -0.3377 -0.3041
7 -0.1092 -0.0766 -0.043 -0.0073 0.0292 -0.0688 -0.2106 -0.2854 -0.3191 -0.3101
8 -0.0218 0.008 0.0388 0.0708 0.115 0.0822 -0.0599 -0.2102 -0.2494 -0.197
9 0.0744 0.1208 0.1819 0.2431 0.3171 0.1719 0.0984 -0.0522 -0.153 -0.0657
10 0.3589 0.4093 0.4609 0.5125 0.5756 0.3924 0.2866 0.1443 0.0253 0.0814
11 0.4706 0.5178 0.566 0.6147 0.6674 0.4629 0.3507 0.2278 0.1797 0.143
12 -0.2534 -0.2337 -0.2111 -0.1672 -0.1537 -0.2128 -0.2716 -0.34 -0.381 -0.3505
13 -0.2928 -0.2523 -0.2111 -0.1672 -0.1537 -0.2691 -0.3236 -0.3872 -0.4253 -0.3969
14 -0.2928 -0.2523 -0.2111 -0.1672 -0.1537 -0.3213 -0.3719 -0.4309 -0.4663 -0.44
15 -0.2928 -0.2523 -0.2111 -0.1672 -0.1537 -0.3698 -0.4168 -0.4716 -0.5044 -0.48
16 -0.2928 -0.2523 -0.2111 -0.1672 -0.1537 -0.4148 -0.4584 -0.5093 -0.5398 -0.5171
17 -0.153 -0.1172 -0.0806 -0.0449 0.0117 -0.1068 -0.382 -0.4232 -0.4197 -0.478
18 0.1217 0.1483 0.1759 0.1996 0.2834 0.3996 0.106 -0.1832 -0.1783 -0.1002
19 0.3863 0.4044 0.4232 0.4395 0.496 0.616 0.5939 0.2876 0.0631 0.2776
20 0.64 0.6503 0.661 0.6704 0.704 0.7732 0.7918 0.7584 0.5545 0.6555
21 0.882 0.8853 0.8888 0.8918 0.9028 0.9259 0.9306 0.9392 0.9626 0.9222
A,2 0.0466 0.0741 0.1025 0.1334 0.1797 0.1224 0.0541 -0.0377 -0.1049 -0.0573
A,3 0.0224 0.0508 0.0801 0.126 0.1797 0.0795 0.0133 -0.0752 -0.1395 -0.0939
A,4 -0.0001 0.0292 0.0593 0.126 0.1797 0.037 -0.0271 -0.1122 -0.1737 -0.13
A,5 -0.021 0.0091 0.0584 0.126 0.1797 -0.0049 -0.0668 -0.1486 -0.2074 -0.1656
A,6 -0.0005 0.0551 0.1187 0.1824 0.2561 0.0538 -0.0729 -0.1498 -0.1969 -0.1796
A,7 0.1217 0.1776 0.237 0.2952 0.3815 0.3996 0.106 -0.1007 -0.1438 -0.0929
A,8 0.3863 0.4044 0.4232 0.4395 0.496 0.616 0.5939 0.2876 0.0631 0.2776
A,9 0.64 0.6503 0.661 0.6704 0.704 0.7732 0.7918 0.7584 0.5545 0.6555
2,2 -0.0842 -0.0153 0.0597 0.1526 0.2282 0.0073 -0.1593 -0.2407 -0.2892 -0.2531
3,3 -0.1377 -0.056 0.0305 0.1272 0.2026 -0.0525 -0.2172 -0.2926 -0.3377 -0.3041
4,4 -0.0218 0.008 0.0388 0.082 0.1516 0.0822 -0.0599 -0.2102 -0.2494 -0.197
5,5 0.3589 0.4093 0.4609 0.5125 0.5756 0.3924 0.2866 0.1443 0.0253 0.0814
6,6 -0.2123 -0.119 -0.0202 0.0824 0.1555 -0.2128 -0.2716 -0.34 -0.381 -0.3505
7,7 -0.1305 -0.0425 0.0508 0.1485 0.2498 -0.0485 -0.3719 -0.4309 -0.4663 -0.44
8,8 0.076 0.1485 0.2234 0.3002 0.4127 0.3254 -0.0202 -0.3865 -0.4803 -0.3717
9,9 0.1961 0.2592 0.3243 0.3931 0.4725 0.3996 0.2352 -0.0774 -0.1783 -0.1002
10,10 0.64 0.6503 0.661 0.6704 0.704 0.7732 0.7918 0.7584 0.5545 0.6555
A,A 0.4706 0.5178 0.566 0.6147 0.6674 0.4629 0.3507 0.2278 0.1797 0.1091

The next table shows the expected return for the player's first two cards, before the dealer's up card is known.

Expected Value of First Two Cards

Player
Hand
Expected
Value
Hard
5 -0.219214
6 -0.238748
7 -0.213827
8 -0.126898
9 -0.005401
10 0.205780
11 0.292516
12 -0.316036
13 -0.347475
14 -0.372529
15 -0.395793
16 -0.417396
17 -0.291688
18 -0.007066
19 0.265895
Soft
13 -0.028239
14 -0.055287
15 -0.081151
16 -0.104935
17 -0.078749
18 0.031321
19 0.265895
20 0.579612
21 1.428994
Splits
A,A 0.277241
2,2 -0.146920
3,3 -0.189896
4,4 -0.123221
5,5 0.205780
6,6 -0.246393
7,7 -0.247467
8,8 -0.145153
9,9 0.066113
10,10 0.579612

The next table shows the expected return for the player's first card, before the player's second card or the dealer's up card is known.

Expected Value of First Card

Player
Hand
Expected
Value
2 -0.134238
3 -0.155243
4 -0.178283
5 -0.197845
6 -0.211117
7 -0.182054
8 -0.087134
9 -0.010700
10 0.143489
A 0.501668

Inside Links

 

 

 

Outside Links

  • For a detailed explanation of blackjack rules in Macau, please visit my companion site, Wizard of Macau.
  • For a simplified explanation of blackjack, please visit my other companion site, Wizard of Vegas.

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