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Last Updated: July 30, 2015

You Way 21

Introduction



Your Way 21 could loosely be described as a cross between pai gow and blackjack. I first saw at the Orleans in Las Vegas on June 26, 2015. The basic idea is that the player and dealer each start with four cards, arrange them into low and high hands of two cards each. Then the player and dealer will play out each hand and the final outcomes will be compared as in pai gow. As in blackjack, if the player busts first, he loses.

Rules



  1. A single 52-card deck is used.
  2. All cards are scored as in blackjack.
  3. The player shall make two bets of equal amounts. In addition, there is an optional poker-based side bet that called the "Poker Bet."
  4. The dealer shall deal the player and himself four cards each. The P wager shall be based on the poker-value of the player's four cards and the pay table below.
  5. The player will arrange his four cards into a two-card low and a two-card high hand. The high hand must have more points than the low hand. For purposes of counting points, aces shall count as 11.
  6. The player shall play each hand as in conventional blackjack under the following rules:
    • Player may double on any two cards.
    • Player may double after a split.
    • Surrender is not allowed.

  7. As in blackjack, if the dealer busts, then that hand shall immediately lose.
  8. The dealer shall then split his cards in the same manner according to the house way below.
  9. The dealer shall play out each hand as in conventional blackjack.
  10. The dealer shall hit a soft 17.
  11. The player's low hand shall be compared to the dealer's low hand, the higher hand, not exceeding 21, shall win.
  12. The player's high hand shall be compared to the dealer's high hand, the higher hand, not exceeding 21, shall win.
  13. All player wins shall pay even money. Ties are a push.
  14. There is no special significance to a blackjack. An ace and a 10-point card shall be counted as 21 points and equal to all other 21-point hands.

At this time I do not know about these rules:

  • Whether re-splitting aces is allowed.
  • How many hands the player may re-split other pairs to.


House Way



Following is the house way.

  1. If a low hand of 19 or more can be made, then the dealer makes the best possible low hand.
  2. Otherwise, if a high hand of 20 or more can be made, then the dealer makes the best possible high hand.
  3. Otherwise, if a low hand of 10 or 11 can be made, then the dealer sets the low hand to 11 if possible or 10 if not.
  4. Otherwise, if a low hand of 18 can be made, then the dealer sets the low hand to 18.
  5. Otherwise, if a high hand of 17 or more can be made, then the dealer makes the bets possible high hand.
  6. Otherwise, if the dealer has exactly two aces, then the dealer places on ace in the high and and one in the low hand.
  7. Otherwise, the dealer makes the lowest-scoring high hand possible.
  8. The high hand must have a score greater than or equal to the low score. When evaluating a hand with aces, aces are counted as 11 points, except two aces are counted as a total of 12 points.

Dealer Probabilities



Low Hand



The following table shows the probability of each final dealer low hand according to the exposed card.

Dealer Probabilities — Low Hand

Exposed
Card
17 18 19 20 21 Bust
2 0.141038 0.140081 0.136097 0.148336 0.148007 0.286442
3 0.137755 0.142297 0.131521 0.147142 0.152411 0.288874
4 0.137572 0.134960 0.140780 0.143045 0.154081 0.289562
5 0.128217 0.133162 0.136514 0.144462 0.153137 0.304508
6 0.108879 0.124830 0.128015 0.147887 0.159525 0.330863
7 0.153579 0.112540 0.113737 0.142024 0.155963 0.322157
8 0.121575 0.127469 0.140191 0.137233 0.157524 0.316008
9 0.123183 0.114199 0.191768 0.108019 0.147034 0.315796
10 0.141782 0.123084 0.155094 0.149405 0.116674 0.313961
A 0.121981 0.116728 0.178387 0.148116 0.128458 0.306330


High Hand



The following table shows the probability of each final dealer high hand according to the exposed card.

Dealer Probabilities — High Hand

Exposed
Card
17 18 19 20 21 Bust
2 0.123038 0.088104 0.065978 0.296282 0.205399 0.221200
3 0.074791 0.072152 0.131196 0.293259 0.200482 0.228120
4 0.065775 0.107497 0.138077 0.285204 0.193281 0.210166
5 0.092675 0.112161 0.133043 0.279237 0.184936 0.197948
6 0.100629 0.109416 0.132167 0.277247 0.181214 0.199327
7 0.179955 0.123526 0.119952 0.264808 0.165956 0.145804
8 0.089787 0.207219 0.154254 0.283650 0.127485 0.137606
9 0.061737 0.083412 0.317847 0.312994 0.129184 0.094826
10 0.038418 0.044455 0.078161 0.559422 0.216943 0.062601
A 0.019336 0.051259 0.071591 0.143033 0.665055 0.049726


Splitting Strategy



My apologies in advance for presenting the splitting strategy this way. My only excuse is that most of the time the decision will be pretty obvious. Those other times, use the tables below to determine the expected value of each combination of player starting hand and dealer up card. For each viable way to play the hand take the sum of the expected values of the low and high hands and play the way with the greatest total.

For example, suppose you have 2-7-9-A and the dealer is showing a 10. Here are the expected values of each possible split:

  • 27/A9: 0.0083 + 0.0067 = 0.0150
  • 29/A7: 0.3703 - 0.5249 = -0.1546
  • A2/79:-0.0061 - 0.7179 = -0.7240

As you can see, playing 27/A9 has the greatest sum of expected values and is thus the best play.

Splitting Strategy — Low HandExpand

Player
Hand
2 3 4 5 6 7 8 9 10 A
5 -0.2407 -0.2393 -0.2395 -0.2198 -0.1870 -0.1892 -0.2054 -0.2004 -0.1942 -0.2153
6 -0.2547 -0.2531 -0.2531 -0.2327 -0.1984 -0.2019 -0.2177 -0.2130 -0.2076 -0.2281
7 -0.2254 -0.2245 -0.2247 -0.2066 -0.1771 -0.1662 -0.1931 -0.1895 -0.1778 -0.2055
8 -0.1369 -0.1363 -0.1385 -0.1236 -0.1026 -0.0826 -0.1135 -0.1115 -0.0933 -0.1281
9 -0.0368 -0.0371 -0.0388 -0.0262 -0.0112 0.0029 -0.0172 -0.0039 0.0083 -0.0224
10 0.1414 0.1398 0.1396 0.1682 0.2021 0.2157 0.1877 0.2227 0.2475 0.1986
11 0.2782 0.2781 0.2768 0.3055 0.3440 0.3532 0.3237 0.3404 0.3703 0.3263
12 -0.3279 -0.3281 -0.3287 -0.3184 -0.3037 -0.2979 -0.3114 -0.3049 -0.2957 -0.3140
13 -0.3759 -0.3761 -0.3767 -0.3671 -0.3383 -0.3481 -0.3606 -0.3546 -0.3460 -0.3630
14 -0.4205 -0.4207 -0.4209 -0.3910 -0.3383 -0.3557 -0.3680 -0.3684 -0.3721 -0.3873
15 -0.4271 -0.4223 -0.4209 -0.3910 -0.3383 -0.3557 -0.3680 -0.3684 -0.3721 -0.3873
16 -0.4271 -0.4223 -0.4209 -0.3910 -0.3383 -0.3557 -0.3680 -0.3684 -0.3721 -0.3873
17 -0.2861 -0.2845 -0.2833 -0.2628 -0.2294 -0.2021 -0.2464 -0.2452 -0.2303 -0.2654
18 -0.0050 -0.0044 -0.0108 -0.0014 0.0043 0.0640 0.0026 -0.0078 0.0346 -0.0267
19 0.2712 0.2694 0.2650 0.2683 0.2572 0.2903 0.2703 0.2981 0.3127 0.2685
20 0.5557 0.5480 0.5488 0.5493 0.5331 0.5460 0.5477 0.5979 0.6172 0.5950
A2 -0.0453 -0.0464 -0.0477 -0.0378 -0.0223 -0.0149 -0.0317 -0.0209 -0.0061 -0.0310
A3 -0.0817 -0.0827 -0.0838 -0.0682 -0.0449 -0.0409 -0.0573 -0.0487 -0.0378 -0.0616
A4 -0.1078 -0.1073 -0.1079 -0.0912 -0.0658 -0.0634 -0.0795 -0.0716 -0.0617 -0.0849
A5 -0.1306 -0.1298 -0.1303 -0.1126 -0.0853 -0.0843 -0.1001 -0.0928 -0.0839 -0.1065
A6 -0.1115 -0.1113 -0.1117 -0.0959 -0.0723 -0.0598 -0.0845 -0.0773 -0.0639 -0.0917
A7 -0.0050 -0.0044 -0.0108 -0.0014 0.0043 0.0640 0.0026 -0.0078 0.0346 -0.0267
A8 0.2712 0.2694 0.2650 0.2683 0.2572 0.2903 0.2703 0.2981 0.3127 0.2685
A9 0.5557 0.5480 0.5488 0.5493 0.5331 0.5460 0.5477 0.5979 0.6172 0.5950
A,10 0.8520 0.8476 0.8459 0.8469 0.8405 0.8440 0.8425 0.8530 0.8833 0.8715
2,2 -0.2241 -0.2242 -0.2248 -0.2060 -0.1748 -0.1758 -0.1923 -0.1869 -0.1798 -0.2014
3,3 -0.2547 -0.2531 -0.2531 -0.2327 -0.1984 -0.2019 -0.2177 -0.2130 -0.2076 -0.2281
4,4 -0.1369 -0.1363 -0.1385 -0.1236 -0.1026 -0.0826 -0.1135 -0.1115 -0.0933 -0.1281
5,5 0.1414 0.1398 0.1396 0.1682 0.2021 0.2157 0.1877 0.2227 0.2475 0.1986
6,6 -0.3279 -0.3281 -0.3287 -0.3184 -0.3037 -0.2979 -0.3114 -0.3049 -0.2957 -0.3140
7,7 -0.4205 -0.4201 -0.4207 -0.3768 -0.3085 -0.2782 -0.3449 -0.3320 -0.2994 -0.3704
8,8 -0.2121 -0.2113 -0.2168 -0.1807 -0.1323 -0.0808 -0.1567 -0.1476 -0.0995 -0.1873
9,9 -0.0050 -0.0044 -0.0108 -0.0014 0.0043 0.0640 0.0026 0.0220 0.0455 -0.0199
10,10 0.5557 0.5480 0.5488 0.5493 0.5331 0.5460 0.5477 0.5979 0.6172 0.5950
A,A 0.4064 0.4054 0.4036 0.4322 0.4680 0.4821 0.4495 0.4693 0.5053 0.4560


Splitting Strategy — High HandExpand

Player
Hand
2 3 4 5 6 7 8 9 10 A
5 -0.3814 -0.3896 -0.4030 -0.3938 -0.3877 -0.3687 -0.3804 -0.4467 -0.5819 -0.7106
6 -0.3953 -0.4011 -0.4185 -0.4152 -0.4094 -0.3911 -0.4024 -0.4664 -0.5968 -0.7209
7 -0.3727 -0.3908 -0.4122 -0.4056 -0.3980 -0.3918 -0.4252 -0.4863 -0.6117 -0.7312
8 -0.3108 -0.3502 -0.3641 -0.3476 -0.3381 -0.3053 -0.3495 -0.4815 -0.6271 -0.7359
9 -0.2449 -0.2711 -0.2735 -0.2564 -0.2476 -0.2132 -0.2260 -0.3459 -0.5803 -0.7015
10 -0.1013 -0.1118 -0.1135 -0.0992 -0.0912 -0.0631 -0.0605 -0.1311 -0.3591 -0.5948
11 0.0145 0.0021 -0.0031 0.0079 0.0146 0.0363 0.0344 -0.0290 -0.1799 -0.4083
12 -0.4425 -0.4551 -0.4614 -0.4530 -0.4476 -0.4307 -0.4407 -0.4993 -0.6206 -0.7367
13 -0.4823 -0.4940 -0.4999 -0.4921 -0.4871 -0.4714 -0.4807 -0.5350 -0.6477 -0.7555
14 -0.5193 -0.5301 -0.5356 -0.5284 -0.5237 -0.5091 -0.5178 -0.5683 -0.6728 -0.7729
15 -0.5536 -0.5438 -0.5688 -0.5621 -0.5577 -0.5442 -0.5522 -0.5991 -0.6962 -0.7892
16 -0.5576 -0.5438 -0.5797 -0.5933 -0.5893 -0.5767 -0.5842 -0.6277 -0.7179 -0.8042
17 -0.4346 -0.4690 -0.5139 -0.5114 -0.5007 -0.5284 -0.6139 -0.6543 -0.7381 -0.8182
18 -0.2234 -0.3220 -0.3406 -0.3066 -0.2907 -0.2250 -0.3380 -0.6035 -0.7535 -0.8106
19 -0.0693 -0.1187 -0.0950 -0.0614 -0.0491 0.0185 0.0235 -0.2022 -0.6309 -0.6878
20 0.2929 0.3058 0.3282 0.3509 0.3603 0.4033 0.4614 0.4286 0.0067 -0.4731
A2 -0.2017 -0.2146 -0.2167 -0.2046 -0.1979 -0.1736 -0.1745 -0.2454 -0.4100 -0.5967
A3 -0.2323 -0.2449 -0.2471 -0.2355 -0.2290 -0.2056 -0.2070 -0.2755 -0.4341 -0.6131
A4 -0.2627 -0.2691 -0.2772 -0.2660 -0.2598 -0.2373 -0.2390 -0.3053 -0.4578 -0.6291
A5 -0.2846 -0.2887 -0.3011 -0.2961 -0.2901 -0.2686 -0.2705 -0.3344 -0.4811 -0.6449
A6 -0.2689 -0.2856 -0.3022 -0.2939 -0.2861 -0.2768 -0.3014 -0.3630 -0.5037 -0.6602
A7 -0.2204 -0.2567 -0.2678 -0.2509 -0.2415 -0.2080 -0.2449 -0.3693 -0.5249 -0.6694
A8 -0.0693 -0.1187 -0.0950 -0.0614 -0.0491 0.0185 0.0235 -0.2022 -0.5062 -0.6443
A9 0.2929 0.3058 0.3282 0.3509 0.3603 0.4033 0.4614 0.4286 0.0067 -0.4731
A,10 0.7946 0.7995 0.8067 0.8151 0.8188 0.8340 0.8725 0.8708 0.7831 0.3349
2,2 -0.3596 -0.3740 -0.3820 -0.3724 -0.3661 -0.3465 -0.3585 -0.4271 -0.5671 -0.7004
3,3 -0.3953 -0.4011 -0.4185 -0.4152 -0.4094 -0.3911 -0.4024 -0.4664 -0.5968 -0.7209
4,4 -0.3108 -0.3502 -0.3641 -0.3476 -0.3381 -0.3053 -0.3495 -0.4815 -0.6271 -0.7359
5,5 -0.1013 -0.1118 -0.1135 -0.0992 -0.0912 -0.0631 -0.0605 -0.1311 -0.3591 -0.5948
6,6 -0.4425 -0.4551 -0.4614 -0.4530 -0.4476 -0.4307 -0.4407 -0.4993 -0.6206 -0.7367
7,7 -0.5193 -0.5301 -0.5356 -0.5284 -0.5237 -0.5091 -0.5178 -0.5683 -0.6728 -0.7729
8,8 -0.5576 -0.5438 -0.5797 -0.5933 -0.5893 -0.5767 -0.5842 -0.6277 -0.7179 -0.8042
9,9 -0.2234 -0.3220 -0.3406 -0.3066 -0.2907 -0.2250 -0.3380 -0.6035 -0.7535 -0.8106
10,10 0.2929 0.3058 0.3282 0.3509 0.3603 0.4033 0.4614 0.4286 0.0067 -0.4731
A,A 0.0934 0.0762 0.0522 0.0573 0.0708 0.0311 0.0187 -0.1607 -0.3854 -0.5802


Basic Strategy



The following table shows the basic strategy for the low hand.

The following table shows the basic strategy for the high hand.

Key to basic strategy tables:
S = Stand
H = Hit
D = Double
P = Split

It should be noted that the mathematician on record for this game has a few differences in his basic strategy. Here is how he would play these few hands we differ on:

  • Low hand — 9,9 Vs. 10 or A: Stand
  • Low hand — 7,7 Vs. 2: Split
  • High hand — A,A Vs. 9: Hit


House Edge



After I completed my analysis, I found that the mathematician on record for the game gets a house edge of 1.64%. This is lower than what I get at 2.61%. I consider my analysis rather rough so will defer to the 1.64% figure.

Poker Side Bet



The following table shows the probability and return for each possible outcome of the Poker side bet. The lower right cell shows a house edge of 7.40%.

Poker Side Bet

Event Pays
Four of a kind 250 13 0.000048 0.012005
Straight flush 75 44 0.000163 0.012189
Flush 9 2,816 0.010402 0.093615
Straight 7 2,772 0.010239 0.071674
Three of a kind 5 2,496 0.009220 0.046098
Two pair 4 2,808 0.010372 0.041489
Pair 1 82,368 0.304250 0.304250
All other -1 177,408 0.655307 -0.655307
Total 270,725 1.000000 -0.073987


Discussion about Your Way 21 at Wizard of Vegas.

Methodology



This analysis was rather difficult. The final house edge is the product of three spreadsheets and two separate computer programs containing over 2,000 lines of code. As noted above, I have about a 1% disagreement with the mathematician on record for the game, whom I do not disagree with. For now, I would take any analysis on the game with a grain of salt.


Written by: Michael Shackleford

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