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Last Updated: November 27, 2019

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Andar Bahar

Introduction

Andar Bahar is a simple card game, said to originate in southern India, and has since spread all over India and now Internet casinos. Read on for the rules and analysis.

Rules

There are variations of the rules so I will endearvor to explain how the game is generally played and mention which rules are fundamental to the game and which are optional side bets.

  1. A single 52-card deck is used.
  2. The two main bets are Andar and Bahar.
  3. Before the first card is dealt, the players may or may not be able to make side bets on what it will be. Possible bets are on the rank or suit of the first card.
  4. The dealer shall deal the first card and place it in the middle of the table. If there were side bets based on that card, the dealer shall adjudicate them. This first card is sometimes known as the "joker," which I know is confusing. This first card is not wild and has nothing to do with the card generally referred to as a "joker." I prefer to call this card as the "Middle Card," to make explaining the game easier.
  5. At this point the player may make an Andar or Bahar wager. There may also be side bets on the total cards to be dealt after this point, for example the 20+.
  6. After bets are made, the dealer will deal cards one at a time until he gets another card matching the rank of the Middle Card. The dealer shall alternate placing cards on the left and right of the Middle Card. In some versions, the dealer starts on the left side of the Middle Card and in others he randomizes it, based on the color of the Middle Card. However, which side the dealer starts on does not matter.
  7. If the total number of cards dealt after the Middle Card is odd, then the Andar bet shall win. Depending on the version, the Andar bet may pay 0.9 to 1 or 0.95 to 1.
  8. If the total number of cards dealt after the Middle Card is even, then the Bahar bet shall win. Depending on the version, the Bahar bet may pay 0.95 to 1 or 1 to 1.
  9. After the Middle Card is matched, any side bets based on the total number of cards dealt after the Middle Card shall be adjudicated.

Andar and Bahar Analysis

The following table shows the probability of all possible total cards dealt after the Middle Card. The middle column shows the probability of exactly that number of cards. The right column shows the probability that the total number of cards will be that number of less. For example, the probability the probability of exactly 20 cards is 2.2329% and the probability of 20 or less cards is 78.4154%.

Total Cards Dealt

Cards Probabiltiy
(exact)
Probabiltiy
(equal or less)
1 0.058824 0.058824
2 0.056471 0.115294
3 0.054166 0.169460
4 0.051909 0.221369
5 0.049700 0.271068
6 0.047539 0.318607
7 0.045426 0.364034
8 0.043361 0.407395
9 0.041345 0.448739
10 0.039376 0.488115
11 0.037455 0.525570
12 0.035582 0.561152
13 0.033758 0.594910
14 0.031981 0.626891
15 0.030252 0.657143
16 0.028571 0.685714
17 0.026939 0.712653
18 0.025354 0.738007
19 0.023818 0.761825
20 0.022329 0.784154
21 0.020888 0.805042
22 0.019496 0.824538
23 0.018151 0.842689
24 0.016855 0.859544
25 0.015606 0.875150
26 0.014406 0.889556
27 0.013253 0.902809
28 0.012149 0.914958
29 0.011092 0.926050
30 0.010084 0.936134
31 0.009124 0.945258
32 0.008211 0.953469
33 0.007347 0.960816
34 0.006531 0.967347
35 0.005762 0.973109
36 0.005042 0.978151
37 0.004370 0.982521
38 0.003745 0.986267
39 0.003169 0.989436
40 0.002641 0.992077
41 0.002161 0.994238
42 0.001729 0.995966
43 0.001345 0.997311
44 0.001008 0.998319
45 0.000720 0.999040
46 0.000480 0.999520
47 0.000288 0.999808
48 0.000144 0.999952
49 0.000048 1.000000

 

Following are the probabilities of the two main bets winning:

  • Andar: 51.5006%
  • Bahar: 48.4994%

Following are is the house edge on the Andar bet, according to what a win pays:

  • 0.85 to 1: 4.72%
  • 0.9 to 1: 2.15%

Following are is the house edge on the Bahar bet, according to what a win pays:

  • 0.95 to 1: 5.43%
  • 1 to 1: 3.00%

Side Betting Analysis

The following table shows some side bets I'm aware of on the Middle Card. Pays are expressed on a "to one" basis. Some bets are listed twice at different pays I'm aware of. The right column shows the expected value of each bet.

Middle Card Side Bets

Bet Pays Probability Exp. Val.
Below 8, Above 8 1 0.461538 -0.076923
Below 8, Above 8 1.05 0.461538 -0.053846
Exactly 8 11 0.076923 -0.076923
Exactly 8 11.45 0.076923 -0.042308
Specific suit 2.8 0.250000 -0.050000
Specific color 0.9 0.500000 -0.050000
2 to 10 0.35 0.692308 -0.065385
Specific rank 11.45 0.076923 -0.042308

The next table shows some side bets I've seen based on the number of cards needed to repeat the rank of the Middle Card. Wins are on a "to one" basis.

After Middle Card Side Bets

Bet Pays Probability Exp. Val.
20+ 2.9 0.238175 -0.071116
1 to 5 2.5 0.271068 -0.051261
6 to 10 3.5 0.217047 -0.023289
11 to 15 4.5 0.169028 -0.070348
16 to 25 3.5 0.218007 -0.018968
26 to 30 14 0.060984 -0.085234
31 to 35 24 0.036975 -0.075630
36 to 40 49 0.018968 -0.051621
41+ 119 0.007923 -0.049220

The next table shows bets available on the number of cards dealt (not including the middle card) by Woohoo Games.

Bets on Number of Cards Dealt (Woohoo Games)

Cards Pays Probability Exp. Val.
2 16 0.056471 -0.040000
3 16.7 0.054166 -0.041268
4 17.25 0.051909 -0.052665
5 18 0.049700 -0.055702
6 19 0.047539 -0.049220
7 20 0.045426 -0.046050
8 21 0.043361 -0.046050
9 22 0.041345 -0.049076
10 23 0.039376 -0.054982
11 24.5 0.037455 -0.044898
12 25.5 0.035582 -0.057071
13 27 0.033758 -0.054790
14 29 0.031981 -0.040576
15 30.5 0.030252 -0.047059
16 32 0.028571 -0.057143
17 34 0.026939 -0.057143
18 36.5 0.025354 -0.049220
19 39 0.023818 -0.047299
20 41.5 0.022329 -0.051020
21+ 3.4 0.215846 -0.050276

In case you were wondering, here are some other miscellaneous statistics.

  • The side that gets the first card will win 51.5% of the time.
  • It takes 13 cards on average to resolve the game, not counting the Middle card.
  • The median number of cards to resolve the game is 11, again not counting the Middle card.

External Links

Discussion about Andar Bahar in my forum at Wizard of Vegas.


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