The odds of being the Bhabhi, from two to six players
If everyone at the table plays equally well, each player should be the Bhabhi one time in however many players there are. Is it that simple? We played 1.7 million rounds on the real engine to find out, with 100,000 games for every table size.
The fair share
With equal players the average is one in n: 50% for two, 33% for three, 25% for four, 20% for five, 17% for six. A shuffled deal gives nobody an advantage before the first card, so seat numbers do not matter. What does matter, as it turns out, is who holds the Ace of Spades, because that player must open with it.
The results
Every table below had Hard bots in every seat. The first column is the player who holds the Ace of Spades and opens; the others are counted clockwise from that player.
| Players | Fair share | Opener (♠A) | Next player | Others, average |
|---|---|---|---|---|
| 2 | 50.0% | 50.4% | 49.6% | 49.6% |
| 3 | 33.3% | 35.1% | 32.0% | 32.4% |
| 4 | 25.0% | 27.3% | 24.1% | 24.2% |
| 5 | 20.0% | 23.1% | 19.1% | 19.2% |
| 6 | 16.7% | 21.7% | 16.6% | 15.6% |
Each figure is how often that player ends the game as the Bhabhi; the margin of error is about ±0.3 points.
- The opener loses more than a fair share at every table of three or more: about 1.8 points more at three players, 2.3 at four, 3.1 at five and 5.1 at six. That is real: it is many times larger than the margin of error.
- Everyone else is close to fair. At a four-player table the other three each lose about 24%, a little under the fair share, because the opener takes the extra.
- With two players there is no edge. The opener loses 50.4% and the other player 49.6%, which is a tie within the margin.
Why the Ace of Spades costs you
We measured the effect, not the reason, but there is an obvious candidate. The holder of the Ace of Spades has to open with it, which puts the holder in the lead for the second trick as well. Leading is the risky part of Thulla: a player who leads a suit that somebody is out of picks up the pile. The Ace wins the first trick, so the holder is the first player to have to lead into a table where nobody has revealed anything yet. The effect grows with more players because there are more hands that could be out of the suit.
We also tested it with weaker bots. With four Easy bots the opener loses 26.9%, and with four Hard bots 27.2%. With four Medium bots it is odd: the opener loses only 14.3%. We have not investigated why, and we do not want to guess in print: it may come from the way the Medium bot leads. It is a reminder that a result about the rules is partly a result about the players.
What to do about it
- Do not despair. An extra 2 to 5 points is small next to what skill is worth: see how a strong player loses about 1 game in 100 against weaker opponents.
- Holding the Ace of Spades? Plan your second lead before the first trick ends. Think about which suit you can lead safely after the opening trick shows you who threw a dead card instead of a spade.
- Bigger tables are more luck. More players means a lower fair share but more thullas per game, so the result swings more. A friends table of six is the most chaotic version.
How to read these numbers
We played bots against bots, so these odds describe the rules, not you. Real players make different mistakes. And with five or six players the cards do not divide evenly (a five-player deal gives 11, 11, 10, 10 and 10 cards), a detail that the figures include.
More: all the simulation results · the rules · play now
Frequently asked questions
What are the odds of being the Bhabhi?
Between equal players, one in the number of players: 50% with two, 33% with three, 25% with four, 20% with five and about 17% with six. The player who holds the Ace of Spades loses a little more often than that.
Is it bad to have the Ace of Spades?
Slightly. In our simulation the player who opens with it loses about 2 points more often than a fair share at a four-player table, and about 5 points more at a six-player table.
Does it matter where I sit?
Seats themselves do not matter: the cards are dealt randomly. What matters is the order from the Ace of Spades. The next players around the table lose at about the fair rate.
Do these odds apply to people?
They describe strong bots playing each other. Human tables will differ, but the shape, with the opener slightly worse off, is a property of the rules.
More guides
How to play Thulla (Bhabhi)
The full rules, step by step.
A Thulla round, trick by trick
A worked example: a clean trick, a thulla, and how a round ends.
Thulla, Bhabhi or Bhabi? The names and every term
The names of the game, where house rules differ, and every word explained.
Thulla strategy tips
Habits that keep you from being the Bhabhi.