Cho-Han game: how the odd-even dice bet pays and what you keep

The Cho-Han game is a two-dice bet: you call whether the total is odd or even, with 18 of 36 outcomes producing each result. The key formula is expected value = win probability × total payout − stake; the payout and any house cut decide whether that expected value is zero or negative.

How a round works

You bet on either an even total (chō) or an odd total (han) before the dice are revealed.

Wikipedia’s Chō-han, Gameplay section (undated), describes the sequence:

1. The dealer shakes two standard six-sided dice in a bamboo cup.
2. The cup is overturned onto the floor, keeping the dice hidden.
3. Players bet on odd or even.
4. The dealer lifts the cup to reveal the result.

For another rules overview, see What are the rules of Cho-Han, gamerules.com (undated).

What are the odds?

Odd and even each have a probability of 0.5, assuming fair dice.

Probability = matching outcomes / all outcomes. For odd, that is 18 / 36 = 0.5.

There are 6 doubles—matching faces—and all produce even totals. They are already included above, not an extra advantage for even.

How does the payout change expectation?

A 1.9 payout instead of a fair 2x costs you 5 per 100 staked. The reduced payout creates the house edge, not the choice of odd or even.

Wizard of Odds lists a 1.9 payout for 1 on odd and even. In this article, payouts include your original stake, and return means the average amount paid back per unit bet.

Without a cut, 2x is a 1:1 payout: the net win equals the stake. A 1.9 payout means a 5% house edge per bet; the house edge calculator explains that relationship.

Diagram: payout 1.9 for 1 versus 2x with a 5% commission on winnings, expected result per unit stakedEducational calculation: with 2x and no cut the expectation is zero; with a 1.9 payout or a 5% commission on winnings it is negative.

What does the house cut change?

At 2x, increasing the house cut from 0 → 5% → 10% moves expectation from 0 → −2.5 → −5 per 100 staked.

If the payout is 2x with no cut, the bet is mathematically fair. With a 5% commission on winnings, the expected result is −2.5%; at 10%, −5%. A 1.9 payout costs you more than 2x with no cut.

Who acts as the house?

The dealer may collect losing bets, or players may bet against one another while the house takes a cut. Wikipedia’s Chō-han (undated) describes the latter as more common but gives no percentage; expectation therefore depends on the actual terms.

What should you expect from a session?

For 10 bets of $8 at 2x with a 5% commission on winnings, the expected result is −$2 on $80 staked. This assumes the same terms throughout, with no additional fees or payout rounding; the session bankroll calculator concerns the expected session result, not a loss limit.

Doubling after a loss does not change the bet’s expected value. The Martingale simulator illustrates why increasing stakes does not remove the payout or commission disadvantage.

What does one venue offer?

The undated page on chohan.carrd.co does not name its publisher; its link back points to The Crimson Lotus. It lists a 2x payout with a 5% commission on winnings. These are one venue’s terms, not a general standard.

Where does Cho-Han come from?

Wikipedia’s Chō-han article (undated) describes Cho-Han as a Japanese dice game and gives no account of its origin.

What can’t the calculation tell you?

Expectation describes an average across many bets, not a guaranteed session outcome; no betting system turns a negative expected value into a positive one. These results do not transfer to another venue without checking its payout, commission basis and settlement rules.