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Last Updated: May 16, 2016

Faro

Introduction

Faro, a simple game of luck using a single deck of cards, is said to have originated in France in the 17th century. It spread to England and then the United States via New Orleans. The game was likely the most popular game of chance in 19th century America, but its popularity gradually faded through the 20th century. It is believed the last casino to offer the game was the Reno Ramada in the 1980s. Personally, I've seen faro tables in museums and old paintings several times.

Rules

  1. After shuffling, the top card in the deck, known as the "Soda," is exposed.
  2. Following are the bets available that I am aware of.
    • Flat: Player may bet on any of the 13 ranks in the deck.
    • Split: Like a Flat bet, but on two ranks.
    • High Card: Player may bet whether the Winning or Losing card will be higher.
    • Odd/Even: Player may bet whether the Winning card is odd or even.
    • Turn: Betting on the order of the last three cards in the deck.
  3. After wagers are placed, the dealer deals a card, known as the "Losing Card."
  4. The following card is known as the "Winning Card."
  5. Wagers are resolved, according to the specific rules for each bet (described below).
  6. The dealer marks off on an abacus-like device the cards that were played.
  7. Play continues from the deck until there is only one card, known as the "Hock," remaining.

Following is a list of the specific bets, including the rules and odds.

Flat Bets

There are 13 Flat bets (sometimes known as "Denomination bets") available, one for each rank. Here are the specific rules:

  1. If the Winning card and Losing card are different in rank, then bets on the rank of the Winning card will win and bets on the rank of the Losing card will lose. Bets on all other ranks will push.
  2. If the Winning card and Losing card are equal in rank, then bets on that rank will lose half.
  3. The player has the option to reverse the Winning and Losing cards by putting a penny on his wager. This action is known as a “copper.

The following table shows all the possible outcomes on the Flat bets, assuming a full 52-card deck.

Flat Bets

Event Pays Combinations Probability Return
Win 1 192 0.072398 0.072398
Tie 0 2256 0.850679 0.000000
Lose half -0.5 12 0.004525 -0.002262
Lose all -1 192 0.072398 -0.072398
Total 2652 1.000000 -0.002262

The lower image--rightell reflects a house edge of 0.23%. If we ignore ties, then the expected loss per bet resolved is 1.52%.

Case Bets

In the event the player bets on a rank when there is only one of that card left in the deck, it is known as a "Case" bet. Absent any other rule changes, there would be zero house advantage, because it would be impossible to lose half, which is where the house gets its edge. In the case of Case bets, the dealer charges a 5% commission on wins.

The odds of the Case bet depend on how many cards are left in the deck. The more cards left, the lower the house advantage. The following table shows the probability of a win, push, and loss, as well as the expected return, according to the number of remaining cards. The image--rightolumn for the expected return shows the house edge ranges from 0.10% with 49 cards left to 1.67% with 3 cards left.

Case Bet

Cards
Remaining
Probability
Win
Probability
Push
Probability
Loss
Expected
Return
49 0.020408 0.959184 0.020408 -0.001020
47 0.021277 0.957447 0.021277 -0.001064
45 0.022222 0.955556 0.022222 -0.001111
43 0.023256 0.953488 0.023256 -0.001163
41 0.024390 0.951220 0.024390 -0.001220
39 0.025641 0.948718 0.025641 -0.001282
37 0.027027 0.945946 0.027027 -0.001351
35 0.028571 0.942857 0.028571 -0.001429
33 0.030303 0.939394 0.030303 -0.001515
31 0.032258 0.935484 0.032258 -0.001613
29 0.034483 0.931034 0.034483 -0.001724
27 0.037037 0.925926 0.037037 -0.001852
25 0.040000 0.920000 0.040000 -0.002000
23 0.043478 0.913043 0.043478 -0.002174
21 0.047619 0.904762 0.047619 -0.002381
19 0.052632 0.894737 0.052632 -0.002632
17 0.058824 0.882353 0.058824 -0.002941
15 0.066667 0.866667 0.066667 -0.003333
13 0.076923 0.846154 0.076923 -0.003846
11 0.090909 0.818182 0.090909 -0.004545
9 0.111111 0.777778 0.111111 -0.005556
7 0.142857 0.714286 0.142857 -0.007143
5 0.200000 0.600000 0.200000 -0.010000
3 0.333333 0.333333 0.333333 -0.016667

Split Bets

I discovered these bets from the Wichita Faro demo. It works like a Flat bet, except the player bets on two ranks, for example King and Queen. Here are the possible events, in this example, and what happens:

  • Winning card is King or Queen and Losing card is anything else = Win even money.
  • Losing card is King or Queen and Winning card is anything else = Lose all.
  • Both cards kings or both cards queens = Lose half.
  • Neither card king or queen = Push.
  • One card king and one card queen = Push.

The player may also copper Split bets. The following table shows the odds of Split bets. The lower image--rightell shows a house edge of 0.45%. The house edge per bet resolved is 1.65%.

Split Bets

Event Pays Combinations Probability Return
Win 1 352 0.132730 0.132730
Tie 0 1924 0.725490 0.000000
Lose half -0.5 24 0.009050 -0.004525
Lose all -1 352 0.132730 -0.132730
Total 2652 1.000000 -0.004525

High Card

For purposes of the High Card bets, an ace counts as one point, 2 to 10 according to pip value, a jack is 11, queen 12, and king 13 points. The player may bet whether the Winning or Losing card will be higher. Here are the rules for bets that the Winning card is higher.

  • Winning card is higher than Losing card = win even money.
  • Winning card is lower than Losing card = lose all.
  • Winning and Losing cards the same rank = lose half.

The following table shows all the possible outcomes that the Winning card will be higher. The lower image--rightell shows a house edge of 2.94%.

Winning Card Higher Bet

Event Pays Combinations Probability Return
Win 1 1248 0.470588 0.470588
Lose half -0.5 156 0.058824 -0.029412
Lose all -1 1248 0.470588 -0.470588
Total 2652 1.000000 -0.029412

Bets on the Losing card are the opposite. In other words, it wins if the Losing card is higher.

Odd Bet

For purposes of the Odd bet, an ace counts as one point, 2 to 10 according to pip value, a jack is 11, queen 12, and king 13 points. Following are the possible outcomes of the Odd bet.

  • Winning card odd and Losing card even = win even money.
  • Winning card even and Losing card odd = lose all.
  • Winning and Losing cards the same rank = lose half.
  • Both cards odd or both even, but of different ranks = push.

The following table shows all the possible outcomes of the Odd bet, for the non-counter.

Odd bet

Event Pays Combinations Probability Return
Win 1 672 0.253394 0.253394
Tie 0 1152 0.434389 0.000000
Lose half -0.5 156 0.058824 -0.029412
Lose all -1 672 0.253394 -0.253394
Total 2652 1.000000 -0.029412

The lower image--rightell reflects a house edge of 2.94%. If we ignore ties, then the expected loss per bet resolved is 5.20%.

Even Bet

The Even bet is the opposite of the Odd bet. In other words, it wins if the Winning card is even and the Losing card is odd. The odds are exactly the same as the Odd bet.

Turn

When there are only three cards left, of three different ranks, then the player may bet on the order of them.

There are six possible permutations of three cards, so the odds of winning are one in six. Fair odds would be 5 to 1, but the actual odds pay 4 to 1. The following table shows all the odds of the Turn bet. The bottom image--rightell shows a house edge of 16.7%.

Turn bet

Event Pays Combinations Probability Return
Win 4 1 0.166667 0.666667
Lose all -1 5 0.833333 -0.833333
Total 6 1.000000 -0.166667

In the Wichita Faro game, the Turn bet pays 2 to 1 if there is a pair remaining in the last three cards. This would be fair odds, with no house advantage.

Strategy

My advice for Faro is to make only two types of bets: (1) Flat bets on ranks when exactly two cards are left in the deck of a given rank and (2) Case bets. The reason for the Flat bets is the low probability of losing half, where the house gets its edge. However, with just one card left, the rules revert to paying a 5% commission, which may or may not be better, according to the number of cards left in the deck.

Let's call this the "Wizard's Faro Strategy." According to this strategy, the odds are better on the Flat bets with 23 or more cards left in the deck. With exactly 21 left, the odds are equal. With 19 or less, the odds are better on the Case bets.

Expected Return of Wizard's Faro Strategy

Cards
Remaining
Flat
Bet
Case
Bet
49 -0.000425 -0.001020
47 -0.000463 -0.001064
45 -0.000505 -0.001111
43 -0.000554 -0.001163
41 -0.000610 -0.001220
39 -0.000675 -0.001282
37 -0.000751 -0.001351
35 -0.000840 -0.001429
33 -0.000947 -0.001515
31 -0.001075 -0.001613
29 -0.001232 -0.001724
27 -0.001425 -0.001852
25 -0.001667 -0.002000
23 -0.001976 -0.002174
21 -0.002381 -0.002381
19 -0.002924 -0.002632
17 -0.003676 -0.002941
15 -0.004762 -0.003333
13 -0.006410 -0.003846
11 -0.009091 -0.004545
9 -0.013889 -0.005556
7 -0.023810 -0.007143
5 -0.050000 -0.010000
3 -0.166667 -0.016667

Acknowledgement

The Doctrine of Chances by Stuart N. Ethier was enormously helpful to me in the creation of this page. Ethier devotes the 18th chapter (23 pages) entirely to Faro.


Written by: Michael Shackleford

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