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Last Updated: May 16, 2016

Stos

Introduction





Stos is a game developed by Gamesys for use in some Internet casinos. It is based on the game faro.

Rules



General Bets



  1. The game is played with a six-deck shoe.
  2. There are 17 bets available — each of the 13 ranks and the four suits. The player must make a Rank bet and the Suit bet is optional.


Rank Bets



Following are the rules of the Rank bets.

  1. The player may bet on any number and combination of the Rank bets he wishes.
  2. After the player is finished making his wagers, the dealer shall deal an "Odd" card and an "Even" card.
  3. If the Odd card matches in rank any of the player's bets, then that bet shall lose.
  4. If the Even card matches in rank any of the player's bets, then that bet shall win, except per rule 5.
  5. The Odd card is always adjudicated first. So, if the Odd and Even card were the same in rank, then any bets on that rank would lose.

Suit Bets



The Suit bet is a zero house edge bet that may be made along with a Rank bet. Much like the pass and odds bet in craps, the Rank bet is mandatory and the Suit bet is optional. The Suit bets are hard to explain, so listen carefully. A word of terminology — when I say "matching in color" I mean a color, but not suit, match. For example, clubs and spades.

  1. The player may choose only one suit to bet on.
  2. If the Odd card matches in rank to any rank the player bet on and in suit to the player's Suit bet, then the player will lose an amount equal to the Suit bet.
  3. If the Odd card matches in rank to any rank the player bet on and in color (but not suit) to the player's Suit bet, then the player will lose an amount equal to the Suit bet.
  4. If the Even card matches any rank the player bet on and in suit to the player's Suit bet, then the player will win an amount equal to the Suit bet.
  5. If the Even card matches any rank the player bet on and in color (but not suit) to the player's Suit bet, then the player will win an amount equal to half of the Suit bet.
  6. All other events shall result in a push.
  7. The player may not bet more than four times on the Suit bet than his greatest Rank bet.

Confused? So was I when I tried to figure out how the Suit bets work. Maybe some example will help.

Examples

  • Player bets $5 on a jack and $20 on diamonds. The Odd card is the jack of diamonds and the Even card is the two of clubs. The player will lose both bets, because if the Odd card causes the match, then the player loses.
  • Player bets $5 on a jack and $20 on diamonds. The Odd card is the two of hearts and the Even card is the jack of diamonds. The player will win both bets, because if the Even card causes the match, then the player wins.
  • Player bets $5 on a jack and $20 on diamonds. The Odd card is the jack of hearts and the Even card is the two of clubs. The player will lose the full $5 on the jack bet, because it matched the Odd card, and half, or $10, on the diamond bet, because the Odd card matched in color.
  • Player bets $5 on a jack and $20 on diamonds. The Odd card is the jack of hearts and the Even card is the jack of diamonds. The player will lose the full $5 on the jack bet, because it matched the Odd card. The fact that it also matched the Even card doesn't matter, because the Odd card is adjudicated first on Rank bets. For the Suit bet, the player will lose an amount equal to $10, or half, because the Odd card matched in color to the Suit bet. However, it will also win the full $20 the Even card, because it matched in suit to the Suit bet. So, the net win on the Suit bet is -$10 + $20 = $10.
  • Player bets $1 on a jack, $2 on a queen, and $8 on spades. The Odd card is the queen of hearts and the Even card is the jack of clubs. The player shall lose $2 on the queen bet, because the queen matched the Odd card. The player shall win $1 on the jack bet, because it matched the Even card. The player shall not lose anything pertaining to the Suit bet on the Odd card, because the Odd card was the opposite color to the player's chosen suit (spades). The player shall win $4 on the Suit bet because the Even card matched in color to the player's chosen suit.
  • Player bets $1 on a jack, $2 on a queen, and $8 on spades. The Odd card is the ace of spades and the Even card is the queen of diamonds. The bet on the jack shall push because neither card was a jack. The bet on the queen shall win, because the Even card was a queen. The Suit bet shall push because (1) although the Odd card was a spade, it didn't match in rank to any of the player Rank bets, so its suit was irrelevant and (2) while the Odd card did match in rank to the player's queen bet, the suit of the Odd card was the opposite color to the spades bet.

Another way to think of the Suit bet is that it is really two bets. The first, on the Odd card, can only lose, lose half, or push, depending on how it matches the Odd card in suit, assuming there is a matching rank. The second, on the Even card, can only win, win half, or push, depending on how it matches the Even card in suit, also assuming a matching rank.

I would hate to be a dealer in a real casino trying to explain this to players.

Analysis



Rank Bets



Normally I define the house edge as the ratio of the expected player loss to the initial wager, including pushes. The following return table shows the breakdown of the Rank bets that way. The lower right cell shows a house edge of 0.57%.

Rank Bets — Including Ties

Event Pays Permutations Probability Return
Even card only matches 1 6,912 0.071234 0.071234
Neither match 0 82,656 0.851843 0.000000
Odd card matches -1 7,464 0.076923 -0.076923
Total 97,032 1.000000 -0.005689


However, this is not how the house edge is usually stated on place, buy, and hard way bets, in craps, which often take many rolls to resolve, and can be taken down any time. With bets that players generally leave up until resolved, the pushes are ignored in calculating the house edge. The following table does it that way, ignoring pushes. The lower right cell shows a house edge of 3.84%.

Rank Bets — Not Including Ties

Event Pays Permutations Probability Return
Even card only matches 1 6,912 0.480801 0.480801
Odd card matches -1 7,464 0.519199 -0.519199
Total 14,376 1.000000 -0.038397


The way this game is actually played is that if nothing happens, then the player has about one second to click the "pause" button, otherwise the next set of two cards will be dealt. In the event of any win or loss, all unresolved bets will remain on the table. So, bets must actively be taken down, lest they eventually win or lose.

Suit Bets



The odds of the Suit bet depend on how many Rank bets the player makes. The expected value is always exactly zero (no house edge) but the probability of a push depends on the number of Rank bets made. To keep the math easy, the following table shows the possible outcomes with one Rank bet only.

Suit Bets — Including Ties

Odd Card Even Card Net win Permutations Probability Return
Suit match Suit match 0 30 0.000309 0.000000
Suit match Color match -0.5 36 0.000371 -0.000186
Suit match No match -1 1,800 0.018551 -0.018551
Color match Suit match 0.5 36 0.000371 0.000186
Color match Color match 0 30 0.000309 0.000000
Color match No match -0.5 1,800 0.018551 -0.009275
No match Suit match 1 1,800 0.018551 0.018551
No match Color match 0.5 1,800 0.018551 0.009275
No match No match 0 89,700 0.924437 0.000000
Total 97,032 1.000000 0.000000


Here is a more compact table, summarizing the probability of each outcome.

Suit Bets — Including Ties

Event Pays Permutations Probability Return
Win all 1 1,800 0.018551 0.018551
Win half 0.5 1,836 0.018922 0.009461
Push 0 89,760 0.925056 0.000000
Lose half -0.5 1,836 0.018922 -0.009461
Lose all -1 1,800 0.018551 -0.018551
Total 97,032 1.000000 0.000000


Combining a one-unit bet on any rank and a four-unit bet on any suit, the combined house edge is 0.14% per bet made (counting ties) and 0.77% per bet resolved (not counting ties).

Zero House Edge



There is another version of this game with the following rule changes:

  • In the event both the Odd and Even are the same rank, any bets on that rank shall push, instead of lose.
  • The player may bet as much as he wishes on the Suit bets.

The house edge on this version is 0%. However, at the casino where I saw this option, there is a 10% commission charge on any net win per session. A "session" is defined as a period of play with no break longer than an hour and not to exceed 24 hours.





Written by: Michael Shackleford

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