The goal of this project is to use mathematics to find the exact optimal strategy for every extant casino table game.
Anyone is welcome to contribute! Email me if you want to contribute strategies to the site
This symbol ✅ means a game is "confirmed optimal", meaning we did the math to find the exact best strategy possible.
Due to their complexity, most of these games have not been optimally solved, with a few exceptions 😔
Fold unless your cards are a pair, your cards are the same suit, or if they form the inside of two different potential straights (like how 4 and 5 can make 345 or 456, but Ace and King can only make one potential straight).
If Straights pay 5:1 on your pay table, don't fold if your cards form any part of a potential straight (for example 4 and 6 are separated but have the potential to make 456).
Always raise with a pair or better
Always fold with less than an Ace+King
The Wizard of Odds website has a chart explaining what to do if you have an Ace+King
Do this correctly, and you will have a house edge of 5.2243%
Optimally you will only fold 18% of the time
It can definitely be said that you should raise with a pair or better, or if you have four cards of the same suit.
I found a convoluted strategy within 0.29% of optimal, but more detailed strategies should be investigated.
Until extremely recently, the general rule here was to fold if you didn't have a K+Q+8+4 or better. Now with modern computers we can find the true optimal strategy.
K+Q+8+4+3 and K+Q+7+6+5 should be folded if there are two suits, and K and Q are different suits.
You should fold on K+Q+8+4+2 if King and Queen are different suits
This might be the complete optimal strategy, I am in the process of verifying!
Play if one card is nine or higher, Play if your cards form a pair, and Play if your cards are the same suit (except for 3-8, 2-8, and 2-7), otherwise Fold.
Do this correctly, and you will have a house edge of between 2.57%-5.29%, depending on the pocket bonus pay table.
Play if you have a pair of fives of better. If you just have a pair of threes or no pair, Fold.
If you just have a pair of fours, Fold if you also have a three, otherwise Play.
Raise if you have at least one card jack or higher, a pair, three to a flush, or three to any straight, otherwise fold.
Raise x3 with a pair of tens or better, raise x1 with a pair of twos or better, and to fold otherwise.
Pair of Aces or better: Bet x3
Pair of Kings: Bet x3, except bet x1 against an Ace and you don't have an Ace nor 4.
Pair of Queens or Jacks: Bet x3, except bet x1 if the dealer's card outranks pair your pair rank and does not match a singleton in your hand.
Pair of 9s or 10s: Bet x3, except bet x1 if dealer card outranks your pair rank.
Pair of 8s: Bet x1, except bet x3 against a 2
Pair of 4s thru 7s: Bet x1
Pair of 3s: Bet x1, except fold against a Jack if your highest kicker is a 10 or lower
Pair of 2s or AKQ: Fold, except bet x1 if dealer card matches a rank in your hand
AKJT: Fold, except bet x1 against a Jack
AKJ9 or lower: Fold
I have heard rumors that gambling expert James Grosjean has developed an even more advanced strategy.
My analysis also shows that you should actually bet x1 with AKJ9 if the dealer is showing an Ace or King :)
Raise x4 if you have an Ace, if you have a King with 5-Queen, if you have a Queen with a 8-Jack, or a Jack with a 10.
Additionally raise x4 if you have a suited King with anything, a Queen with 6 or 7, or a Jack with 8 or 9.
The Wizard of Odds website includes some strategic analysis of this game, but much more research is needed.
'Let it ride' if you have a paying hand or four cards of the same suit, more strategy research must be done to find the perfect strategy.
When you have two cards: raise x3 any pair or better, raise if you have a Jack-Ace, if both cards are 6-10, or if you have 5/6 suited, otherwise fold.
The rest of the strategy is hard to summarize (I'll do it later), but it can be found on a chart on the Wizard of Odds website.
If you need a straight or better to win on the Ante, fold a 2 with a 3-7 if they have different suits.
If you need a flush or better to win on the Ante, fold a 2 with a 3-7 if they have different suits, or an unsuited 3+4.
More research is needed to find the optimal moves for the next decisions.
Play if you have a Q+6+4 or better, otherwise Fold. This will yield you a 3.37% to 4.28% house edge.
Play if you have a Q+6+4 or better, otherwise Fold. This will yield you a house edge of 2.96%.
The strategy will be released alongside the game in December
Raise x4 if you have an Ace, if you have a King with 7-Queen, if you have a Queen with a 10 or Jack
Additionally raise x4 if you have a suited King with 5 or 6, a Queen with 8 or 9, or a Jack with 10.
Play if you have a pair of fives of better. If you just have a pair of threes or no pair, Fold.
If you just have a pair of fours, Fold if you also have a three, otherwise Play.
Due to their relative simplicity, all baccarat variants have been mathematically solved ✅
The best bet here would be the Banker, with a notably small house edge of around 0.76% (as opposed to 1.24% for the Player).
The best bet here would be the Banker, with a house edge of around 1.02% (as opposed to 1.24% for the Player).
The best bet here would be the Banker, with a house edge of around 1.06% (as opposed to 1.24% for the Player).
The best bet here would be the Player, with a house edge of around 1.24% (as opposed to 1.45% for the Banker).
Due to their relative simplicity, all baccarat variants have been mathematically solved ✅
If there are eight spots with "5", it means "5" is the best bet with 11.1111% house edge. Otherwise "1" is the best bet with 11.1111% house edge.
All bets return the same house edge of 11.1111%
If "la partage" is offered in roulette, only play the 1:1 bets like Red, Black, and Odd. Otherwise, do any bet except for the "top line" bet (0-00-1-2-3) on double zero wheels.
Due to their relative simplicity, all dice games have been mathematically solved ✅
The best bets are the main ones: Player and Banker are equal with a house edge of 1.2731%.
All bets have the same house edge of 0.4630%.
All bets have the same house edge of 5%.
There is no strategy, the house edge is 2.4691%
Laying on 2 or 12 has a very low house edge of 0.8264%. If not available, combining Pass with Odds will yield the lowest house edge.
Don't Pass/Don't Come is the most optimal bet with a house edge of 1.36% - taking Odds will decrease the house edge percentage-wise
If you have the chance to fold or double down in case of a tie, the confirmed optimal strategy is to never fold and to double down instead
The best main bet (which is required) in this game is 1B, but even better are the Red/Black side bets.
Heads, Tails, and Odds all have a house edge of 3.125%.
Some of these games lack strategy, others have very complex strategies which depend on the 'house way'
No Strategy. First see if any possible combination can beat the house, and if not, see if any possible combination can push.
No Strategy. First see if any possible combination can beat the house, and if not, see if any possible combination can push.