The relative advantage X traditionally has over O by going first is negated by the opening Flip which decides which brand actually leads (plays first). All X and O bet placement MUST close prior to the Flip.
The Flip consists of turning over the first of 36 freshly-shuffled cards - A (as "1") through 9 in the four suits - and declaring X the Lead if the suit is black, or O if the suit is red. The rank shown on this card also indicates the number of the square into which this first Lead tile is placed. Suit is irrelevant after the very first card of a new game. The next card is then dealt, and if its rank is different from that of the first card, the first Follow tile is placed into the square with that number. Each brand takes turns filling the squares as each new rank appears. Cards are dealt one-at-a-time repeatedly as necessary on the same turn for either brand until a yet-undealt rank is introduced.
The first three-line (any line horizontally, vertically, or diagonally of three tiles of the same brand) to appear pays even money to the bet on the winning brand. If the Lead forms two intersecting three-lines simultaneously on the ninth move (called a Xmack-dOwn), the payout is 3 to 1 (OPTIONALLY: 2 to 1).
A Cat's Game (full board with no three-line) pushes the bet whose tile occupies the Center (square #5) and collects the other (OPTIONALLY: pays 1 to 2). 32 of the possible 252 full boards each show a Cat's Game; 16 have an X in the Center and 16 have an O. So, the probability of a Cat's Game is 12.7%, or 160 out of 1,260 bets, with 80 each to X and to O. A Cat's Game is not a tie, as one brand will always lose while the other will push or win.
First card: 4 of Diamonds - Red card >> O leads and is placed in square #4.
Second Card: 8 of Hearts - an X is placed into square #8.
Third Card: 3 of Spades - an O is placed in square #3.
Fourth card: 6 of Hearts - an X is placed in square #6.
Fifth Card: 2 of Hearts - an O is placed in square #2.
Sixth Card: A of Diamonds - an X is placed in square #1.
Seventh Card: 2 of Clubs - square #2 is filled, so another card is dealt.
Eighth Card: 2 of Diamonds - deal again.
Ninth Card: 3 of Spades - square #3 is filled, so yet another card is dealt.
Tenth Card: 5 of Spades - an O is placed in square #5.
Eleventh Card: 9 of Spades - an X is placed in square #9, leaving empty only square #7 into which to place an O and thus form a diagonal three-line (#3, #5, #7) of Os. All O bets are paid even money; all other bets are collected.
The Lead will win 58.5% of all games, or 737 out of 1,260, with 44 (3.5%) as Xmack-dOwns; 363 (28.8%) will be won by the Follow.
As for the side bets:
Cat's-Game - unlammered, pays 6-to-1 for any Cat's Game. Lammered with an X, pays 13-to-1 whenever an X occupies the Center in a Cat's Game and loses otherwise. Similarly, lammered with an O, pays 13-to-1 whenever an O occupies the Center in a Cat's Game and loses otherwise.
All-Points - for same brand in all four Corners (squares #1, #3, #7, and #9) - unlammered, pays 17-to-1. Lammered with an X, pays 35-to-1 whenever all four Corners have Xs and loses otherwise. Similarly, lammered with an O, pays 35-to-1 whenever all four Corners have Os and loses otherwise. (NOTE: This bet can win even if some Corners don't actually fill before the X and O bets are settled).
As for probabilities, in 1,260 games:
The Lead wins on the fifth Move in 120 games. (This phenomenon might be called a natural.)
The Follow wins on the sixth Move in 111 games
The Lead wins on the seventh Move in 333 games.
The Follow wins on the eighth Move in 252 games.
The Lead wins on the last Move in 284 games - 240 with a single three-line; 44 with double three-lines.
The Lead and Follow force a Cat's Game in 160 games, with an X and an O in the Center 80 times each.
Sixty out of 1,260 games will show all four Corners with the same brand.
So, adding these up shows the Lead of any game winning 693 out of 1,260 bets at 1-to-1, and 44 at 3-to-1, while the Follow will win 363 games out of 1,260 at 1-to-1. So the expected value E of all X and O bets is (693 + 44*3 - 363 - 80 + 363 - 80 - 737)/2,520 = -72/2,520 = -2.86%.
NOTE: Under OPTIONAL payout rules, E = (693 + 44*2 + 80*0.5 - 363 - 80 + 363 + 80*0.5 - 737 - 80)/2,520 = -36/2,520 = -1.43%.
For the unlammered Cat's-Game bet paid at 6-to-1, E = (160*6 - 1100)/1,260 = -11.11%. For any lammered Cat's-Game bet paid at 13-to-1, E = (80*13 - 1180)/1,260 = -11.11%.
For the unlammered All-Points bet paid at 17-to-1, E = (60*17 - 1,200)/1,260 = -180/1,260 = -14.29%. For any lammered All-Points bet paid at 35-to-1, E = (30*35 - 1,230)/1,260 = -180/1,260 = -14.29%.
Play spots can read along the lines of:
|Goes First||Goes Second|
|Win pays 1:1||Win pays 6:5|
Why not eliminate the X/O cards, and say that X always goes first? This will also make the terms "lead" and "follow" unnecessary. I think it might be difficult for players to follow which symbol goes first if it is random on every game.
The only thing I'm afraid of is that, since the Lead always has a 58.5% chance of winning overall, bettors would always choose the "X" if they knew it always went first, thus having a 23.33% advantage over the house. No one knowledgeable would ever choose "O". By making "X" switch from Lead to Follow half the time (on average), it goes from having an overwhelming advantage to having an overwhelming DISadvantage, a scenario which is simultaneously shared by "O", and the overall return balances out near the middle, slightly in favor of the House, just where one would expect it. So, IMHO, the key to making the betting fair is making either bet as likely to be "strong" as it is to be "weak".
How many placements does National Table Games have with their version of Tic Tac Toe? My guess is there is, at most, room for one Tic Tac Toe variant and they have been out there trying to sell theirs for a while.
Yes. I would want this at a place where the NTG variant hadn't succeeded or hadn't been offered, so that the "classic" play of the game might seduce curious players who hadn't become disillusioned with their version. Not to downplay the NTG TTT, just that most players who had tried that game might assume that mine was just like it, and say "been there, done that" and mistakenly move on.