CGM 109: Carnival Game RTP by Wager, Paytable, and Strategy

A carnival-game RTP belongs to one exact wager under one exact set of rules. It is not a single percentage attached permanently to the game’s brand name.

At the same table, the Ante/Play structure, a Pair Plus-style wager, a Trips bet, a progressive, and another bonus circle can each have a different return to player. Change one payout line, require another wager, alter the strategy assumption, or change the amount that counts as the denominator, and the RTP can change even though the felt still carries the same game name.

An RTP number needs an address

Before comparing percentages, identify all of the following:

1. Game and version. Proprietary games can have approved variations.
2. Exact wager. Main game, bonus, side bet, and progressive are separate products.
3. Paytable. The posted payouts determine the return of hand-rank bets.
4. Rules. Dealer qualification, pushes, required raises, and bonus conditions matter.
5. Strategy. A decision game’s published return may assume correct play.
6. Denominator. Some figures use the initial wager; others compare expected loss with average total action.

A statement such as “this game returns 97%” is incomplete unless those assumptions are supplied. The carnival-game house-edge guide explains the casino-side expression of the same mathematics. The paytable guide shows why the printed payout schedule is part of the game, not decoration.

The calculation behind RTP

For a one-unit wager with mutually exclusive outcomes:

RTP = Σ(probability of outcome i × total return for outcome i)

Total return includes the returned stake. A losing outcome returns zero. If a winning result is paid 3 to 1, the player receives three units of profit plus the original one-unit stake, so the total return is four units.

The connected formulas are:

House edge = 1 − RTP
Expected loss = total action × house edge

RTP is a long-run weighted average. It does not mean a $100 session should end with $97 when the listed RTP is 97%. Carnival-game results are discrete and often volatile: many losses, ordinary wins, and rare premium payouts can produce session outcomes far from the average.

Worked example from an official Three Card Poker paytable

The Massachusetts Three Card Poker rules list a minimum posted Pair Plus schedule of:

There are C(52,3) = 22,100 possible unordered three-card hands from one standard deck. Using standard Three Card Poker hand ranking, their counts are:

The expected total return is:

RTP
= [(3,744 × 2) + (1,096 × 4) + (720 × 6)
   + (52 × 26) + (48 × 36)] ÷ 22,100
= 19,272 ÷ 22,100
≈ 0.872036

So this specific schedule has:

RTP ≈ 87.2036%
House edge ≈ 12.7964%

A $10 wager made repeatedly under this exact schedule therefore has a long-run expected loss of about:

$10 × 0.127964 ≈ $1.28 per resolved wager

The official rules say the posted Pair Plus paytable must pay no less than the listed odds, so a casino may offer a stronger approved schedule. The calculation above prices only the displayed schedule. The Massachusetts Gaming Commission’s Three Card Poker rules also separate the Ante/Play procedure, Pair Plus wager, and other bonus payouts—exactly why one game name cannot be reduced to one universal RTP.

Why a small payout change can move the return

Suppose the same Pair Plus schedule increased the straight from 5 to 1 to 6 to 1. A straight occurs in 720 of 22,100 hands. The additional one unit of profit on those outcomes changes RTP by:

RTP increase = 720 ÷ 22,100
≈ 0.032579
≈ 3.2579 percentage points

Nothing about the cards, dealing procedure, or game name changed. One line on the paytable raised the return from approximately 87.20% to approximately 90.46%.

That is why Why Paytables Matter and table signage and paytable control are practical, not theoretical, subjects. The sign presented at the table defines the wager being sold and the payout due when it wins.

Main-game RTP is not the cost of the whole round

A player often makes more than one wager. The expected loss of the round is the sum of the expected losses on each component:

Round expected loss
= main-wager action × main-wager edge
+ side-bet action × side-bet edge
+ progressive action × progressive edge

Consider a hypothetical fixed-exposure main wager of $20 with a 97% RTP, combined with a $5 Pair Plus wager using the 87.2036% schedule calculated above.

Main expected loss = $20 × 0.03 = $0.60
Side-bet expected loss = $5 × 0.127964 ≈ $0.64
Total expected loss ≈ $1.24 on $25 of action
Blended RTP ≈ 1 − ($1.24 ÷ $25) ≈ 95.04%

Although the side bet is only one-fifth of the money wagered, it contributes slightly more expected loss than the $20 main wager in this illustration. The main-game edge versus side-bet edge comparison examines this effect, while total action explains why the table minimum alone understates the amount exposed.

The blended figure is useful for a fixed mix of bets. It is not a permanent property of the table. Change the wager amounts or omit the side bet and the combined return changes.

Decision games require another caution

Some carnival games let the player fold, raise, or choose among wager sizes after seeing cards. Two analysts can publish different-looking percentages while both are mathematically correct if one divides expected loss by the initial mandatory wager and another divides it by average total action.

Strategy also matters. The advertised mathematical return may assume that the player makes the correct decision with every hand. Folding too often, raising weak hands, or failing to make a profitable maximum raise reduces the return actually achieved. Strategy cannot improve a fixed side-bet paytable, but it can prevent avoidable losses on decision-dependent wagers. See carnival-game strategy truth for that boundary.

Progressive RTP can move with the meter

A progressive wager may combine fixed hand awards with a jackpot whose current amount changes. If the jackpot contribution is part of the return, the wager’s RTP can rise as the meter grows. Calculating it requires the probability of each qualifying result, the current payable award, any envy or secondary payouts, contribution rules, and the exact amount wagered.

A large displayed jackpot does not by itself prove a high RTP. The top event may be extraordinarily rare, and other payout tiers may be weak. Without the complete approved paytable and probabilities, the meter is an attraction, not enough information for a return calculation.

A reliable way to compare tables

Before using an RTP figure:

• photograph or record the actual paytable where permitted;
• name the exact wager being evaluated;
• confirm whether payouts are “to 1” or “for 1”;
• include every mandatory and optional amount you plan to bet;
• check the rule and strategy assumptions;
• separate initial-wager house edge from any average-action measure;
• convert the percentage into expected dollars using realistic rounds and stakes.

The expected loss calculator is more useful than a percentage alone once the actual wagering volume is known.

Carnival-game RTP is precise only when its assumptions are precise. A percentage without a wager, paytable, rules, strategy, and denominator is not a price—it is an incomplete label.