Calculating the Edge of Any Side Bet Yourself

The idea in one line

The house edge on a side bet is the average amount you lose per unit staked, written as a percentage. It comes from two ingredients: how likely each winning outcome is, and what each one pays. Everything below is just careful bookkeeping of those two things. The payouts used here are invented to keep the arithmetic clear. They are not any casino’s actual table.

The method

1. Define the winning outcomes. List each paying result separately and make sure no two overlap. A pair that is also suited counts once, in whichever tier is stated.
2. Count the ways each can happen. Count the favourable combinations, and the total number of possible combinations. The count depends on the number of decks.
3. Turn counts into probabilities. Divide each favourable count by the total.
4. Multiply each probability by its payout. Use the “to 1” profit figure, not the “for 1” total return.
5. Add those products. This is the average profit you collect from wins per unit staked.
6. Subtract the chance of losing the stake. That is one minus the sum of all winning probabilities, since each loss costs one unit.
7. Read the result. A negative number is the expected value per unit, and its size without the minus sign is the house edge.

A check at the end helps: your probabilities for all outcomes, winning and losing, should add up to exactly 1.

Worked example one: a one-tier bet

Imagine a bet that wins when your first two cards form a pair, and the table pays 15 to 1. Use a single 52-card deck.

• After the first card, 3 of the 51 remaining cards match its rank. The probability of a pair is 3 ÷ 51 = 1 ÷ 17, about 5.88%.
• The chance of losing is 16 ÷ 17.
• Expected result per unit staked: (1 ÷ 17) × 15 − (16 ÷ 17) = (15 − 16) ÷ 17 = −1 ÷ 17.

That is an edge of about 5.88%. The same shortcut works as a check. The fair payout is 16 to 1, because (16 ÷ 17) ÷ (1 ÷ 17) = 16. A table paying 15 to 1 pays one unit less than fair, and one unit in 17 is the edge.

Worked example two: a two-tier bet

Now invent a bet that pays 40 to 1 when your first two cards are a pair of aces and 12 to 1 for any other pair, again from a single deck. Here you need counts. There are 52 × 51 ÷ 2 = 1,326 possible two-card hands.

• Pairs of aces: 6 hands (4 aces, choose 2).
• Other pairs: 12 ranks × 6 hands = 72.
• Losing hands: 1,326 − 6 − 72 = 1,248.

Expected result, in units of 1 ÷ 1,326: (6 × 40) + (72 × 12) − 1,248 = 240 + 864 − 1,248 = −144.

So the edge is 144 ÷ 1,326, which is about 10.86%. As a check, the two pair tiers together are 78 hands, and 78 ÷ 1,326 = 3 ÷ 51, matching the first example.

How deck count changes the answer

Keep the first example’s “any pair” definition, but deal from six decks instead. After the first card, 23 of the remaining 311 cards match its rank, so the chance of a pair is 23 ÷ 311, about 7.40%, against 5.88% for one deck. Pair-based bets therefore win more often in a shoe, and a pay table that works for one deck is not priced the same way for six. Two different tables can share a name and carry quite different costs.

If the bet needs a fixed number of decks to be possible at all, as with a pair of identical cards, then the single-deck count is simply zero. That is a reminder to read the rules before trusting any published figure.

Common slips

• Using total return instead of profit. “25 for 1” means a 24 to 1 profit plus your stake coming back.
• Letting categories overlap. If a hand qualifies for two tiers, only the tier the rules assign should count.
• Forgetting the denominator changes. The second card is dealt from a deck that already has one card removed.
• Assuming independence between the side bet and your hand. Where the bet uses the dealer’s upcard or your own cards, count the combinations exactly rather than multiplying rough chances.
• Averaging pay tables. Compute each outcome separately.

For bets that depend on how the whole hand plays out, hand counting becomes impractical. Analysts then rely on simulation basics, often a Monte Carlo run over many millions of deals, but the logic of the final step is the same: add up probability times payout, then subtract the chance of losing.

What the number means

A house edge of 6% does not mean you lose 6% each time. It means that over a very long run the average loss tends toward 6 cents per dollar staked. A single bet either returns a win or loses the stake. The wider the gap between rare big wins and frequent losses, the larger the standard deviation and the less a short session tells you. Edge describes the long-run cost, never what will happen tonight.

Seeing a side bet’s edge as a price is useful. It shows what the entertainment costs, and it can make clear why spending a larger share of your stake on side bets raises the expected cost. Set a budget you can afford to lose and stay within it. If gambling is causing harm, free support is available from local services.