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Over/Under 13
Introduction
Over/Under 13 are a pair of side bets on whether the player's first two cards will total under or over 13. The bets have been around since the 1980's at least and I believe to be among the first blackjack side bets.
Rules
- Both side bets are based on the sum of the player's initial two cards.
- Aces count as one point.
- Both the Over 13 and Under 13 bets lose on a total of 13.
- Wins on both bets pay even money.
- The Majestic casino in Panama City offers a bet on a total of exactly 13, which pays 10 to 1.
Analysis
The following table shows the probability of winning and house edge of the Under 13 bet.
Under 13
| Decks | Probability | House Edge |
|---|---|---|
| 1 | 44.95% | 10.11% |
| 2 | 44.96% | 10.08% |
| 4 | 44.97% | 10.07% |
| 6 | 44.97% | 10.07% |
| 8 | 44.97% | 10.06% |
The following table shows the probability of winning and house edge of the Over 13 bet.
Over 13
| Decks | Probability | House Edge |
|---|---|---|
| 1 | 46.61% | 6.79% |
| 2 | 46.68% | 6.65% |
| 4 | 46.71% | 6.58% |
| 6 | 46.73% | 6.55% |
| 8 | 46.73% | 6.54% |
The following table shows the probability of winning and house edge of the Exactly 13 bet at a win of 10 to 1.
Exactly 13 — Wins pay 10 to 1
| Decks | Probability | House Edge |
|---|---|---|
| 1 | 8.45% | 7.09% |
| 2 | 8.36% | 7.99% |
| 4 | 8.32% | 8.44% |
| 6 | 8.31% | 8.58% |
| 8 | 8.30% | 8.66% |
Card Counting
Both Under 13 and Over 13 bets are highly vulnerable to card counting (shut up Wiz!). For an thorough treatment of the topic, I recommend Professional Blackjack by Stanford Wong. He covers the topic in chapter 11 of the 1994 edition.