Blackjack: I’ve got 13 Dealer showing a 3 – Hit or Stay?


After my poor performance last trip to Vegas one of the areas of my game that I’ve been examining is my range.  Specifically how aggressive should I be on the lower end of the deck.  In this case if I have 13 and the dealer is showing a 3 what is the right play?

The book says stay in this situation.  In the past I’ve always followed that advice without any question since in general I play a conservative game and it basically made sense.

In reviewing my last trip I started looking at some of the low-end cards since I seemed to run into more than usual 12/13 vs. 2/3 and ended up on the losing end more often than not.

The low-end cards provide a lot of coin-toss situations and I often see novice players working hard to make decisions every time they face them.  I’ve usually played it conservatively and stand when holding a 13 vs. a dealer showing 3 as the book recommends.

Today I’m looking at the 13 vs 3 since I may start testing out a more aggressive strategy going forward.  According to the great folks at Wizard of Odds the dealer has only a 37% chance of busting when he starts with a 3 showing.  On the flip side if I’ve got a 13 my odds of busting when taking one card are only 38%.

So in this situation I have >60% chance of staying in the hand when taking a card vs. 100% of staying in the hand without hitting.  My odds of improving my hand to a quality hand (18+) are 31%.  So I’ve given myself a reasonable chance of improving while the dealer is only going to bust 4 out of 10 times.

I’m going to try this out in my next sessions and closely track the impact to see how it affects my results.


Never Play Tables That Pay 6:5 For Blackjack

One of my favorite sites is The Wizard of Odds – it provides all types of great info on the probabilities and statistics related to various gaming activities.  I hope the person who runs it is a multi-millionaire from busting casinos.  So when I had a question about the seemingly increasing trend of 6:5 pay-outs for blackjack – meaning you get your wager plus a 1/5 or 20% bonus for blackjack – easiest example is a $10 bet = $12 win at 6:5 whereas a $10 bet = $15 win at the standard 3:2 payout –  I turned to the Wiz to see how bad this really is.

According to the Wiz the odds for getting a blackjack in a six deck shoe are about 1/21 or 4.75% so if you’re sitting down to play at a 6:5 table vs. the standard 3:2 table your losing a fairly decent amount every shoe.  I’m not a statistician so I’m going to keep this high-level.  If you are playing by yourself with a 6 deck shoe = 312 cards, take out 33% for the cut (called the penetration) that leaves roughly 200 cards, and if the average hand takes 6 total cards you get 30+ hands per shoe and the average number of blackjacks hits at 4.75% and you split those evenly with the dealer you could expect to see 1-2 blackjacks per shoe.

So if you are playing a 6:5 table at $25/bet you’d win $30×1.5 or $45 on your blackjack hands.  If you are playing at a 3:2 table at $25/bet you’d win $56.25 on your blackjack hands…that is a potential Delta of $11.25 in one shoe!

Obviously getting a couple of blackjacks per shoe is a problem we’d all like to have when we’re playing and my math is not nearly as tight as the Wiz, but $11/shoe adds up over the course of a night or a three day stay in Vegas.

No matter what the actual difference in payout amounts the basic principle is the same – if you are playing blackjack make sure you get the maximum possible benefit from your investment and do your best to find a 3:2 payout table at your favorite casino.