Blackjack: player in last position makes no difference

Monday, October 04, 2010

Blackjack: player in last position makes no difference

A few weeks ago I was playing blackjack in a bricks & mortar casino on the south coast of the UK. I was to the left of the only other player at the table, and therefore the person to play directly before the dealer played out his hand, otherwise known as last position, or "third base".

Players typically blame the third baseman for their losses, based on the belief that the play of that hand determines the dealer outcome. This is wrong. In the first place, the decisions of all the players at the table, not just the third baseman, have the same bearing on the dealer outcome. In the second place, and more importantly, everything evens out in the long run: if today my drawing a card helps the dealer to make a good hand, tomorrow it will result in a dealer bust.

My fellow player didn't know this - he started lecturing me on how you should play "differently" at third base so as not to help the dealer. I offered to change places with him so that he could play at third base. He refused, saying he didn't like playing there.

To illustrate the fallacy of the thinking that the player in last position can be detrimental to the other players, I offer the following couple of scenarios, in which the player at last base has 16, the dealer's upcard is a 10, and the other live hands are all below 20.

In the first example, the next three cards to be dealt from the shoe are 5, 10 and another 10.

The player hits his 16 with the 5 and makes 21. The dealer draws the 10 to his 10 upcard and makes 20. All other players lose, but last base wins with the 21.

In the second example, the order of the next three cards in the shoe is 10, 5 and 10 - the first two cards in the above example have been reversed

The player hits his 16 with the 10 and busts. The dealer draws the 5 followed by the 10, and busts also. All other live hands win.

The only difference is the order of the first two cards to be dealt from the shoe, but the results of the two examples are the precise opposite of each other - in the first, last base beats the dealer, who in his turn beats all the other players, and in the second, last base loses to the dealer, who then loses to all the other players.

For every occasion in which a 5 and a 10 are waiting to be dealt, there will be a 10 and a 5 waiting with equal probablity - the chances of both are about one in 41.

In other words, both above scenarios have exactly equal probability of occuring. For every time that the decision of the player in last position hurts the other players, there will be the same number of times when that same decision helps them.

What happens if, rather than following correct basic strategy and hitting the 16, the player stands?

In the first example, the dealer busts and all players win.

In the second, the dealer makes 20 and all players lose.

So again, it all evens out in the long run. Different play strategy, different card order...it all evens out.

The only thing that affects outcomes is the way you play your own hand, which affects your monetary return. Play optimally and you will lose less in the long run; play sub-optimally and you'll lose more. So whether you're in first position or last at the blackjack table, play your hands correctly and don't worry about what the dealer might or might not draw.

The last hand I played that night in the company of my table companion was a soft 18 against dealer 10. I took a card, the correct play but unusual for a casual gambler. The dealer took a 5 followed by a 10, and busted. If I'd stood pat, the dealer would have made 20 and we'd have both lost.

The player thanked me profusely, and left.

I suspect he didn't see the irony.

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You should have pointed him to this url and told him to have a bit of a read up.

By Sandracer, at 12:58 pm

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