By Stanford Wong
(From Blackjack Forum Vol. XV #III, September 1995
© 1995 Blackjack Forum
Arnold has asked me to write something on casino tournament strategy, so I thought I would share a typical application of my new Tournament Blackjack software.
Here is a situation I encountered in a mini blackjack tournament I entered at Isle of Capri in Biloxi, Mississippi, a few weeks ago. Only one person was advancing in the tournament from my table. The maximum bet was $300.
It was the 29th round out of 30, and I was BR1 (meaning I had the largest bankroll at the time) with $900. Several other players were still in close contention. I was betting second. I bet $300, and my opponents all made bets around $100.
Then we got our cards. The dealer showed 10, I got eleven, and the other players ended up with totals of eighteen to twenty.
The decision I had to make was should I double down? The argument for doubling down is if I won I would have a commanding lead going into the last round of the tournament, perhaps even a lock. A lock would be especially nice because on the last round I would be betting and playing first. The argument for not doubling down is that I would still have a chance to win the table if lost only one bet, whereas losing a doubled bet would knock me out of contention.
In the actual tournament I had to make a decision quickly, and could not ask for time out to run a simulation. I doubled down, ended up with a twenty for a push, and so achieved the same result as if I had hit instead of doubling.
But was my double down correct? Tournament Blackjack can give the answer.
Blackjack Tournament Solutions
I do not recall the rest of the details of the actual situation—how many other players were left, their bankrolls, their bets, or exactly what their hand totals were—so I will use numbers that seem reasonable. I will use five other players with bankrolls of 825, 800, 750, 775, and 850. I will give them bets of 100 each. I will give them hand totals of 20, 19, 18, 19, and 20.
I boot up Tournament Blackjack. In the rules I ask for six players, minimum bet of 10, maximum of 300, double any two cards including after splitting, and dealer stands on soft seventeen because those were the rules I faced in Biloxi. I ask for one winner only. Then I close the rules box. I set the game to play hand 29 of 30. I set the bankrolls to the appropriate amounts, putting my own bankroll in the sixth position. I put the puck by the fifth player, meaning that player bets first this round.
So now we are ready for the bets. I want to control the bets of all the players this round, and an easy way to do it is to set all the players to manual (as opposed to automatic). Then I press F5 to start. The computer asks how much the fifth player wants to bet. I type in 100. Then I type in a max bet for me, the sixth player. Then I enter bets of 100 each for the other players.
Oops! Placing a bet for player 4 is automatically followed by dealing of cards. (I could have specified the bets by a different method, in which case the computer would have waited for me to assign cards.
But, no problem. I use Deja Vu to pick up all the cards and bets, and go back to the beginning of the round. Then I hit F1 six times to reconstruct the six bets. Now the computer waits for me to assign cards.
Assigning cards is easy. I deal myself a 5 and everyone else a 10 as the first card, including the dealer. Then another 10 to the fifth player, a 6 to me, 10-9-8-9 to the first four players, and 10 for the dealer’s hole card. (What I give to the dealer for a hole card does not matter if I am going to run a simulation; a new hole card will be randomly assigned each pass through.)
OK, each player has two cards totalling what I want each player to have, and the dealer has a 10. Now I hit F5 to start live play. The computer asks me how I want to play hand 5, and I stand on it. Now it asks me how I want to play my eleven. I want to simulate both hitting it and doubling down on it. So I select Simulate from the Run menu. I select double for 300 and hit as my two options. Then I hit the OK button and the simulation is on its way.
The simulation works this way. First the tournament is finished with my hand doubling down. I win the tournament. Then it is finished with my hitting the eleven. I win the tournament again. Then it is finished with me doubling down. I win again. Then it is finished with me hitting. Player 5 wins the tournament.
And so it goes time after time, finishing the tournament with me doubling on my eleven alternating with finishing the tournament with me hitting my eleven. Each pair of finishes takes eight seconds on my 586-66. After 50 finishes with each play, doubling down has won the tournament 42% of the time and hitting has won 35% of the time.
The program tells me that difference is not significant, and that the standard error applicable to each number is at most .071. A much larger sample size is going to have to be run, so I leave the room to attend to other business. (Actually, it is 9:30 pm as I write this, and the other business is drinking a beer while I read Newsweek.)
…later…
Now it is 10:30 pm. The sample sizes are up to 500. Doubling down is ahead, 44.9% to 31.6%, and the significance box shows five stars. This means the difference between the two sample means is greater than four standard errors. The standard error applicable to each number is down to .022.
We can say with certainty that doubling down was the better thing to do in this casino tournament situation. ♠
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