Fallsview Follies

The latest event at the Fallsview (https://www.blackjacktournaments.com/tournaments/blackjack-21-tournament.1235/) produced yet another interesting situation.

Once again, Cadillac Tim and I found ourselves at the same table and the final hand of the preliminary round found Tim in an interesting situation. Once again, this situation can be developed in stages. This time we'll start with a simplified situation and see if and how things change as information is added.

To refresh the rules and conditions: 500 max, 25 min with precise betting allowed (smallest chip is 2.50). 2 advance, however the situation really was about Tim defending his position as BR2, and I can't remember BR1's bankroll . If Tim remembers, then we can add it to the mix later. The simplified situation is as follows:

BR3: bankroll 1850: Bet 500, doubles for 500 ending up with 16
Tim: bankroll: 2000: Bet 500, hard 19
Dealer: 4

What should Tim do and why?

 

Ok, first you and Tim need to try to get on different tables
I think Tim can only win if the dealer makes a hand 17-21 (about 62% off the top of my head). So, Tim can double down for 200-500 with no risk. If he busted out, he will still advance if the dealer makes a hand.

 

The minimum Tim needs to double for is 352.50, since his lead is 150.

With the information presented there is no reason not to simply double for the full amount, but maybe that will change when we learn Gronbog's BR and bet...

 

Right more than $350. I got it backwards in my post.

 

The Professional came to the same conclusion that we did when discussing things between rounds. In this simplified situation, Tim had a free double. What's more is that if Tim were to double and survive without busting, he would earn himself a lock over BR3.

Colin has been reading my posts for many years now and has correctly guessed where I'm going next. There was a slight fly in in the ointment for Tim, and here it is. When you factor my position into the situation we now have:

BR3: bankroll 1850: Bet 500, doubles for 500 ending up with 16
Tim: bankroll: 2000: Bet 500, hard 19
Gronbog: bankroll: 587.50: Bet 500, soft 16
Dealer: 4

Does this change your mind if you are Tim?

 

It does because now he cannot bet over 325 without losing the low to you, assuming you will double for less. I probably would stand then.

 

I'll see what I can come up with using my simulator.

 

Right. But, to be pedantic about the terminology, it's not losing the low, it's opening up the possibility of a swing.

I think I too would have stood at the table. With more time to [over-]think about it I did begin to wonder if that might be the wrong choice. But I've gone through the maths, and it seems that standing is much better.

Standing has the same probability of advancing as it does in the first situation. It's the probability that the dealer does not bust: 60.4%.

By my calculation, the probability of advancing by doubling is only 48.8%.

 

Right. I realized afterwards that I used the terminology "low" loosely

 

I think the comparison of the effectiveness of different bets can be somewhat quickly estimated with the help of my “rule of one percent”.

This rule is the result of the fact that in many situations we need to look for result of hitting once and the results for the final outcome will be 1/13th (7.7%). If we look at dealer’s final results (not the busts and not the pat hands that are ten points higher than the upcard, like 7-17, 8-18, 8-18, 10-20) the vast majority of them are rounded to about 13%. Now, 1/13x13%~=1%

So, for example, we can quickly estimated the chances for a player doubling on A6 and having to beat a dealer with a small upcard and not busting. Player will end up 1/13th of the time with 18 to 21 each. 18 beats only 17 (=1%), 19 beats two outcomes (17 and 18), which gives another 2x1%, 20 adds 3%, and 21 adds 4%, for a total of about 10%.

Back to our case,

Tim has a free double if there is no other competitions, his gain by doing so is whenever he doesn’t bust and the dealer busts. That’s rounding 15% x 40% = 6%.

If there is another player (gronbog) who can overcome Tim by winning his double (as we showed above) and Tim busting his double for less (85%) then the penalty is 10% x 85% = 8.5%

The benefits are smaller than the possible penalty. Stand on 19.

Tim’s double should be for less in the range of 352.50 to 410. If Tim doubles for more than412.50 and busts then BR4 doesn’t have to double down and just hits to at least 18, which almost double the penalty for Tim.


S. Yama

 

I'm confused. All the above makes sense, yet it seems to be giving a radically different answer to the one I calculated.

If I'm understanding correctly, Yama's method is estimating a net reduction of (8.5% - 6%) = 2.5% for doubling, compared to standing. The probability of advancing by standing is 60.4%, so that would mean around 59% for doubling.

I tried to calculate the probability directly and got an answer of 48.9%, a reduction of around 11.5%, compared to standing.

The method I used is -
p(Tim advances) =
p(Tim 21) +
p(Tim 20) +
p(Tim bust and Dlr 17 and Gronbog not 18,19,20,21) +
p(Tim bust and Dlr 18 and Gronbog not 19,20,21) +
p(Tim bust and Dlr 19 and Gronbog not 20,21) +
p(Tim bust and Dlr 20 and Gronbog not 21)

 

I just tried to simulate the full situation and my software crashed. I did some recent work on the strategy generation engine for another purpose and i guess I broke something in the tournament mode. I don't know how long it will take me to find the time to fix it. Stay tuned.

 

Could you expand on what you mean? It looks to me like the two figures Yama's method compares are deltas, needing to be simultaneously applied to the probability of advancing by standing if you want to compute the probability of advancing by doubling.

I used the same methodology for hard 18 as I did for hard 19 and got a result of 53.5%, still considerably worse than the 60.4% due to standing. Something's wrong, somewhere. (Quite possibly in my method).

 

London, please add to your calculation:
p(Tim bust and Dlr 21))

S. Yama

 

D'oh! That's it. How did I manage to miss that?

I now get 58.4% for doubling on 19 (a 2.0% reduction, compared to standing).
And I get 62.1% for doubling on 18 (a 1.6% gain, compared to standing).

The gain/reduction in both cases is pretty close to the estimate that your quick method yields.

Thanks.

 

Br1 2,800ish, I was primarily focused on BR2 (between these two).

 

OK -- just to flesh out the BR1 information in case it brings up any more considerations, the full story is now:

BR3: bankroll 1850: Bet 500, doubles for 500 ending up with 16
BR1: bankroll 2800: Bet 500, stands on hard 14 (*)
Tim: bankroll: 2000: Bet 500, hard 19
Gronbog: bankroll: 587.50: Bet 500, soft 16
Dealer: 4

(*) BR1 liked to act as if he was a skilled player, but he was not. He often took long periods of time considering no-brainer decisions. He agonized over whether to double his 14 when he already had a lock on at least finishing second. Does anyone see a better bet for BR1?