Strategies for Must Win One Bet

[gronbog]

The situation in which you must win at least 1 x your original bet in order to survive, advance, win more money or to improve your chances for eventually advancing comes up quite often in tournament play, and it has been discussed here many times. I have occasionally referred to the optimal strategy for achieving this goal. Here it is again for reference:

http://gronbog.org/results/blackjack/strategy/tournament/mustWin/8/h17/optimal/originalHand.html

Often, when I have posted a link to this table, I have mentioned that one must go on to play the optimal strategy for any split hands in order to achieve the optimal success rate of 43.81%. Of course, none of us can possibly hope to memorize the entire optimal strategy, even if I were to post it. There is a separate strategy for every combination of split hands both completed and unplayed. If splitting to 4 hands is allowed, this becomes a very large number of tables to memorize. Even if we could memorize the complete strategy, would it be worth the effort?

Let me start by clarifying that the strategy above is for 8 decks, 75% pen, S17, DOA, DAS, SP4 and 1 card only on split aces. If you were to play the normal basic strategy for these rules, then your success rate for winning one or more bets would be 43.39%. So you gain 0.42% by playing the complete optimal strategy. Is it worth it? Maybe - maybe not. Once we accept that we can never execute the complete optimal strategy, the next question is: what kind of improvement can we, as mere mortals, reasonably accomplish? Let's examine a few possibilities:

Play the original initial hand strategy (above) for all hands
If you do that then your success rate will be 43.45%, an improvement of 0.06% over the normal basic strategy. That's not much of a benefit by any measure. Perhaps we can do better.

Play the original initial hand strategy (above) for all hands, but don't split
If you do that then your success rate will be 43.56%, an improvement of 0.17% over the normal basic strategy. Better and still only one table to remember.

Play one strategy for the initial hand and one other for all split hands
If you were to play one strategy for your initial hand and another for all split hands, these strategies would be:
http://gronbog.org/results/blackjac...stWin/8/h17/basic/allSplits/originalHand.html
and
http://gronbog.org/results/blackjac...mustWin/8/h17/basic/allSplits/splitHands.html
respectively and your success rate would be 43.66%, an improvement of 0.27% over the normal basic strategy. That's more than 1/2 of the benefit of the complete strategy for a two-table strategy. Not bad.

Play one strategy for the initial hand and a separate strategy for each of split hands 1, 2 3 and 4
If you were to play one strategy for the initial hand and a separate strategy for each of up to 4 split hands, these strategies would be:
http://gronbog.org/results/blackjac.../h17/basic/individualSplits/originalHand.html
http://gronbog.org/results/blackjac.../8/h17/basic/individualSplits/splitHand1.html
http://gronbog.org/results/blackjac.../8/h17/basic/individualSplits/splitHand2.html
http://gronbog.org/results/blackjac.../8/h17/basic/individualSplits/splitHand3.html
and
http://gronbog.org/results/blackjac.../8/h17/basic/individualSplits/splitHand4.html
respectively and your success rate would be 43.65%, an improvement of 0.26% over the normal basic strategy and a surprising decrease of 0.01% over the previous two-table strategy. I thought that this was odd, but repeated simulations consistently result in this 0.01% degradation in the success rate. Clearly it's not worth the extra effort to remember 5 tables vs 2.

So it would seem that when it comes to winning one or more bets, an improvement of 0.27% over the normal basic strategy is reasonably achievable using a two-table strategy. I was going to go on to give examples of when this would and would not be worth the effort, however, I'm having trouble coming up with the former.

Even if winning your hand meant the difference between winning $50,000 (first) or $10,000 (second) on the last hand of a final table, the improvement is only worth 0.0027 x $40,000 or a whopping $108. Even if we could execute the complete optimal strategy, the improvement would be only $168. When applied to advancing or not, the improvement also seems negligible.

Now it is likely that, even using the two-strategy tables as a guide, a reasonable player can do somewhat better. For example, if you had doubled your first hand for a total of 21, you would know enough not to double or split your second hand (wouldn't you??). However, my conclusion for the case of needing to win one or more bets is that, if you can't remember the correct strategy deviation for your hand(s), play basic strategy and don't sweat it.

 

[London Colin]

Wouldn't the simplest, and perhaps most valuable rule of thumb be -

If you've already stood stiff on your first split hand(s), then you may as well take any available opportunities (i.e. further re-splits and/or doubling on non-stiffs) to try and get more bets in action without the risk of busting, in the hope that the hands on which these bets ride may reach totals of more than 17, giving you a way for the stiff(s) to lose to the dealer while you still win +1 net bet overall.

It's the converse of your example of having doubled the first hand to 21, and thus wanting to avoid adding any further bets. In this case you do want to add further bets, so long as there is no risk of busting, until you either reach a point where you've given yourself an extra way to win, or you run out of ways to add more bets.

And in fact, if you should manage to split to four hands, I think you could end up with a free-hit situation on the final hand. You could bust it and still be OK if the dealer busts -

You've stood stiff on the first two hands.
You've doubled to 18 or more on the third hand.
There is now no point in standing on less than 17 on the fourth hand. (and maybe you should even hit on 17?)

I'm not sure I've expressed all of that very well. Hope it makes some kind of sense.

 

[gronbog]

Special Situations

Yes, I agree that there would certainly be special situations that a skilled player would recognise which would allow him to do better than the simple strategies that I've proposed. You and I have pointed out only two of them. The complete set of them would comprise the actual optimal strategy. The more of these situations that a player could recognise and react to, the better he would perform.

I just wanted to enumerate a couple of what I think of as "basic " strategies for this particular goal. A basic strategy, in my mind, is one in which the player reacts only to information about the particular hand being played, disregarding the results/totals of any other hands which have been or have yet to be played. I was hoping to show that such an approach could yield a practical gain in situations such as this (must win one or more bets). What I found, in this case at least, is that even playing the complete optimal strategy is of questionable value.

You do bring up a very valuable concept, however. It is possible (even likely) that a few rules of thumb would be a lot easier to remember than a set of tables and would perhaps provide significant value in situations where the optimal strategy is of some value but impossible to learn.

 

[London Colin]

I just wanted to enumerate a couple of what I think of as "basic " strategies for this particular goal. A basic strategy, in my mind, is one in which the player reacts only to information about the particular hand being played, disregarding the results/totals of any other hands which have been or have yet to be played. I was hoping to show that such an approach could yield a practical gain in situations such as this (must win one or more bets). What I found, in this case at least, is that even playing the complete optimal strategy is of questionable value.

You do bring up a very valuable concept, however. It is possible (even likely) that a few rules of thumb would be a lot easier to remember than a set of tables and would perhaps provide significant value in situations where the optimal strategy is of some value but impossible to learn.

My instinctive feeling is that whenever the outcome of other hands plays a role (whether that's the more usual case of your opponents' hands, or as in this example your own split hands) you will be better off taking account of all the information before you, and trying to work out your strategy from first principles, rather than refer to a basic strategy; even allowing for the inevitable mistakes that will be made (in my case, at least).

I hadn't properly grasped how little there is to be gained even from totally optimal play here; the figures somehow didn't quite penetrate my brain. I suppose this stems from the rarity of being dealt a splitworthy pair in the first place.

 

[S. Yama]

brief strategy splitting must win 1 bet

Playing absolutely optimally “Must win one bet” can involve looking up many tables.
The main playing dilemmas may come from playing pairs. But I think that it can be summarized into a very brief concept.
Play all hands as in gronbog’s prime original hand table and deal with pairs as follow:
1. Always split all 2, 3, 4, 6, 7, 8, (and 9 vs. dealer 8 to A).
2. Double first hand if two-cards total is 8 to 11, or any soft hand, otherwise hit to at least 18.
3. If the first hand is doubled hit the second hand to one point higher than your double.
4. If the first hit hand is 21 play the second “Push as good as win”;
if the first hand is 20 hit the second to one point less than the above;
if the first hand is 19 double on the second hand total 10-11, otherwise don’t bust, except hit to 15 vs. 7, 8, and A;
if the first hand is 18 double on the second two-card hand if it is 9-11, otherwise don’t bust;
if you bust your hit first hand double any second hand.

Of course, this is not the optimal play but should get you most of the benefits and could be easily memorized if you look and recognize the logic in the system of this strategy.

S. Yama

 

[gronbog]

Proposed Simulation

The main playing dilemmas may come from playing pairs. But I think that it can be summarized into a very brief concept.

The moment this was posted, I knew that I wanted to simulate this "algorithmic" strategy to see how it does. I finally have the time to do it. In order for this strategy to be executed by a computer, I need some clarification of the grey areas.

3. If the first hand is doubled hit the second hand to one point higher than your double.

The grey areas here are when the first hand has been doubled to 21 or is stiff. In the case of 21, we can't hit to one point higher but, fortunately, we don't need to. The second hand is irrelevant, provided that we don't double or split it. Most players in real life would just play basic strategy without doubling or splitting here. Unless there are any objections, my simulation will do the same.

When the doubled first hand is stiff, the second hand is almost irrelevant, since the doubled hand can't push. It could be a factor if there is a chance for a resplit. If we don't double or split, then it does become irrelevant. So playing non-pairs here could be basic strategy without doubling or splitting. I'm not sure how to best handle pairs here.

4. If the first hit hand is 21 play the second “Push as good as win”;

This is beyond a grey area. This is a whole new messy can of worms. We haven't yet decided on a strategy for "Push as good as win". We could define it the way Wong does, or I could develop a set of tables for it the same was I did in this thread, or S. Yama could kindly provide an additional "algorithmic" strategy to be used. My expectation is that the complete optimal strategy for "Push as good as win" will yield a microscopic improvement over basic strategy, similar to the one we found here for "Must win one bet". So using basic strategy here might also be a viable option. Perhaps we should do all four. I had intended to examine "Push as good as Win" after we were done with this thread, but it seems that we are forced to examine it now.

if the first hand is 19 double on the second hand total 10-11, otherwise don’t bust, except hit to 15 vs. 7, 8, and A;
if the first hand is 18 double on the second two-card hand if it is 9-11, otherwise don’t bust;

"Don't bust" is easy for hard hands. But what about soft ones? We need a rule of thumb for strong soft hands. There are a few reasonable possibilities: Play "Push as good as win", play basic strategy, hit to some fixed total (soft 18, 19 or 20). I'm sure there are other reasonable approaches.

Once we get these grey areas ironed out, I can run the simulation. We can then try tweaking these rules to see if we can improve them.

 

[gronbog]

Result

Being impatient when it comes to seeing the results of a proposed simulation, I went ahead and simulated S. Yama's strategy with the grey areas resolved as follows:

• First Hand is doubled to 21: play second hand using basic strategy with no doubling or splitting
• First Hand is doubled stiff: play second hand using basic strategy with no doubling or splitting
• First Hand is hit to 21: play second hand using basic strategy with no doubling or splitting (as opposed to the proposed "Push is as good as win").
• Don't Bust: play soft hands using basic strategy.

The result of simulating this strategy is a success rate of 43.76%! When compared with 43.39% for basic strategy and 43.81% for the complete optimal strategy, this represents 88.10% of the advantage gained by playing the complete optimal strategy; all from applying a few very logical rules of thumb combined with my initial hand strategy and some no-bust and basic strategy.