Thunder said:
There was no maximum bet limit. I chose 1/4 of my BR because if I lost the hand, I wouldn't be totally screwed and it would allow me to split if need be. I'm not sure what the optimum bet would have been (perhaps going all in would have but then if you needed to split, you'd be screwed)
If the goal is definitely to double up or bust out trying, then doing it with a single bet has by far the greatest chance of success.
If the goal is a bit more uncertain than that, then splitting the tens doesn't seem like quite such a good move after all. Had you stood on the 20 and won, you could have used the last two hands as a progression, giving a high chance of adding another 1/3 to your new BR. (i.e. the final BR could be 5/4 * 4/3 = 5/3 of your BR at the start of hand #13).
And if you lost with the 20, you could go all-in on the next hand and attempt to reach 3/4 * 2 = 3/2 of the BR.
I think the notion of 'needing' to split is a false one. Splitting when BS calls for it may increase EV, but it will quite often result in a push, winning one hand and losing one hand. And EV is irrelevant with so few hands to go; the need to win a specific amount trumps all other considerations. (In fact, if you find yourself all-in on the
final hand, needing to win, you should even deviate from basic strategy in certain ways, such as standing on 12 v 2 or 3, because BS incorporates possible pushes into the EV calculation, and a push is no good to you.)
It's true there are some hands for which a split can only improve the probability of winning (e.g., for 7,7 and 8,8 vs 2-to-6, if you are all-in you will stand and hope for a dealer bust, whereas if you can split you might make 18 or above on one or both split hands, giving more ways to beat the dealer). But, equally, betting the full amount you need to win up-front means you never have to reduce your probability of winning the hand by doubling down and limiting yourself to one hit card.
Thunder said:
While counting wouldn't make a big difference, I'll take all the help I can get in a short tournament like that.
The topic of counting (or not) in tournaments gets debated at regular intervals over at the bjt site.
Have a read through the following thread. It starts off talking about elimination tournaments, but moves onto accumulation tournaments such as the one you played -
https://www.blackjacktournaments.com/threads/6076/
I confess that thread stuck in my mind because of the praise from Ken which my contribution received.
With 15 hands and 8 decks I suspect you may not see a shuffle before the tournament round is over, meaning counting is of no benefit for betting purposes, as described in the above thread.