I think it may be beneficial to look at the table with most of the possible outcomes.
Note that $Kept is the same as losing a single bet. D (doubled) loss/win is not that significant as doubling for less is often a better play. I omitted tripled bets for lack of horizontal space.
Looking at this table allows us to find ranges of bets that “James” could have made.
Dealer: 7 .. BRL .. CARDS .. BET .. $KEPT ... WIN .... BJ ...... SURR .. D WIN .. D LOST
Connie .. 10,750 .. 16 .. 5,000 .. 5,750 .. 15,750 .. 18,250 .. 8,250 .. 20,750 .... 750
Regina .. 10,400 .. 17 .. 5,000 .. 5,400 .. 15,400 .. 17,900 .. 7,900 .. 20,400 .... 400
Michael . 11,800 .. 15 .. 4,000 .. 7,800 .. 15,800 .. 17,800 .. 9,800 .. 19,800 .. 3,800
James ..... 8,400 .. 19 .. 1,000 .. 7,400 ... 9,400 ... 9,900 ... 7,900 ...10,400 .. 6,400
LamarB wrote: "The other issue with this hand is whether he should have taken the low or bet half his bankroll."
Betting half the bankroll (4,200) is not a good idea if winning that bet doesn’t get you to a specific place. James’s winning 4,200 would bring him to 12,600 which is no better than having 11,900 -enough to overcome all other players pushing, surrendering or losing.
Blackjack would make him 14,700 – not enough to cover single wins by any other player.
Now, compare being paid for blackjack on 5K bet. That would get him to 15,900 - more than any other player winning single bet. Uncontested bj (by one or two players and the dealer) happens slightly more than four percent of times, nevertheless, it is a slightly better bet.
Counter argument could be made that betting half bankroll allows splitting pairs. That would apply only to situations where splitting is better than doubling. However, winning both split hands happens mostly when dealer breaks, which would be of no help if any of the opponents made a double or got a blackjack.
A big bet made by a player in James’s seat would swing all other players less than seven percent of times in normal game. But here, thanks to tendency of other players to make more extreme plays, either by surrendering or doubling more often, it may jump up toward ten percent.
A mid range bets (1,500 to 3,700) have a lot of possibilities but its effectiveness is limited for a few reasons. Usually, three players acting before the last bettor would cover opposite types of play. It may be a hit, dd and surrender, or two doubles and surrender, or surrender, hit or stand on pat and surrender - which actually happened. This kind of play, in effect, gives the last bettor slightly better chance for second place – but not for the more coveted first place.
The key factor in estimating success of this bet depends mainly on knowing opponents’ playing tendencies but I think it is less than ten percent.
Small bets- they carry danger of Michael surrendering and locking James out. Unless James bets and wins 1,500, or gets blackjack on bet of 1,000, or wins doubled bet of 800. If James accepts risk of Michael not surrendering then everybody else has to lose or surrender and James can bet and lose only 100. Even better play is to bet 200 and surrender anything but twenty-one, this way Connie may be lulled into false thinking that her surrender will keep her ahead of James if he loses. Let’s keep in mind that BR2’s (Connie) surrender may force BR1 (Michael) to surrender almost anything if BR3 (Regina) doesn’t have a strong hand.
Chances? You tell me. Another ten percent?
Bad cards to your opponents,
S. Yama
PS
You guys are picky, okay Tirle bj, if I include 17 hitting 21 and dealer making 20 it is 3.9%. Do you want me quit my beloved california cabs?