"However, say the count goes TC+5, you have a max bet out, dealer has a 10 and you have 8,8. Basic strategy says split but do I want to lose another max bet?"
We never want to lose any bets, but that doesn't mean that we don't make certain plays, if they're correct.
"The odds, even when you split, are that you would lose both bets."
That's not necessarily true and is probably false in this case. With the higher count, you are probably about 65% to lose one hand and 35% to win (exclude ties). So, to lose both hands is 42.25%, but to win one and lose one is 2 x 0.35 x 0.65 = 45.50%. You're more likely to break even than to lose both. Surprised? The problem is that you're very unlikely to win both, so your overall expectation is rather negative.
"Now, with a minimum bet out, in the long run, you would lose less by splitting."
You would also lose less with a maximum bet out, but you are risking more. So, you are correct that, from a risk-aversion point of view, there comes a point (right around +5!) above which splitting is no longer optimal. This is one of those times where you get the "right" answer for the "wrong" reason. Or, maybe you just have a good instinct as to when to make a risk-averse play!
"However, it's not often you get an 8,8 with a TC+5."
You get 8,8, vs. 10 once every 615 hands. The TC is greater than or equal to +5 about once every 36 hands. Ignoring any interaction between the two concepts, you get this holding once every 22,140 hands, or once every 221 hours! For some people, that represents an entire year's worth of play!! Bottom line: do whatever makes you happy.
"Fact is that some pros do not split in such a situation, to save one max bet."
Well, the first part may be true, but it isn't to "save one max bet." It's to forfeit a sliver of e.v. to save the greater variance on the play, by not splitting.
Don
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