Real Money Game - Final Hand 1 winner advances Min bets 5 Max bets 500 BR1 - 400 BR2 - 380 BR3 - 300 BR1 bets first. No secret bets. Surrender available. What's the best bet for BR1?
If it's real money then I suppose it depends on how much you might win by advancing. If the EV of advancing is low, due to either a small amount of prize money or a fairly high probability that you might advance and yet still win nothing (or relatively little) then $5 looks like a good bet, otherwise I'd say take the high by betting $365 and go for glory. I don't think there's anything to be gained by looking for a middle way between those two extremes.
Bankrolls Less Than Max Bet BR1's best bet is 365 or more. BR2 could take the low and bet 155 to surrender trap BR3 and deny your surrender. About the only thing BR3 can do here is go all in. Lots of opponents as BR2 would go all in. This is your best hope. If you bet 15 you're hoping neither of two opponents wins. That's not as likely as your winning your own hand. This example is why position is so important in this game. You have the lead yet your chances of winning are less than half (if BR2 has a clue) because you go first. Still, your chance of winning is better than that of the other two.
My Thoughts When I first read the question and gave myself 30 seconds to answer I went with $365 and after pondering it for a while I still go with $365. When I have to bet first and have the high I like to keep the high. That simple.
I may have misunderstood ... but I thought the motive behind the question was to ask how the real-money factor influences things. I'd have thought we'd all take the high if it was 'funny money'. Hence my answer that it depends on the unstated factors of how much you stand to win by advancing, and how likely you are not to finish in the money despite advancing. [Actually, if you are taking the high, then $370 is marginally better, since it covers the (admittedly remote) possibility of BR1 and BR2 both getting a BJ (with BR2 all-in). Even with real money it's probably worthwhile to risk the extra $5 as insurance against that particular dagger to the heart!]
Either/Or I agree with you Colin that there are unstated factors. For me on the last hand as BR1 and betting first it doesn't matter to me if it's for real or funny money I'm going to take the high. Even for real money I wouldn't want to open up the door for BR2 or BR3.
I think the perfect bet is 370! If you win your bet you have better than a 90% chance to go to the next round. It is easier to win one bet than two have both opponets lose two bets. If both opponets bet high they will have a very small chance of beating you by the swing or getting blackjack only. If they bet low and everybody loses they will win. If they bet the max then you will be in the best position to win. If everybody loses you win if everybody wins you win!
