Lets say there are only 3 players remaining in the game on the final hand and the payout structure is 70% of the pot for the winner and 30% for the runner up. Firstly, betting stage: first to bet is BR1 2625, then BR2 2101, and then BR3 1000. For the ease of it lets say there is no surrender. bet min/max 100/1000. BR1 bet 500. - Should BR2 lock in his lead with a bet of 100 or should he bet at least 763 in order to take first place with a double down or with a blackjack ? OK, lets say BR2 did a bet of 763 (I think this is actually much better than 100 on per total winning value - I think this would be better even if blackjacks would pay only 1 to 1) and the table look as follows: BR1 stand on 20, BR has hard 20 (but if soft ? - I think is double) BR3 20. Should BR2 split ? (I think yes) PS: What I want to do with this thread would be to later come up with different last hand scenarios where we will have to analyze various situations when we have a lock (or near lock) for lower paid places but if we keep the lock we can`t go for the top places for both betting stage and playing decision. But the following scenarios will have betting limits 100/1000 surrender rule allowed, double after split, no double for less, no insurance for less, resplit allowed up to 3 times, and the following payout percentages: 1st place 42%, 2nd place 25%, 3rd place 15%, 4th place 10%, 5th place 8%. (mostly intersted in bets)
No numbers here, just some logic, similar to what I would go through at the table. With a bet of 763 and doubling/splitting on anything , I believe that BR2 has a better chance of succeeding, in which case he will finish first, than he does of being swung or 1/2 swung by BR3. Furthermore, the gain in prize money (40%) for a successful double is greater than the loss (30%) if he gets swung. I would therefore figure that the upside is higher than the downside and that the overall EV of going for the double is higher than the overall EV of attempting to lock on BR3 by betting 100. Note that while finishing second for 30% of the prize money is the most likely outcome of betting 100, BR3 is not actually locked out as he could get blackjack on a large bet (negative EV) and BR2 could pull off a full swing vs BR1 (positive EV). Still, I would probably go for the double in this situation. I'm sure someone can break down all the cases by percentage and come up with the EV of each bet. I am almost certain that I would get it wrong.
