How would surrender as an option affect your optimal bets? Given that you have position it could be the most useful tool in your arsenal.
Yes, surrender can change things quite a bit. It can allow you to over bet your lead in order to cover a high threshold while leaving you the option to retake the low if you or your opponent are dealt a weak hand. So in situations where you would normally bet your lead minus one chip, you can bet twice that amount instead. If you are dealt a strong hand, you can play on, but if your hand is weak you can force your opponent to win his hand by surrendering.
Another option is the surrender trap, which works against players who know enough to take the low, but perhaps aren't thinking about surrender. At the same time, the required bet can often strengthen your high position. For example:
You: Bankroll: 1975, BR2: Bankroll: 1500, min 25, max 1000
This is a case where you would probably bet 450 in order to preserve the low. Betting 475 doesn't cover BR2's double and exposes you to a 1/2 swing. However, if you believe that BR2 knows to take the low you might mutter something along the lines of not wanting to give up the low while assembling your bet and then bet something like 550. This covers BR2's max bet but gives up the low. For added effect, after betting, you might then indicate that you thought you had made a mistake by swearing under your breath and acting like you are upset with yourself. If all goes well, BR2 will notice your overbet and bet the minimum 25. He might even smile to himself while doing do, thinking that he is being clever in capitalizing on your mistake. At this point, no matter what you are dealt, you can pretty much lock him out by surrendering. He would need a 4 way split, all doubled in order to tie you. If he doesn't take the bait, you still have him high and low with his double covered.
You don't need to be able to completely lock him out or need to cover some high position in order for the trap to be effective. If you can lock out is double or even his single bet, it can be an effective play, if you believe that there is a decent chance that he will take the bait. I believe that Grosjean did an analysis of how sure you need to be and how big you lead should be relative to the minimum bet in order for this play to be effective.
How do you quickly figure insurance bets into your calculations? It is obvious the optimal insurance bet for BR3 would be $675 (if nobody else took insurance) and BR1 could only take at most $400 insurance but has no reason to take insurance unless someone else does. Now the trouble is they can bet a combo of insurance bets that can cause you difficulty. Are insurance bets made in playing order or as a free-for-all?
This is a really weak part of my game. I am eager to see some of the responses to this. I concentrate on covering the normal high and low positions before I consider insurance. Even then I usually only end up using it as a hail mary if my position is weak and can be improved with an insurance bet, or if I am correlating a key opponent how has taken insurance.
