The old coin-flip debate

[Bozeman]

I am not regularly reading the forum now, but PM sent me a pm about this thread, so I think I should try to respond.

General points about near bubble play:

1) -CEV is essentially always -$EV.

2) +CEV is often -$EV

3) The $ value of the various stacks will depend on the way other people play. For example, suppose stacks of 5x, 3x, 1x. If the 3x wants first, the 5x stack will have less $EV than if the 3x is playing to outlast the 1x.

4) Better calculations than AM's are available, but there will always be debate, mostly because of (3).

5) Small stacks are worth more per chip than large stacks.

6) When two stacks tangle, the stacks not involved gain $EV. Possible exception to this for VERY large stacks.

7) Reasonable players should not call big bets even with some hands that are better than the hand they are facing.


Now more detail: Suppose you are playing with 4 equal players with equal stacks, and everyone is aiming for 1st. Now you have 25% chance of each place. With three players that have 2x, 1x, 1x, and payouts of 50%, 30%, 20%, the big stack is worth 38.6% ($38.6 for a $10 tourney) (P1=50%, P2=35.8%, P3=14.2%). This is very close to the method used by PvSexton, which I have called the independent chip method (slight advantage to smaller stacks). In fact, this is the method used in my PalmApp for calculating fair deals ( DealCalc ), since the more accurate method I used above is very intensive for more than 4 places ( 4 way and independent chip source code ). A review of my research on this subject is at ( Tourney finish place probability ).

Given that the two smaller stacks may want to try to wait each other out, the big stack may be worth slightly more than 38.6%, so PM's $40 estimate is reasonable.

As for not knowing what hand the other player may have, this is mostly a strawman, because it is not usually difficult to place bounds on what sort of hand this player would need to make this move. Then instead of your win % against this particular hand, you can look at your weighted average % against his range of hands (twodimes doesn't do this, but many other showdown calculators do).

This brings up one mistake that I see many players make: they call when they think they are better than the worst hand that this player needs to make this move, even though they are -EV (and often even -CEV) against the range of hands.

The difference of hands chosen by AM and Pitcher (for example) is accounted for by the difference in level of play. If a good player knows (or even suspects) you will fold 99, you will be blinded off very often. But if several players will call with many hands, as often happens at lower limits, you can be virtually assured of a money finish with no risk if you fold. At higher levels, generally fewer players make the mistake of calling too often, AND generally fewer players make the mistake of raising too infrequently. Also, at lower limits the bubble occurs at lower blinds.

Finally, you must sometimes make -$EV plays because the alternative is even more -$EV. For example, going allin with a small stack and a bad hand UTG may be better than waiting for your BB even though you have only a small chance of picking upthe blinds and you are virtually certain to be an underdog when called. I think that some of the +CEV, -$EV calls fall into this category.

What have I forgotten?
Craig

PS Is it possible to search for posts more than 7 months old? It is not returning my older posts.