Quote:
Originally Posted by Monteroy
Shove 10,000 hands pre-flop for 100BB each
Assume 70% of the time nobody calls so you earn 1.5BB x 7,000 = 10,500 BB
3,000 times you are called - you win 1,500 and lose 1,500. Each of those hands you pay net 5 BB of rake (depends on the stakes, at 100NL or above its as low as 1BB or less) so the cost is 7,500 BB in rake on hands you are called.
Net expected profit is 10,500-7,500 = 3,000 BBs.
If you do this at higher limits the profit goes up quite a bit, but of course a proper bankroll is required to handle any short term variance on the "coin flips." As well, you increase your returns considerable by buying in for a shorter than 100BB stack if at that limit an all-in will reduce the amount of rake paid (not an issue at 200NL where the full buy in will get blind steals far more often and rake is capped regardless).
This model lacks distinction to be considered an acceptable statistical model. Most notably, statistical variances is given no consideration in this model. Not to mention that in a six-handed game where you are in the blinds one-third of the time, you can only steal the blinds 6,667 times in 10,000 hands.
What your simple model does show, is that you are only winning the blinds. In this case, you bet $1 million to win $3,000 over 10,000 hands, which at 100 hands per hour, is 100 hours. The break even point in your example is a pre-flop fold percent of 62.5%. Anything higher, you make money, anything less and you lose money.
So lets look at something more realistic and I will try to incorporate as much of you scenario in to this as I can.
10 handed game, Full Table, Auto Top off for all players, all players at max buy in, 1,000 orbits for 10,000 hands, no player changes, $100NL, 100BB max buy in, $5 max rake on all-in hands.
Player A is all-in every hand. Player A begins in the BB. On every shove Player A makes while in the BB, SB, and on the button, he is called by Player B on his immediate right. On all other hands (when he is UTG to UTG+6) he shoves and get the entire table to fold. Therefore, 7 hands per orbit (70%) he picks up the SB and BB cleanly. The other 3 hands per orbit (30%) are with Payer B.
Variance:
During the first 5 orbits. Player A experiences negative variance in that he losses every BB and SB shove but wins his button shove. His short term variance of 33.33% has him winning only 5 of the first 15 hands of the all in hands with Player B.
On orbit 6, things change for Player A. He still losses his BB, but he starts to win his SB and continues to win on the button. This trend continues for the rest of the session. So for 995 orbits, Player A wins 1,990 hands (66.67%). Combined with the 5 hands he won in the first 5 orbits, he wins 1,995 (66.5%) of the possible 3,000 hands played all-in versus Player B.
Conclusion:
So short term and long term variance does exist in poker all-in coin flips, and this variance can have a dramatic affect on the results achieved by this strategy. This example is just one of thousands demonstrating have variance can have significant impacts on results. So I hope all of of you who think that shoving every hand is +EV, is not at all a EV situation. I, for one, do not want to lose this type of money over 100 hours of play.