This is a temporary promotion which will last until €100,000 has been distributed. Only a little over €8,000 has been awarded as of this writing, so it may go on for a while. The exact value of the individual prizes awarded is based on the rake the player generates and thus on the stakes being played. So far, it seems that most prizes are worth around 2000 big blinds at the microstakes tables and a bit lower than that at higher stakes where the rake is proportionally less.
How does it work?
The promotion applies only to Texas Hold’em and Omaha cash game tables. In Omaha games, only the player’s first two hole cards count, so the odds of winning are the same in both games.
Upon sitting down, players are given a grid of 14 cards to fill out in order to win a prize. Cards in the grid are checked off whenever the player receives the corresponding card among her hole cards, but are unchecked if the player receives the same card a second time. The player thus needs to be dealt each card in the grid an odd number of times in order to collect the prize – no small feat. Meanwhile, the player has only 50 hands in which to complete the grid, after which he is dealt a fresh grid of 14 unchecked cards and has to start all over.
When a player does succeed in hitting a bingo, the prize won is determined according to a formula which is proportional to the square root of the “Miles” (rewards points) generated by the player during that particular grid, divided by the number of hands it took them to hit the bingo. Thus, each quadrupling of rake produces a doubling of the jackpot, while hitting the bingo in fewer than 50 hands produces a small increase in prize money. Hypothetically, you could hit the bingo in as few as seven perfect hands – giving you 2.67 times the prize you’d get by hitting in 50 – but the odds of that happening are vanishingly small.
Players also get a “Booster” hand of two specific cards along with their grid – if they’re dealt those exact cards and go on to complete the grid, they receive ten times the usual prize; this will happen about one time in 26 wins.
So what are the actual odds?
Because hitting a card twice unchecks it, the probabilities of hitting a jackpot are difficult to work out by hand. Fortunately, it’s easy enough to build a computer simulation to estimate them empirically. I’ve done so, and it turns out that the mechanics produce a little over four bingos per million hands dealt. Put another way, you’re about 5000-1 to complete any given grid within the 50-hand window.
Those are long odds, of course, but maybe not as bad as they look. When you look at the microstakes tables where the prizes are bigger in terms of big blinds, and take into account the occasional “Boosted” jackpot, the total EV works out to be a little over 1 big blind per 100 hands, which is small but not insignificant.
Is there any skill involved at all?
Despite appearances – and the name – Cash Game Bingo does allow some room for a clever player to increase her EV above the baseline calculated above. This is because players have the option to reset their grid at any point with the click of a button, getting 14 new cards and – critically – another 50 hands in which to complete the new grid.
Presumably, Winamax included this option because they realized that some players would game the system anyway by leaving their seat when doing poorly on the current grid, then sitting down again to get a new grid. Rather than encourage players to annoy their opponents in this way, they simply included the grid-resetting option as an explicit part of the mini-game.
What this means is that, when a player reaches a situation where they’re a few hands into a grid and looking less likely than average to complete it, they can reset and try again without waiting the full 50 hands. This is not insignificant; a player is, for instance, about 15% more likely than average to hit a bingo when their first hand dealt checks off two cards, and about 10% less likely when the first hand whiffs entirely.
Since a whiff is 53% likely to occur, then we can manage an overall EV increase of about 5% even with the super-simplistic strategy of just resetting every time the first hand misses and letting the grid play out for the full 50 hands as long as the first hand connects. It wouldn’t be particularly difficult to use computer simulation to work out an optimal resetting strategy for the full 50 hands, and I may do so later in the week for a follow-up article. I’m going to take an educated guess and say that such a strategy should produce gains of at least 25% over simply ignoring the mechanic and trusting in luck, and maybe as high as 100%. Of course, it’s important to remember that we’re now talking about a fraction of a big blind per 100 hands, but especially at mid-to-high stakes, even tiny edges can eventually add up.
Alex Weldon (@benefactumgames) is a freelance writer, game designer and semipro poker player from Montreal, Quebec, Canada.